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https://onepetro.org/SPWLAALS/proceedings-abstract/SPWLA-1976/All-SPWLA-1976/SPWLA-1976-AA/19897 | ABSTRACT
When employing the borehole gravity meter for remote sensing applications, it is useful to reduce the borehole gravity data to the Bouguer anomaly before interpretation. This paper deals with the calculation and subsequent quantitative interpretation of the borehole Bouguer anomaly. Numerical modeling of lateral density contrasts such as reefs and salt domes are shown to illustrate the effect that these mass distributions have on the bulk density calculated from borehole gravity measurements. The borehole Bouguer anomaly data for several borehole gravity surveys dramatically indicate the presence of inhomogeneities which do not intersect the borehole.
This content is only available via PDF. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8733119964599609, "perplexity": 3478.369644965561}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046152236.64/warc/CC-MAIN-20210727041254-20210727071254-00679.warc.gz"} |
http://mathhelpboards.com/basic-probability-statistics-23/draw-sample-space-amp-find-probabilty-19906.html?s=9278ceb6188b675b9c2ddddfeb0e6f5e | Thread: Draw the sample space & find the probabilty
1. Having trouble in drawing the sample space in the grid
2. Originally Posted by mathlearn
Having trouble in drawing the sample space in the grid
Hey mathlearn!
Each intersection of dotted lines corresponds with a set of possible 2 bangles.
If they are the same color, the outcome is that the girl wears them - let's abbreviate that with 'w'.
If they are of different colors, the outcome is that the girl does not wear them - abbreviated 'n'.
Put the letters 'w' and 'n' at the intersections and presto!
We have our sample space representing all possible outcomes.
Originally Posted by I like Serena
Hey mathlearn!
Each intersection of dotted lines corresponds with a set of possible 2 bangles.
If they are the same color, the outcome is that the girl wears them - let's abbreviate that with 'w'.
If they are of different colors, the outcome is that the girl does not wear them - abbreviated 'n'.
Put the letters 'w' and 'n' at the intersections and presto!
We have our sample space representing all possible outcomes.
Hey ILS
I updated the sample space grid
Correct ?
4. Originally Posted by mathlearn
Hey ILS
I updated the sample space grid
Correct ?
Yep.
5. Not quite. Remember that she does not return the first bangle to the drawer before she draws the second! Because of that, (W1, W1), (W2, W2), (W3, W3), (B1, B1), and (B2, B2) are not in the sample space. Those points should not be marked at all. Instead of having 5*5= 25 points in the sample space there are 25- 5= 20 (the -5 from the diagonal points that are removed). Instead of 3^2+ 2^2= 9+ 4= 13 "W"s there are 13- 5= 8 "W"s.
6. Originally Posted by mathlearn
Having trouble in drawing the sample space in the grid
The earrings are drawn without replacement,
There are $\displaystyle 5\cdot4 = 20$ outcomes, not 25.
$\displaystyle \begin{array}{cccc}W_1W_2 & W_1W_3 & W_1B_1 & W_1B_2 \\ W_2W_1 & W_2W_3 & W_2B_1 & W_2B_2 \\ W_3W_1 & W_3W_2 & W_3B_1 & W_3B_2 \\ B_1W_1 & B_1W_2 & B_1W_3 & B_1B_2 \\ B_2W_1 & B_2W_2 & B_2W_3 & B_2B_1 \end{array}$
. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5689460635185242, "perplexity": 1919.866809416382}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806615.74/warc/CC-MAIN-20171122160645-20171122180645-00721.warc.gz"} |
https://pillowlab.wordpress.com/author/fdamani1/ | # The Loss-Calibrated Bayesian
By Farhan Damani
In lab meeting this week, we discussed loss-calibrated approximate inference in the context of Bayesian decision theory (Lacoste-Julien et. al. 2011, Cobb et. al. 2018). For many applications, the cost of an incorrect prediction can vary depending on the nature of the mistake. Suppose you are in charge of controlling a nuclear power plant with an unknown temperature $\theta$. We observe indirect measurements of the temperature $D$, and we use Bayesian inference to infer a posterior distribution over the temperature given the observations $p(\theta|D)$. The plant is in danger of over-heating and as the operator, you can either keep the plant running or shut it down. Keeping the plant running while the plant’s temperature exceeds a critical threshold $T_{\text{critic}}$ will cause a nuclear meltdown, incurring a huge loss $L(\theta > T_{\text{critic}}, \text{'on'})$ while shutting off the plant for benign temperatures incurs a minor loss $L(\theta < T_{\text{critic}}, \text{'off'})$
In figure 1 we observe the true posterior $p(\theta|D)$ is multi-modal. Our suite of approximate inference techniques characterize general properties of the posterior, attempting to match either the first or second moment of $p$. Both strategies underestimate the posterior mass for the safety-critical region. Instead, the dash-dotted line, while failing to characterize typical properties of the posterior, results in the same decision as the true posterior by optimizing for task-specific utility. The point is the “best” approximate posterior is subjective, and therefore, we should tailor our inferential resources to find an approximation that is well suited for the decision task at hand.
Bayesian decision theory extends the Bayesian paradigm by including a task-specific utility function $U(\theta, a)$, which tells us the utility of taking action $a \in \mathcal{A}$ when the world is in state $\theta$. According to this view, the optimal action minimizes the posterior risk: $\underset{a}{\arg \min} \text{ } \mathcal{R}(a) = \mathbb{E}_{p(\theta|D)}[U(\theta, a)]$. Typically, this is computed using a 2-step procedure. First approximate the posterior $p(\theta|D)$ with a $q(\theta|D)$ and then minimize the risk under $q$. This approach, however, assumes our approximate $q$ measures properties of the posterior that we care about. This by definition requires our utility function, so therefore, we should jointly optimize the approximate posterior with the action that minimizes the posterior risk. Cobb et. al. 2018 show how to derive a variational lower bound that depends on a task-specific utility function. In their setup, they show that minimizing the KL divergence between an approximate posterior q and a calibrated posterior scaled by the utility function results in the standard ELBO loss plus an additional utility-dependent regularization term. This formulation is amenable to stochastic optimization, allowing for the practical deployment of this framework to supervised learning. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 16, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.935523271560669, "perplexity": 558.795612024309}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401600771.78/warc/CC-MAIN-20200928104328-20200928134328-00161.warc.gz"} |
http://mathhelpforum.com/differential-geometry/181303-lebesgue-integral-print.html | # Lebesgue Integral
• May 22nd 2011, 06:01 AM
gilgames
Lebesgue Integral
hi, i need help for this question:
${f}_{n}(x)=n*{\varphi }_{[0,1/n]}$ where ${\varphi}_{[0,1/n]}$ is characterestic function.
1-)what is the value of $\int {f}_{n} d\mu$ over the interval [0,1] ?
2-) if n goes to infinity and ${f}_{n}(x)\to f(x)$ , what is the value of $\int f d\mu$ over the interval [0,1]
thanks for any help.
• May 22nd 2011, 06:03 AM
girdav
1) What is the integral of a characteristic function ?
2) Try to find $f$.
• May 22nd 2011, 06:12 AM
gilgames
1-)well the function ${f}_{n} (x)$ will be equal to $n$ for $x \epsilon [0,1/n]$ and otherwise it is 0.
so i find that $\int {f}_{n } d\mu = \int n d\mu$ over [0,1]. $\int nd\mu =n\int d\mu =n$ over [0,1].
is that right?
2-) i can't figure how to find f. i sense f(x) must be zero when i graph ${f}_{n}$
• May 22nd 2011, 06:20 AM
girdav
1) No, we have $\int f_nd\mu =n\mu ([0,\frac 1n])=1$.
2) $f=0$ almost everywhere, so what about $\int fd\mu$ ?
• May 22nd 2011, 06:26 AM
gilgames
1-) i got it now when graphing. i used the measure of [0,1].
2-) it equals 0
thanks anyway. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9722780585289001, "perplexity": 1163.94257440142}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246659319.74/warc/CC-MAIN-20150417045739-00279-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/140652/separation-of-variables-in-differential-equations | # Separation of variables in Differential Equations
I am scratching my head to figure out a way to separate variables of the following equation:
$$(t+3)(t-2)dx = (t+tx^2)dt$$
Doesn't matter how many times I divide and multiply, I always get $x$ and $t$ on one side. Is there a trick applicable here?!
-
$(t+tx^2) = t(1+x^2)$ – Antonio Vargas May 3 '12 at 23:38
## 1 Answer
$$(t+3)(t-2) dx = (t+tx^2)dt \Rightarrow (t+3)(t-2)dx=t(1+x^2) dt \Rightarrow \frac{dx}{1+x^2}=\frac{t}{(t+3)(t-2)} dt$$ I assume you can take it from here.
- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7907757759094238, "perplexity": 416.81664086798855}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802768044.102/warc/CC-MAIN-20141217075248-00135-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://aviation.stackexchange.com/questions/56025/what-is-the-drag-or-c-d-vs-c-l-of-the-airbus-a320-in-cruise-flight | # What is the drag (or $C_D$ vs $C_L$) of the Airbus A320 in cruise flight?
Is there any website or data-sheet that I can find drag of airplane for cruise conditions. $$C_D$$ vs $$C_L$$ graph is also acceptable.
To be more specific I am searching drag values of A320 in cruise flight.
• In unaccelerated, straight and level flight, total drag is equal to total thrust. Perhaps you may find the data on the total thrust provided by the engines of the A320 under cruise conditions. That would answer your question. – xxavier Oct 14 '18 at 15:20
• Thank you for your answer, I cannot find a website that provide information about cruise thrust – Samet Kocaman Oct 16 '18 at 17:37
• Try to find the best L/D for the A320. Probably, that's also the L/D at cruise flight. From the weight of the A320 and the L/D, you can easily compute the total drag of that airplane... – xxavier Oct 16 '18 at 18:00
• At level flight, constant speed, the total drag is not equal to total thrust , since total thrust is weight related. So certainly not in « accelerated » flight – user40476 May 28 '19 at 16:33
1. The aircraft flies close to its optimum L/D - which is 18 for the A320-200 in cruise. So the $$c_D$$/$$c_L$$ is 0.055556. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4329926073551178, "perplexity": 1610.8045565404384}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250593295.11/warc/CC-MAIN-20200118164132-20200118192132-00372.warc.gz"} |
https://calculla.com/calculators/converter/amount_of_substance | Amount of substance units converter
Converts amount of substance from one unit to another e.g. from millimoles (mmol) to number of particles (atoms or molecules depending on substance) or vice versa.
# Beta version#
BETA TEST VERSION OF THIS ITEM
This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
Feel free to send any ideas and comments !
# Symbolic algebra
ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations
# Inputs data - value and unit, which we're going to convert#
Value Unit yottamole [Ymol]zettamole [Zmol]examole [Emol]petamole [Pmol]teramole [Tmol]gigamole [Gmol]megamole [Mmol]kilomole [kmol]hektomole [hmol]mole [mol]decimole [dmol]centimole [cmol]milimole [mmol]micromole [µmol]nanomole [nmol]pikomole [pmol]femtomole [fmol]attomole [amol]zeptomole [zmol]yoctomole [ymol]number of particles [particles] Decimals 0123456789
# SI#
Unit Symbol Symbol(plain text) Value as symbolic Value as numeric Notes Unit conversion formula yottamole Show source$Ymol$ Ymol Show source$\text{...}$ - Derived amount of substance unit in SI system. One yottamole is equal to septylion of moles: $1\ Ymol= 10^{24}\ mol$ Show source$...$ zettamole Show source$Zmol$ Zmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One zettamole is equal to sextillion of moles: $1\ Zmol= 10^{21}\ mol$ Show source$...$ examole Show source$Emol$ Emol Show source$\text{...}$ - Derived amount of substance unit in SI system. One examole is equal to quintillion of moles: $1\ Emol= 10^{18}\ mol$ Show source$...$ petamole Show source$Pmol$ Pmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One petamole is equal to quadrillion of moles: $1\ Pmol= 10^{15}\ mol$ Show source$...$ teramole Show source$Tmol$ Tmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One teramole is equal to trillion of moles: $1\ Tmol= 10^{12}\ mol$ Show source$...$ gigamole Show source$Gmol$ Gmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One gigamole is equal to billion of moles: $1\ Gmol= 10^{9}\ mol$ Show source$...$ megamole Show source$Mmol$ Mmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One megamole is equal to million of moles: $1\ Mmol=1000000\ mol= 10^{6}\ mol$ Show source$...$ kilomole Show source$kmol$ kmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One kilomole is equal to thausand of moles: $1\ kmol=1000\ mol= 10^{3}\ mol$ Show source$...$ hektomole Show source$hmol$ hmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One hektomole is equal to hundred of moles: $1\ hmol=100\ mol= 10^{2}\ mol$ Show source$...$ mole Show source$mol$ mol Show source$\text{...}$ - The basic amount of substance unit in the SI system. One mole corresponds to the amount of substance that contains $6.023 \times 10^{23}$ particles (→ see Avogadro's number). Depending on the type of substance, it can be the number of atoms, ions or chemical molecules.$1\ mol = N_A\ \text{particles} = 6.023 \times 10^{23}\ \text{particles}$ Because definition and properties of the single particle depends on type of substance there is no constant relation between number of moles and mass. It means that, for example, one mole of water has different mass than one mole of atomic helium. Show source$...$ decimole Show source$dmol$ dmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One decimole is equal to one tenth of mole: $1\ dmol=0.1\ mol= 10^{-1}\ mol$ Show source$...$ centimole Show source$cmol$ cmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One centimole is equal to one hundredth of mole: $1\ cmol=0.01\ mol= 10^{-2}\ mol$ Show source$...$ milimole Show source$mmol$ mmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One milimole is equal to one thousandth of mole: $1\ mmol=0.001\ mol= 10^{-3}\ mol$ Show source$...$ micromole Show source$\mu mol$ µmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One micromole is equal to one millionth of mole: $1\ \mu mol=0.000001\ mol= 10^{-6}\ mol$ Show source$...$ nanomole Show source$nmol$ nmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One nanomole is equal to one billionth of mole: $1\ nmol= 10^{-9}\ mol$ Show source$...$ pikomole Show source$pmol$ pmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One pikomole is equal to one trillionth of mole: $1\ pmol= 10^{-12}\ mol$ Show source$...$ femtomole Show source$fmol$ fmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One femtomole is equal to one quadrillionth of mole: $1\ fmol= 10^{-15}\ mol$ Show source$...$ attomole Show source$amol$ amol Show source$\text{...}$ - Derived amount of substance unit in SI system. One attomole is equal to one quintillionth of mole: $1\ amol= 10^{-18}\ mol$ Show source$...$ zeptomole Show source$zmol$ zmol Show source$\text{...}$ - Derived amount of substance unit in SI system. One zeptomole is equal to one sextillionth of mole: $1\ zmol= 10^{-21}\ mol$ Show source$...$ yoctomole Show source$ymol$ ymol Show source$\text{...}$ - Derived amount of substance unit in SI system. One yoctomole is equal to one septillionth of mole: $1\ ymol= 10^{-24}\ mol$ Show source$...$
# other#
Unit Symbol Symbol(plain text) Value as symbolic Value as numeric Notes Unit conversion formula number of particles Show source$particles$ particles Show source$\text{...}$ - Number of particles in the probe. Depending on the type of substance, it can be the number of atoms, ions or chemical molecules. Number of particles equals to Avogadro's number is one mole of substance.$N_A\ \text{particles} = 6.023 \times 10^{23}\ \text{particles} = 1\ mol$ Show source$...$
# Some facts#
• The basic SI unit of amount of substance is one mole.
• One mole of substance contains the same number of molecules (or atoms in the case of free elements that do create molecules) as 12 grams of carbon isotope 12C.
• In one mole there is 6,022140857 (74) × 10 23 particles (atoms, molecules, ions, etc.). This number is often called Avogadro number:
$N_A = 6,022140857(74) \times 10^{23}$
• One mole of substance may correspond to different mass. For example, one mole of water weighs 18,01528 g, but one mole of carbon dioxide 44,01 g. The mass of one mole of substance is called molar mass and is substance specific. You can read more about molar mass (including molar masses of selected substances) visiting our another calculator: Molar mass.
• One mole of perfect gas under normal conditions (temperature 273K, pressure 1023 hPa) occupies a volume of 22.42 dm3. You can find more about the volume occupied by various gases in our another calculators: Molar volume of gases and Clapeyron's equation.
# How to convert#
• Enter the number to field "value" - enter the NUMBER only, no other words, symbols or unit names. You can use dot (.) or comma (,) to enter fractions.
Examples:
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https://scma.maragheh.ac.ir/?_action=article&sb=1589&_sb=Real+and+Harmonic+Analysis | ##### 2. Admissible Vectors of a Covariant Representation of a Dynamical System
Volume 14, Issue 1, Spring 2019, Pages 55-61
10.22130/scma.2018.72232.291
##### 5. Abstract structure of partial function $*$-algebras over semi-direct product of locally compact groups
Arash Ghaani Farashahi; Rajab Ali Kamyabi-Gol
Volume 02, Issue 2, Autumn 2015, Pages 23-44
##### 6. A tensor product approach to the abstract partial fourier transforms over semi-direct product groups
Ali akbar Arefijammal; Fahimeh Arabyani Neyshaburi
Volume 02, Issue 2, Autumn 2015, Pages 73-81 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6137161254882812, "perplexity": 6625.7205303997}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153966.60/warc/CC-MAIN-20210730122926-20210730152926-00683.warc.gz"} |
https://olympiaelectricians.com/why-is-the-dipole-plate-electric-field-non-uniform | # Why is the dipole plate electric field non uniform?
Date created: Thu, May 20, 2021 8:35 AM
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Those who are looking for an answer to the question «Why is the dipole plate electric field non uniform?» often ask the following questions:
### 👉 Why is the dipole plate electric field not uniform?
An electric dipole always experiences a torque when placed in uniform as well as non-uniform electric field. But in non-uniform electric field, dipole will also experience net force of attraction. So the electric dipole in non-uniform electric field experiences both torque and force.
### 👉 Is electric field uniform in dipole?
Consider an electric dipole in a uniform electric field which is due to some other source.The dipole moment ( ) makes an angle θ with the electric field () as shown in Figure. The forces on charges +q and -q are qE and -qE respectively. Note:The net force on a dipole in a uniform electric field is zero.
### 👉 Dipole kept in uniform electric field will?
In a uniform electric field, both the point charges comprising the dipole will experience force, equal in magnitude and opposite in direction. Though the net force will always be zero, the torque will be in same direction for both the charges. Hence torque will not be zero.
The premise of your question is faulty in that when a dipole is placed in a non-uniform electric field, the direction of the net force experienced by it is not always along the direction of increasing electric field. (I will work with the assumption that you don't speak of a case in which the dipole is titled with respect to the electric field) Two cases exist--the dipole is either parallel or ...
If a dipole placed in non-uniform electric field, it will experience net force of attraction per meter towards electric field of large magnitude that is, F(net)=p(E2-E1).
The magnitude of charges of electric dipole is 3. 2 × 1 0 − 5 and distance between them is 2. 4 A. If it is placed in an electric field 4 × 1 0 5 V / m then its diple moment is (in C-m) Hard
It's Griffiths, in a footnote on page 165. I will quote it: 'In the present context Eq. 4.5 could be written more conveniently as F=∇(p.E).However it is safer to stick with (p.∇)E because we will be applying the formula to materials in which the dipole moment (per unit volume) is itself a function of position and this second expression would imply (incorrectly) that p too is to be ...
This is because the electric field is uniform between the plates. In more general situations, regardless of whether the electric field is uniform, it points in the direction of decreasing potential, because the force on a positive charge is in the direction of E and also in the direction of lower potential V .
As we know that, when a dipole is placed in a uniform electric field, both the charges as a whole do not experience any force, but it experiences a torque equal to τ which can be given as, This torque rotates the dipole unless it is placed parallel or anti-parallel to the field.
charge to the positive charge. This implies that the electric dipole moment vector points from the negative charge to the positive charge. Note that the electric field lines run away from the positive charge and toward the negative charge. There is no inconsistency here, because the electric dipole moment has to do with the positions of the charges, not the field lines.
This is because the parallel plates do not extend out to infinity in each direction. Because it is a conducting plate the charges will build up on the surface. Therefore there will be a charge on the front of the plate, as well as on the back of the plate. This happens on both plates for both charges.
Further, since the electric field stays non-uniform, the pieces of paper get attracted in the direction of the comb. Question: An electric dipole is placed at an angle of 30 o with an electric field of intensity 2 × 10 5 N/ C. It experiences a torque of 4 N m. Calculate the charge on the dipole if the dipole length is 2 c m. 4; 2; 8; 1
To show that the vector of electric intensity changes direction in the centre of the plate, the electric intensity reaches negative values after crossing the centre of the plate. The electric field is uniform outside the plate with intensity $$E\,=\, \frac{\varrho a}{2 \varepsilon_0}$$.
We've handpicked 24 related questions for you, similar to «Why is the dipole plate electric field non uniform?» so you can surely find the answer!
### What happens when a dipole is placed in non uniform electric field?
If an electric dipole is placed in a nonuniform electric field, then the positive and the negative charges of the dipole will experience a net force. And as one end of the dipole is experiencing a force in one direction and the other end in the opposite direction, so the dipole will have a net torque also.
### A uniform electric field?
A uniform electric field is a field in which the value of the field strength remains the same at all points. In a uniform electric field, as the field strength does not change and the field lines tend to be parallel and equidistant to each other. They are equally spaced.
### Is electric field uniform?
A uniform electric field is a field in which the value of the field strength remains the same at all points. In a uniform electric field, as the field strength does not change and the field lines tend to be parallel and equidistant to each other. They are equally spaced.
### Uniform electric field definition?
A uniform electric field is a field in which the value of the field strength remains the same at all points. In a uniform electric field, as the field strength does not change and the field lines tend to be parallel and equidistant to each other. They are equally spaced.
### What happens when an electric dipole is placed in a non uniform electric field?
If an electric dipole is placed in a nonuniform electric field, then the positive and the negative charges of the dipole will experience a net force. And as one end of the dipole is experiencing a force in one direction and the other end in the opposite direction, so the dipole will have a net torque also.
### What will happen if an electric dipole is placed in non uniform electric field?
If an electric dipole is placed in a nonuniform electric field, then the positive and the negative charges of the dipole will experience a net force. And as one end of the dipole is experiencing a force in one direction and the other end in the opposite direction, so the dipole will have a net torque also.
### When an electric dipole is held at an angle in a uniform electric field?
1) the forces experienced by the 2 charges constituting the electric dipole when placed in an uniform external electric field are equal and opposite in nature, the net force on the dipole is zero. No torque act on the dipole when the moment of electric dipole is parallel to the electric field.
### For what orientation of electric dipole in uniform electric field is potential energy of dipole is greatest and least?
Udipole = -pE cosθ. The potential energy is lowest when the dipole is aligned with E and highest if it is anti-aligned.
### Why is the electric field in a parallel plate capacitor uniform?
Why is electric field uniform in parallel plates The electric field is uniform between the parallel plates of a capacitor since the distance between the plates is kept very small compared to the size of the plates. Was this answer helpful? 0 (0)
### When an electric dipole is held at an angle in a uniform external electric field then the dipole will experience?
Answer: The dipole when released experiences no net force but experiences torque in a uniform electric field. Explanation: No net force because both the positive and negative charges experiences equal force (qE) in the opposite directions.
### At what angle of electric dipole moment with uniform electric field potential energy is maximum?
When the angle between the dipole moment and electric field is 180° then the potential energy of electric dipole is maximum.
### How do dipole produce electric field?
Since in this case the electric field is along the dipole moment, ($$E_+ \gt E_-$$) $$\overrightarrow{E}$$ = $$\frac{1}{4πε_0} \frac{2\overrightarrow{p}}{r^3}$$ Notice that in both cases the electric field tapers quickly as the inverse of the cube of the distance. Compared to a point charge which only decreases as the inverse of the square of ...
### What is dipole in electric field?
A pair of electric charges with an equal magnitude but opposite charges separated by a distance d is known as an electric dipole. The electric dipole moment is a vector having a defined direction from the negative charge to the positive charge…
### What is electric field dipole moment?
An electric dipole is a pair of equal and opposite charges separated by a considerably short distance, whereas an electric dipole moment is the product of the magnitude of charges and the separation between them. The electric dipole moment explains the strength of an electric dipole for producing the electric field. Q2.
### Is uniform electric field 1?
A uniform electric field is a field in which the value of the field strength remains the same at all points. In a uniform electric field, as the field strength does not change and the field lines tend to be parallel and equidistant to each other. They are equally spaced.
### Is uniform electric field realistic?
Is uniform electric field realistic? Thread starter Axe199; Start date Jul 20, 2014; Jul 20, 2014 #1 Axe199. 48 0. I was learning about gauss's law and how to use to determine electric field, one of them is an infinite plane of continuous and uniform charge , eventually E= σ/2ε which means the E is not depend on the distance from the plane ...
### What is uniform electric field?
A field in which the value of the field strength is the same at all points. For example, a uniform electric field exists between two parallel charged plates. At the ends of the plates the field is non-uniform. Uniform magnetic fields may be produced by Helmholtz coils. From: uniform field in A Dictionary of Physics »
### Where is electric field uniform?
A uniform electric field has symmetrical and constant field effect throughout the region is permeates. Or in easier language, the test charge should encounter constant force through out the region when the electric field is uniform or constant. So, according to your query the uniform field is there, where the effect of the uniform is constant.
### Which produces uniform electric field?
For an infinite uniformly charged infinite plane, the electric field only depends on the surface charge density of the plane so it is independent of the distance and hence it remains constant in space. So, an infinite uniformly charged plane generates a uniform electric field.
### In which orientation is potential energy of an electric dipole zero in a uniform electric field?
When an dipole is placed in a uniform electric field with a angle of 90° or π/2, its potential energy is 0.
### Which orientation of an electric dipole in a uniform electric field would correspond to stable equilibrium?
when angle 0 b/w dipole moment vector p and electric field vector E is zero then potential energy of dipole, U=-pEcos0 =-pE and torque=pEsin0=0;which means that the electric dipole is in stable equilibrium.
### Which orientation of an electric dipole in an uniform electric field would correspond to unstable equilibrium?
So interesting query! As we keep the dipole with its dipole moment along the direction of the electric field then it will be in stable equilibrium. IF we keep the same dipole inverted ie its dipole moment opposite to the external field then the dipole will be in unstable equilibrium. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9367406964302063, "perplexity": 217.0298706749942}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585280.84/warc/CC-MAIN-20211019171139-20211019201139-00073.warc.gz"} |
https://socratic.org/questions/how-do-you-find-the-product-3-3-3-2 | Algebra
Topics
# How do you find the product 3^3*3^2?
${3}^{3} \cdot {3}^{2} = \left(3 \times 3 \times 3\right) \cdot \left(3 \times 3\right) = \left(9 \times 3\right) \cdot \left(9\right) =$
$27 \cdot 9 = 243$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7580861449241638, "perplexity": 4033.2726140121526}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738425.43/warc/CC-MAIN-20200809043422-20200809073422-00158.warc.gz"} |
https://physics.stackexchange.com/questions/661241/calculation-of-the-speed-of-the-iss-from-the-circulation-time | # Calculation of the speed of the ISS from the circulation time
This is my first question, and as a chemist, my physics vocabulary is a bit limited. A younger friend of mine asked me about a physics question from school, but I am not able to solve it, and I think the question is not providing enough information. The topic is "Kepler's Law."
The question says:
The circulation time of the ISS is 91 minutes. Which height above ground does the ISS have? What is its speed?
First, I looked up Kepler's law, but to use the third law I would need something else circulating around the earth like the moon and information on its semi-major axis.
Then, I found Newton's gravitation law which needs the masses of the two objects.
So maybe you have some other ideas that I should look up to find an answer how to calculate the semi-major axis of the ISS just from the circulation time without using google for the circulation time of the moon or the mass of the earth.
• "...like the moon" Could you look up its distance and period? Aug 24 at 19:21
• well the moon takes 1 month by definition to go around. Minus 1/12 for the sidereal correction. Don't need to look that up.
– JEB
Aug 25 at 0:28
• I don't understand the aversion to googling the information you need (mass/radius of Earth). The purpose of the question is to test your understanding of physics, not to inform the examiner of the height of the ISS. Aug 25 at 11:57
• @OscarBravo I think the assumption is that a school problem usually has all the information needed in it. If you're meant to use outside sources, you could just google the the altitude and velocity of the ISS right away.
– noah
Aug 25 at 12:00
• Thank you noah, that is exactly what it is about. You are supposed to learn the formula and use it accordingly not looking up information on the internet. It might be different but in germany you are almost never supposed to search for given numbers outside a standard book and then it is explictly mentioned or discussed in class before. Aug 25 at 12:11
Which height above ground does the ISS have?
The wording of this question makes me think that the question assumes the orbit to be circular, since an ellipse will not have a constant height above ground.
Also, since this is at the level of school teaching, I think they are just assuming a circular earth and a circular orbit around the earth.
If that is the case, then you can just use the equation
$$\frac{mv^2}{h+r} = \frac{GmM}{(h+r)^2}$$
where $$h$$ is the height above ground,
$$r$$ is the radius of Earth,
and $$M$$ is the mass of Earth.
For $$v$$, you can substitute the perimeter of the circular orbit / circulation time i.e. $$v=\frac{s}{t}=\frac{2\pi\,(r+h)}{91\text{ minutes}}$$ Take care to convert to same units.
This will give you an equation with only one unknown, $$h$$.
You can solve it to get $$h$$.
Of course, in the real world a lot of these assumptions will not hold. But, I think the school question is going for a more simplistic model with those simplified assumptions.
• This still means, I need to look up the radius and the mass of the earth. Then I could google the height of the ISS as well. Aug 25 at 11:42
• @Inselino Radius and mass of the earth are values that are generally considered as known/given values when studying mechanics etc. I do not think it is the same thing as just looking up the answer. You have mentioned elsewhere about how it is in Germany, but where i come from, those were known values that could be used in calculations as and when required
– user312165
Aug 25 at 12:55
• But this is 9th grade in school not studying mechanics. Aug 25 at 13:52
Kepler's third law relates the period of an orbit to its radius, using only constants like $$G$$ and the mass of the body about which the object is rotating (here: the Earth). This will directly give you the result with information that is readily available. You are correct that, if you wanted to solve that without the mass of the Earth, you could use another set of equations with the same proportionality constant, such as those from the moon.
Then, once you have radius and orbital period, speed should be straightforward to calculate by using the relationship between the radius and circumference of an orbit.
• I wanted to know if I can solve it without using google. Mass of the earth is not provided in the question. Aug 24 at 19:47
• It's probably something that the text the question comes from assumes can be looked up. Often that's in a table at the front or back of an intro physics book. Aug 24 at 20:02
• There's always a missing variable that is easy to look up: radius of the earth, mass of the earth, etc Aug 24 at 22:32
• Yeah but in this case, I could look up the height of the ISS as well. But I found the answer to the question online, the teacher missed out on some information. Aug 25 at 11:42
You know the acceleration g at the radius of the earth. you know the centipededal acceleration of ISS, you can calculate the velocity at the radius of the earth (in vacuum) then you can use Kepplers law to calculate the radius of ISS and therefor the high as diference
thanks for all the answers. As I could notice from the answers, there is NO way without getting more information like the mass of the earth or the distance earth-moon. But if you use google anyway, you could just look up the distance above ground of the ISS. So this is not the solution.
But we looked up the exact question (originaly in german) in the internet and we found out, that there is this exact question. But it originates from a sheet with a lot of questions and a lot of additional variables like the circulation time and the distance of the moon.
In this case, the teacher just copy pasted the question without the additional information provided in the original source.
• Please move this additional insight as a new section to the question. Use formatting options to structure it in a clear way as addition. Answers should only be used for actual answers. Aug 25 at 12:19
• But this is the answer. There is no way without additional information. Aug 25 at 12:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.809402585029602, "perplexity": 270.55249630528215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964364169.99/warc/CC-MAIN-20211209122503-20211209152503-00585.warc.gz"} |
https://robotics.stackexchange.com/questions/20222/arduino-and-stepper-motor | # Arduino and stepper motor
How arduino stepper library handles stepper motor with ULN2003? I mean, for controlling stepper motor one actually needs four pwms. It can be reduced to two by encoding, or maybe even to one by using other techniques. But could you, please, clarify how arduino does it? I could not find the low level code for that from arduino to inspect.
Thanks
• why do you believe that you require PWM signal to control a stepping motor? – jsotola Feb 20 at 16:26
• For not blocking the main code. Like PWM with DC motor. – Pasha Feb 21 at 11:06
There is generally a stepper example in the arduino Compiler, you can find the code there, or look at the stepper library
However arduinos can‘t control steppers directly, but they send signals to stepper drivers, which then send the correct voltages to the stepper to rotate in a specific direction and rotate at a specific frequency.
Arduinos are basically ‚bit banging‘ namely they send a single high and low signal at a specific frequency and duty cycle, which determines the rotational speed of the motor itself. One line is high/low for direction, another for the signal. The advantage is you can count how many times you bit banged, and have an open loop position control system for easy NC applications
No-one would use the analog pins on an arduino to control stepper motors.
4wire stepper motors have A and B coils that require specific timing to excite (read, step) the motor and a large amperage/voltage requirement. Hence the drivers.
Considering read the wiki about steppers to get a better idea about them.
• I mean 28BYJ-48 motor. Can't we control speed? I mean stepper motor rotates with certain speed. And at each sampling time we just change its speed, not give step commands. – Pasha Feb 21 at 10:48
• Speed is a function of steps. $\omega=2 \pi f$ – morbo Feb 21 at 10:50
• Yes, but when you give certain number of steps it is gonna stop after doing that. But we want it to rotate continuously until we change speed. – Pasha Feb 21 at 10:57
• Like PWM, it gives same duty cycle until you change it, – Pasha Feb 21 at 10:57
• So you’ve have to write a function that continuously bit bangs that allows you change freq at will. You’ll have to do some math ;) – morbo Feb 21 at 10:59
Here is Arduino library code specifically for the 28BYJ-48 stepper motor using the ULN2003 controller board. The readme discusses the various driver modes and how they work. It's not done with PWM like a servo motor (where PWM is a repeating square wave control signal). Rather it is done by energizing the coils in the motor such that they attract to magnets. Energizing in a specific pattern will move the motor from magnet to magnet, thus turning the spindle.
There is an example sketch for implementing a differential drive robot using two 28BYJ-48 stepper motors. There is an example sketch that uses a LM393 optical encoder to calculate the steps per rotation of the stepper motor. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18914109468460083, "perplexity": 2174.4613870634194}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347405558.19/warc/CC-MAIN-20200529152159-20200529182159-00249.warc.gz"} |
https://socratic.org/questions/5727c51611ef6b2e2d0f7401 | Chemistry
Topics
# Question f7401
May 22, 2016
$\text{K} \cong {10}^{62}$ which can be regarded as infinitely large.
#### Explanation:
Arrange the ${\text{E}}^{\circ}$ values in increasing order:
" " "E"^(@)("V")
color(red)stackrel(leftarrow)(color(white)(xxxxxxxxxxxxx)
$F {e}_{\left(a q\right)}^{3 +} + e r i g h t \le f t h a r p \infty n s F {e}_{\left(a q\right)}^{2 +} \text{ } + 0.77$
$M n {O}_{4 \left(a q\right)}^{-} + 8 {H}_{\left(a q\right)}^{+} + 5 e r i g h t \le f t h a r p \infty n s M {n}_{\left(a q\right)}^{2 +} + 4 {H}_{2} {O}_{\left(l\right)} \text{ } + 1.51$
color(blue)stackrel(rightarrow)(color(white)(xxxxxxxxxxxxxxxxxxxxxx)#
The Mn(VII) 1/2 cell has the more +ve value so the reaction will be driven in the direction indicated by the arrows
To find ${\text{E}}_{c e l l}^{\circ}$ you subtract the least positive value from the most +ve:
$\text{E"_(cell)^(@)=1.51-0.77=+0.74"V}$.
The Nernst Equation at ${25}^{\circ} \text{C}$ can be written:
${E}_{c e l l} = {E}_{c e l l}^{\circ} - \frac{0.05916}{n} \log \text{Q}$
$\text{Q}$ is the reaction quotient
$n$ is the number of moles of electrons transferred, which in this case $= 5$
As the reaction proceeds, the potential difference between the two 1/2 cells falls.
When it reaches zero the reaction has reached equilibrium so now we can write:
$0 = {E}_{c e l l}^{\circ} - \frac{0.05916}{5} \log \text{K}$
Note that $\text{Q}$ has been replaced by $\text{K}$, the equilibrium constant.
Putting in the value for ${E}_{c e l l}^{\circ}$ and rearranging $\Rightarrow$
$\log \text{K} = \frac{0.74 \times 5}{0.05916} = 62.5$
$\therefore \text{K} = 3.48 \times {10}^{62}$
This is a number so large that we can say that the reaction has gone to completion.
##### Impact of this question
1415 views around the world | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 21, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8819717764854431, "perplexity": 861.6054094747416}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250594101.10/warc/CC-MAIN-20200119010920-20200119034920-00135.warc.gz"} |
https://math.stackexchange.com/questions/1652608/special-purpose-hash-functions | # Special-purpose hash functions
I am trying to create a special purpose hash function that will have as few collisions as possible.
$99\%$ of the input will be sequential numbers, from $1$ to $N$. The size of the hash table will be $\frac{N}{10}$.
Can anyone provide the perfect hash function for this input?
If perfect means as few collisions as possible, you can just do $f(n)=(n \pmod N)/10$ where the divide is integer division. You have to have $10$ of each number in the range $[1,N]$ mapped to each hash value, which this does.
Often we also ask that hash functions be such that one cannot reasonably predict the hash from the number to be hashed, nor invert it to find a number that will match a given hash. If you want that as well, just take any current cryptographic hash function (which will presumably return a number much larger than $\frac N{10}$), then take the output $\bmod \frac N{10}$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6053609251976013, "perplexity": 315.96226120056195}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314959.58/warc/CC-MAIN-20190819201207-20190819223207-00155.warc.gz"} |
https://jcom.sissa.it/archive/20/04/JCOM_2004_2021_A03 | # Step by step towards citizen science — deconstructing youth participation in BioBlitzes
### Abstract:
BioBlitzes, typically one-day citizen science (CS) events, provide opportunities for the public to participate in data collection for research and conservation, potentially promoting deeper engagement with science. We observed 81 youth at 15 BioBlitzes in the U.S. and U.K., identifying five steps participants use to create a biological record (Exploring, Observing, Identifying, Documenting and Recording). We found 67 youth engaged in at least one of the steps, but seldom in all, with rare participation in Recording which is crucial for contributing data to CS. These findings suggest BioBlitzes should reduce barriers to Recording for youth to increase engagement with science.
Keywords:
7 November 2020
2 March 2021
14 June 2021
### 1 Context and objectives
In recent years, opportunities for participation in Citizen Science (CS) have increased, as have expectations of its potential for public engagement, education and scientific research. The majority of the many attempts to define CS [e.g. Haklay et al., 2020; Shirk et al., 2012; Bonney et al., 2009] seem to agree that its “common, shared goal is to collect and analyze information that is scientifically valuable” and that this “distinguishes citizen science from areas such as experiential learning or environmental education” [Hecker et al., 2018, p. 2]. Different typologies of CS projects [e.g. Shirk et al., 2012; Haklay, 2013] are commonly based on the range and extent of participants’ contribution to the scientific process, for example, to determine whether a CS project is best described as “contributory”, “collaborative” or “co-created” [Shirk et al., 2012]. For this study, we move beyond the assumed opportunities for participation in the scientific process to focus on actual participation in CS programs, investigating what activities youth (5–19 years old) actually engage in when participating in BioBlitzes. BioBlitzes fall into the category of “contributory” CS because they are typically scientist-driven [Shirk et al., 2012], with the scientific aim of collecting biodiversity data with the help of non-experts that can be used for scientific research, monitoring or land management.
Our study explores how youth participate in BioBlitzes. We do not evaluate the success of the events as a whole in their contribution to science, instead, we focus solely on youth participation in the scientific process inherent within BioBlitz events. Through our lens, we are able to analyze youth’s experiences of participating in a BioBlitz as a scientific endeavour, as opposed to similar environmental education or public engagement activities (i.e. nature walks or pond dipping activities) that lack this scientific purpose [Hecker et al., 2018].
We operate under the premise that participating in the data submission step of a CS project, known as Recording in biological monitoring, is a crucial aspect of youth participation in BioBlitzes because a) only recorded data can be used for scientific research or monitoring purposes, and b) interaction with and ownership of scientific data they have gathered has proven important for the development of agency within youth, at least in ongoing CS activities [Harris et al., 2020]. Understanding participation is salient for event design and studying the outcomes of short-term CS events. Our research will address assumptions that taking part in a BioBlitz automatically equates to contributing data to the scientific purpose, proposing a more fine-grained framework to describe participation in CS.
#### 1.1 Biological recording and citizen science
One aim of the Convention of Biological Diversity [United Nations, 1992] was to address threats to biodiversity through scientific assessment, such as monitoring climate change impacts on biodiversity. Therefore, the practice of biological recording, established in the 17th century [Pocock et al., 2015], stays relevant today. But, what constitutes a biological record?
According to Pocock et al. [2015], a “biological record is, at its simplest, a record of a species in a particular place at a particular time by a named person.” It consists of answers to four questions [Isaac and Pocock, 2015]: What? (the identity of the species observed), Where? (the spatial location it was observed), When? (the date, or date range, it was observed) and Who? (the person who made the record). The generated records are ideally shared with networks such as the Global Biodiversity Information Facility (GBIF) to make them accessible for further research.
While biological recording has largely been undertaken by non-professionals long before the term ‘citizen science’ was coined, the CS approach broadens the audience for biological recording by involving non-expert members of the public. The paradigm change in science communication from deficit and dialogue to participation [Lewenstein and Brossard, 2009] altered the mission of many science education stakeholders including Natural History Museums (NHMs). Building on their experience of collaboration across amateur-expert communities and aligned with their dual mission of education and scientific research, it is not surprising that NHMs engage in CS through multiple approaches, including capacity building (e.g. in form of guides and training courses) as well as developing and running CS programs. Ballard et al. [2017] demonstrated that NHM-led CS programs can contribute to conservation research, management, education and policy.
#### 1.2 BioBlitzes
While specific definitions vary, BioBlitzes can be described as biodiversity experts and members of the public working together to generate a biodiversity inventory in one particular location over a short time frame (usually 2–24 h) [Ballard et al., 2017]. For the shorter version of BioBlitzes, the term mini-BioBlitz has been introduced [DITOs Consortium, 2019]; this format better describes the NHM-led BioBlitzes observed in this study (see Supplementary Material A for more information on BioBlitzes in general and in this study). Several studies have investigated the potential of BioBlitzes for public engagement and education. Roger and Klistorner [2016] highlight that participants value the opportunity to interact and learn from scientists, and experts enjoyed interacting with members of the public. Leong and Kyle [2014] showed that participants’ motivations included contributing to society and conservation, making life better for the coming generation, and learning about different species. An evaluation of BioBlitzes in the U.K. showed that while adults enjoyed learning opportunities and interaction with experts, children preferred “practical activities, particularly those that involve direct contact with wildlife such as pond dipping and bug hunting” [Postles and Bartlett, 2018, p. 371]. The evaluation of the 2016 National Park BioBlitzes [Hartry et al., 2017] reports increases in students’ comfort in being in nature, appreciation for biodiversity, and in environmental advocacy. Behavioral engagement patterns were studied using observational data, demonstrating that participants were most actively engaged when participating in science practices, and mostly passive during instructions and while walking; but never disruptive. While the qualitative categories in Hartry et al. [2017] provide insights into participants’ engagement levels, they remain vague regarding the specific scientific practices in which participants took part. So, despite this evidence of engagement and education outcomes from BioBlitzes, we continue to lack an understanding of what participants actually do during the events. Are they taking up the opportunity to contribute data to science?
#### 1.3 Participation in Citizen Science
This logic model [Shirk et al., 2012, p. 8] shows how any potential outcomes of CS are linked to the provided activities (input) and the participants’ experience (output) (Figure 1). The similar model proposed by the WTimpact1 project [Bruckermann et al., 2020], further emphasizes the difference between opportunities for participation and actual participation. In both models, participation is directly linked to the outcomes of the CS project.
The affordances and constraints of CS projects vary according to subject area and project design, influencing the degree to which participants can contribute to the scientific goals. It is important to understand what participation in CS means in the specific context of any given program in order to study it effectively. What steps or tasks need to be undertaken to contribute to the scientific goals? In co-created CS projects “at least some of the public participants are actively involved in most or all aspects of the research process” [Shirk et al., 2012, p. 6], yet contributory CS projects are more common, with participation being mostly limited to “contributing data”. Even within the same project type, the range of opportunities available to participants can vary significantly, because they are defined by the scientific goals of the CS project.
To describe the actual participation within or across CS projects, a more fine-grained perspective is needed. Some studies explored engagement in CS, for example, Phillips et al. [2019] proposed degrees of engagement in science from the participants perspective and Golumbic, Baram-Tsabari and Fishbain [2020] identified different engagement styles in participants in an ongoing CS project. In comparison, online CS projects often can track actual participation via log files and, therefore, can easily describe and categorise participation profiles [Herodotou et al., 2020]. For CS projects using kits or surveys that participants need to register for, the registration versus data submission rate can provide some insights into the data submission behaviour of the participants (according to West, Pateman and Dyke [2016], submission rates range from 10% to 50%). However, for more free-form, event-based CS activities, we lack data on patterns in participation; we address this knowledge gap in this study specifically around youth participation in BioBlitzes. The aims of this research were to investigate: 1) what types of participation youth actually engage in at BioBlitzes, 2) to what extent youth themselves participate in contributing data to science during the events, and 3) what patterns of participation by youth in BioBlitzes can be identified.
### 2 Methods
#### 2.1 Data collection
We observed 15 BioBlitzes led by The Natural History Museum in London, the California Academy of Sciences (San Francisco) and the Natural History Museum of Los Angeles County, with each museum (NHM) organising 4–7 events (for further information on the BioBlitzes, see Supplementary material A and for a more detailed version of the methods section, see Supplementary material B). We used ethnographic field observations [Emerson, Fretz and Shaw, 1995] to capture participation data for 81 youth. The sampling method combined random purposeful and stratified purposeful sampling [Creswell, 2014]. All demographic information (Table 1) are suppositions and were unconfirmed, as data were observational only, per ethics approval.
Table 1: Approximate age and presumed gender of the 81 focal youth (31 NHM London, 28 NHM Los Angeles County, 22 California Academy of Sciences) observed.
Our aim was to gather a variety of youth’s BioBlitz experiences to get a broad picture of what youth do when attending BioBlitzes. We opted for focal sampling: observing and documenting all occurrences of behaviors of interest for a particular individual during the entire sampling period [Pellegrini, Symons and Hoch, 2004]. To increase the number of focal youth that could be observed per event, we predetermined the duration of the observation interval. Taking into account how long the average CS data collection task would last and allowing time for youth to orient themselves within the setting and activity, we set the observation duration to 20 minutes. We are aware that in any one youth’s participation, our study may have missed instances of activity that may have happened outside the observation interval. This was an unavoidable limitation, unless we had narrowed the number and range of youth observed in order to follow focal youth for the whole duration of the event. Researchers primarily took the approach of “observer as participant” [Creswell, 2014]. Our protocol ensured that methods were aligned across different settings and observers [Emerson, Fretz and Shaw, 1995].
#### 2.2 Data analysis
To analyze the ethnographic fieldnotes, we adapted Creswell’s steps of Data Analysis for Qualitative Research [2014]. We identified key action/interaction episodes in which youth engaged in CS-related activities. For each key action/interaction episode, we wrote a memo containing a claim about youth participation, a description of the type of participation observed and excerpts from field notes as evidence to support the claim. At the start of the process, researchers went through a calibration phase, discussing and aligning the analytic approach in peer-review, before progressing with data analysis. The memo-writing process for each focal youth was iterative and involved two researchers per memo. Building on Pocock et al.’s [2015] components of a biological record, we identified five ways youth could potentially contribute to a BioBlitz’s scientific goals, and therefore developed a priori codes for these, as follows:
Exploring
— exploring and actively searching the habitat to discover organisms, potentially involving tools such as binoculars or nets.
Observing
— observing organisms in nature, using one’s senses to find and study organisms
Identifying organisms
— putting a name to the organism (e.g. taxon or species) that was observed
Documenting
— documenting the observations by generating evidence of the observation, such as a photograph or writing on a data sheet
Recording
— making the documented observation available for biodiversity monitoring or research purposes, ideally providing the Who, When, Where and What aspects of a biological record [Isaac and Pocock, 2015]
We consider the final two closely-related types of participation separately (Documenting and Recording), as not everything that is documented is necessarily shared for research purposes, and it is this onward sharing of data that distinguishes CS from other forms of engagement, and the external accountability in Recording may have implications for the development of youth agency [Harris et al., 2020].
More detailed and nuanced descriptions of the above types of participation with examples, are provided in the results section, alongside additional types of participation observed. We used these types of participation for thematic coding [Saldaña, 2009] of the memos to enable a participation type frequency analysis. Two researchers coded a sample (4% of the memos) including memos from each museum independently and achieved a substantial agreement (92% agreement, Cohen’s $\kappa =0.73$). The coders discussed disagreements and settled on coding-decisions for these cases [Creswell, 2014; Saldaña, 2009]. The coders then split up the remaining memos between them and coded them independently.
Based on the observed participation types, patterns were identified to propose participation profiles. Detailed descriptions and frequency of occurrence of each profile can be found in the results section.
### 3 Results
We observed 67 of the 81 focal youth (FY) participating in at least one of the anticipated CS-relevant types of participation. Table 2 provides a brief overview of the five types of participation and the number of youth that were observed participating in each during the 20-minute observation period. For the remaining 14 focal youth, observed participation could not be categorised as CS-relevant (e.g. puppet theatre show or lecture-style presentation) and therefore, were not further analyzed.
Table 2: Number of youth ($N=81$) observed participating in each type of participation. Youth could participate in one, all five or any combination.
Our coding approach allowed us to capture multiple ways a young person participated in a 20-minute observation period. The types of BioBlitz participation are not mutually exclusive even within one observation period. Therefore, the numeric statements in our results report the number of youth we observed undertaking each type of participation, to communicate the relative predominance of participation types in our data.
To characterize the participation of the 67 youth who engaged in any of the a priori defined types of participation, we provide a detailed description of the types of participation, examples from the fieldnotes, and how frequently we observed youth engaging in each of the steps.
#### 3.1 Exploring
Exploring included searching for wildlife, interacting with nature (e.g. turning over rocks, looking under leaves), and generally exploring the habitat. Exploring could be done with or without the use of tools (e.g. sweep nets, beating sheets, or sticks). For example, Ben,2 an elementary school-age boy in L.A., participated in Exploring when he used his hands and a spoon to reveal crabs and other tidepool organisms.
Another example, from a beetle walk, shows that for this type of participation, the effort of searching for wildlife was enough to be coded as such; it was not necessary to find organisms.
“Nina walks back towards the logs with her friend, to look underneath another log. They […] continue turning over another 2 or 3 logs in turn, checking underneath them and putting them back down.” (Female, middle school-age, London Hyde Park BioBlitz)
We observed 48 youth participating in Exploring with no major difference in participation based on gender. Of the younger groups, 68% and 70% (elementary and middle school-age respectively) were observed taking part in Exploring, while only 23% of high school-age youth were observed doing so. While Exploring was one of the most common types of participation for the two younger age groups, it was the least common type for older youth.
#### 3.2 Observing
The process of Observing involved the youth using their senses to find, notice, or watch organisms. We observed this type of participation taking place in many different ways, with or without the use of tools (e.g. magnifying glasses, bat detectors), using different senses (e.g. touching wildlife, listening to bird calls, smelling herbs).
In one example of Observing, Layla, a middle school-age girl at an L.A. BioBlitz, looked at plants in detail and at times crouched down to pick up snails and look at them more closely.
A second example demonstrates that Observing could use senses aside from sight and touch.
“Rob [adult participant] asks the group if they just heard that bird. Alex responds, ‘to me it sounds more like a rattle, like a high-pitched beat boxing’.” (Male, high school-age, SF Lee Hill BioBlitz)
Out of 81 total youth, 57 (70%) took part in Observing, making it the most prevalent type of participation. Age and gender did not seem to affect youth engagement in Observing.
#### 3.3 Identifying organisms
We found a wide variety of ways that youth were involved in the identification process (Table 3). Throughout the observation intervals, youth often drew on more than one resource, and we found interesting patterns in these subcategories of Identifying.
Table 3: Variety of ways we observed youth participating in Identifying (finding out what type of organism they have found).
The predominant way youth identified organisms was by using a knowledgeable person at the event as a resource (33 FY). This included parents, peers, or other participants but often were scientists, volunteers, or educators who facilitated the activities. Those more knowledgeable people either identified the organism for the youth (25 FY), engaged them in identifying it themselves through conversation about characteristics, or supported them in using tools such as ID guides or iNaturalist app (see the example of Henry below). As examples of the former, a facilitator announced, “It’s a brittle star.” or a facilitator identified the find of a youth by saying “Oh! You found a millipede!”.
Some participants identified organisms by using their prior knowledge (16 FY, only elementary and middle school-age). However, this mostly led to coarse-grained identifications, e.g. spider, ladybird, woodlouse.
“Facilitator: ‘Do you know that one?’ Vanessa says ‘stinging nettle’, correctly identifying the plant […], points and says ‘Bumblebee!’, as one flits in front of them. The facilitator agrees that it is.” (Female, elementary-school age, London Tring BioBlitz)
Identification tools, such as identification guides or “spotter sheets” (worksheets with images of species and tick boxes to indicate a species was found), were used by participants to find out what organism they had found (12 FY). Some youth were able to use these identification tools on their own, but often needed some support. The following quote illustrates how a young person identified his find by using an ID guide and received support from a facilitator:
“Henry points at a picture on the guide ‘I think it’s this.’ Facilitator: ‘Does it swim on its back?’ Henry looks closely at the animal in the tray: ‘No.’ Facilitator: ‘Then look again.’ Facilitator: ‘When you’ve got a larva like this, you count the bits of the tail. Which ones have three?’ Henry points at three pictures. Facilitator: ‘Only these three, so what do you think it is?’ Henry: ‘Damselfly.”’ (Male, middle school-age, London Hyde Park BioBlitz)
Alternatively, having access to iNaturalist allowed participants to use its machine-learning feature to get suggestions to support them in the identification process (9 FY).
Silje: ‘Whoa!’ Silje’s dad: ‘Wow, that’s a giant roly-poly.’ The two take a picture, look at the iNat suggestions together, discussing the various options of what it could be. They settle on a pillbug” (Female, elementary school-age, SF Silicon BioBlitz)
Three focal youth engaged in learning activities to develop identification skills, like sorting specimens based on certain anatomical characteristics, a precursor to identifying organisms in the field.
While 30 focal youth actively engaged with the process of identification (e.g. using ID guides or iNaturalist on their own, being supported by a knowledgeable person through dialogic conversation, using the identification tools available), 15 focal youth were only told the identification of an organism and/or identified it themselves based on their prior knowledge.
The results did not show major gender- or age-related differences.
#### 3.4 Documenting
Youth Documenting included any form of creating a written or digital record of the observation, including writing down what organism was found, drawing or taking a picture of the organism. This step did not require the document to be shared with anyone but had the potential of being shared and used for monitoring or research.
BioBlitzes that used iNaturalist as the only recording option encouraged participants to take photographs of their findings. To distinguish between Documenting and Recording, cases in which we only saw youth generate the artifact, providing evidence for an observation, but not the act of making it accessible for data analysis were considered to be “Documenting”.
In BioBlitzes that did not use iNaturalist, the equivalent were instances of youth filling out “spotter” sheets or data sheets, drawing in notebooks or similar activities, but without evidence of them handing in these documents to scientists or other facilitators at the event. These “analog” forms of data have been the backbone of citizen science and amateur naturalist documentation for decades but require rigorous quality assurance if they get submitted (see Recording below).
For example, during a London BioBlitz an elementary school-age girl noted down information about her observations, prompted by her mother handing her the data sheet: “Bee” (under what did you see), “1” (under how many did you see) and “Hedge” (under where did you see it)”. During BioBlitzes that used iNaturalist, youth were observed using smartphones or cameras to take pictures of wildlife:
“The facilitator pointed out a spider. Mike took out the camera to get closer. He took the picture.” (Male, elementary school-age, L.A. DD BioBlitz)
We observed 28 youth Documenting observations. Age and gender seemed not to affect participation in Documenting.
#### 3.5 Recording
Each BioBlitz offered one of two ways to participate in Recording: a) submitting data to iNaturalist or b) handing in documented observations in written form to a facilitator at the event. Both of those actions result in data points being made available for scientific analysis by the NHM or local land manager, or to be shared with biodiversity databases.
In some cases, participation in Recording was clear, as when youth generated a biological record by uploading data to iNaturalist:
“Nia is on an iPhone alone, taking a picture of a tree and uploading it. She scrolls through the options for identifications and chooses one […] Nia takes a picture of the moss and uploads it to iNaturalist. She asks why iNaturalist thinks it’s a tortoise? Becky says, ‘Do you think it’s because that’s what the back of a tortoise looks like?’ Nia: ‘I guess so.’ Ally: ‘You can just type in moss.’ Nia does so.” (Female, elementary school-age, SF Silicon BioBlitz)
Further, we observed one young man (high school-age, L.A. BioBlitz) recording his own findings using iNaturalist and then helping others, “You can ID or you can just take the picture if you’re not sure and someone can help you. […] You can still upload even if you don’t know.”
Other cases of participation in Recording were very brief and less obvious moments. We observed the young person using the iNaturalist app to take a picture of an organism and upload it; for example, at a BioBlitz in San Francisco, “Nathan takes a picture of the slug […]. He makes an iNat observation and then almost immediately starts walking ahead”, and “Kris uploads a picture of a poppy then walks ahead”. These youth did not engage any further with the iNaturalist app (e.g. using the machine-learning feature). Nevertheless, these were considered Recording activities.
Instead of iNaturalist, some events provided generic recording sheets asking for species name, location, and number of specimens found; the EarthwormWatch3 activity in London BioBlitzes asked for additional information on their recording sheet (e.g. about the soil characteristics at the survey site). We categorized this as Recording in those cases when youth filled in any provided recording sheet and handed it to a facilitator at the event, as in this example:
“Natalie: ‘It’s a leech’ and draws a tick next to the picture of the leech on the sheet […] Natalie gives this worksheet to the activity leader before she leaves.” (Female, middle school-age. London Tring BioBlitz)
In total, we found 12 focal youth that participated in Recording. There seems to be no correlation between participating in Recording and gender. These youth were spread across all three age groups: three elementary school-age (7% of this age group), three middle school-age (15%) and six high school-age (35%). So, while older youth were more likely to engage in recording, even elementary school-age youth engaged in this type of participation.
#### 3.6 Other types of participation
In addition to the a priori defined types of participation that derived directly from the data collection process of BioBlitzes, we observed youth taking part in other ways. Youth were observed leading and helping others, sharing their science knowledge, skills and findings. At times, youth participated in a more passive way (e.g. when listening to activity leaders). Some youth showed stewardship for wildlife and the habitat, for example, when emptying collection pots to release insects, to make sure organisms they discovered were put back where they were found, or asking others to behave in these ways. These are notable ways youth participated in BioBlitzes that were not directly linked to the contributory citizen science tasks at hand, but are often education goals of BioBlitz leaders.
#### 3.7 Identifying participation patterns
We found that most youth participated in multiple, but not all steps. Rather than examining every possible combination of the five steps, we clustered particular combinations of participation types. We separated Exploring, Observing and Identifying as activities that do not produce any kind of artifact, whereas Documenting and Recording do, and therefore investigated the following combinations (Table 4).
Table 4: Number of FY, total and by age group, observed participating in four clusters of participation.
The clusters of youth who participated in all five steps of the data collection process (3 FY), or participated in Recording plus any other combination of the other types (9 FY), we have labeled the “Citizen Science” profile. They all generated a biological record that can be used for monitoring or research purposes and contributed to science as intended in BioBlitzes as contributory CS programs [Shirk et al., 2012] by collecting information that is “scientifically valuable” [Hecker et al., 2018]. High school-aged youth more often fall into the Citizen Science profile.
We labeled the “Natural History” profile (19 FY) as participation that led to some kind of evidence for observations made, yet without the evidence being shared, meaning any combination of types of participations that included Documenting but not Recording (Table 4). The focus here is on the study of natural history: youth engaging in Exploring, Observing or Identifying, while going one step further by keeping track of their findings (Documenting) and producing evidence of their observation, without sharing it with the broader community. This focus on natural history can be distinguished from “naturalists”, who historically and currently record and submit their data to organized biological recording schemes [Miller-Rushing, Primack and Bonney, 2012; Tewksbury et al., 2014].
We labeled the “Environmental Education” profile (36 FY) to describe youth that engaged in Exploring, Observing and/or Identifying, or any combination of these types of participation, without Documenting or Recording (Table 4). Participation in this category can be found in a wide variety of environmental education and public engagement events such as nature walks, pond dipping or tidepooling activities that are not citizen science as data are not collected for monitoring or research purposes.
### 4 Discussion
Our findings indicate that most BioBlitzes successfully engaged youth in at least some steps necessary to generate biological records. Of the 81 observed youth, 67 participated in one or more steps towards generating a biological record. However, youth participation in Exploring (48 FY), Observing (57) and Identifying organisms (45) was much more common than participation in Documenting (28) and Recording (12).
Exploring was the most common way younger children (ages 5–15) participated, and the least common for older youth (ages 16–19). This reflects Sobel’s [1995] Developmental Stages of Place-Based Education, positing that children aged 8–11 are in the stage of needing to explore their place to get to know it well. Observing is the most common type of participation across all age groups, likely because observing an organism is the foundation for being able to Identify, Document and Record; close observations of an organism provide the necessary information for the Who, When, What and Where of a biological record [Isaac and Pocock, 2015].
Our findings regarding youth participation in Identifying and Documenting revealed important lessons about the design of BioBlitzes. Interestingly, we found some nuance in the engagement of youth, and the tools and resources youth used for this task. Our observational data reflects the presence of both traditional teaching approaches in which expert knowledge is communicated as facts (e.g. facilitator telling youth the name of an organism) and more inquiry-based, active-learning approaches in which youth are positioned to use tools to find out for themselves [Gormally et al., 2009]. Youth participation in Documenting varied based on the structure of different BioBlitzes regarding tools available and the support for their use, e.g. camera phones or digital cameras as compared to paper datasheets. Participation in Documenting was observed less frequently than the previous three steps. Since the need to Document the organism precedes Recording, this may help to clarify why few youth participated in Recording, suggesting that BioBlitz organizers should provide multiple ways to document organisms and provide an abundance of access to tools and training to increase participation in this step, and therefore the subsequent step of Recording.
While our study revealed the many ways that youth participate in the steps towards creating biological records at BioBlitzes, we found they rarely participated in all steps, and Recording was particularly rare (12), meaning very few youth actually submitted data to the CS project. This is in contrast to the assumption that most participants at CS events contribute data to the scientific goal of BioBlitzes. But this act of data collection and sharing distinguishes BioBlitzes as citizen science programs [Robinson et al., 2013; Ballard et al., 2017; Shirk et al., 2012] from other public engagement or educational programs [Hecker et al., 2018]. Therefore, missing this step might mean participants are not as aware of the scientific purpose of the event or their role in contributing to it. The low level of youth participation in Recording poses a challenge for BioBlitz designers to better support youth participation in citizen science.
We acknowledge that whilst our focal youth may not have recorded data themselves, the BioBlitz event as a whole did contribute data that could be used for scientific research; we also acknowledge our focal youth might have handed in data sheets outside of our observation interval or later uploaded their photos to iNaturalist. This may have occurred during the “wrap-up” session that some BioBlitzes include, where participants are encouraged to upload any remaining observations. We consider it unlikely to have happened after the event, however, as a previous study shows that most young iNaturalist users submit to iNaturalist only for the day of the BioBlitz event, and further engagement with iNaturalist is rare [Aristeidou et al., 2021]. Out of the 12 focal youth that recorded, 10 used iNaturalist. Despite the very small numbers and skewed proportion of BioBlitzes in the study that exclusively used iNaturalist, this finding might indicate that recording via iNaturalist enhances the chance of youth participating in Recording, as compared to using written data sheets. However, iNaturalist is the only recording method for most of the observed BioBlitzes (12 out of 15) and for more than half of the observed youth (50 out of 81 FY). Also, we observed more older youth during BioBlitzes that used iNaturalist; further research is needed here.
Fourteen focal youth only engaged in non-CS-related activities, reflecting the multivariate character of BioBlitzes as an event for public engagement, learning and entertainment in addition to citizen science [Baker et al., 2014; da Silva, 2018; Roger and Klistorner, 2016]. Even if these types of participation were not related to the creation of biological records, they may be important scaffolding activities that merit further research, aiming to develop a more holistic picture of the authentic learning opportunities supplied and used [Bruckermann et al., 2020] in this case, BioBlitzes.
#### 4.1 Patterns of participation
Our findings regarding the clusters of youth participation revealed important lessons about science and environmental learning opportunities at BioBlitzes. We identified the clusters as three distinct profiles to describe youth’s participation experience: 1) “Citizen Science” profile, 2) “Natural History” profile and 3) “Environmental Education” profile (Figure 2).
The Citizen Science profile where youth participated in Recording alone or with any or all other types was the rarest (12 youth). Older youth (ages 16–19) more often fit this participation profile than younger youth (Table 4); this may be due to better access to recording tools (e.g. smartphone with iNaturalist) and greater awareness of the scientific goals of the BioBlitz, but more research is needed to examine these age-related differences.
The high proportion of youth in the Environmental Education and Natural History profiles bears highlighting and deserves further study. It might reflect the division of labor common in ecological fieldwork, where the person collecting samples or observations may not be the one to record them, or recording equipment must be shared. This may be especially true in family groups where adults do some activities on behalf of young children. However, this division of labor and/or lack of access to tools could indicate equity challenges, and may inadvertently present barriers to participation in the entire scientific process for youth, potentially removing valuable learning opportunities.
By examining youth participation in BioBlitzes using these profiles, we see that youth experiencing the Environmental Education or the Natural History profiles can still be seen as engaging in valuable environmental education activities, in the sense of authentic learning [Braund and Reiss, 2006], participation as learning [Lave and Wenger, 1991], and a successful public engagement experience [Roger and Klistorner, 2016]. However, these differences in participation should be taken into account when evaluating the scientific, engagement or learning outcomes of BioBlitzes and field-based CS programs in general, depending on the goals that the program organizers have for the events. If the primary goal is for youth to engage with nature, science practices and learning activities such as Exploring, Observing and Identifying wildlife, then whether or not youth engage in the CS process by Recording does not matter as much. When aiming for participants to gain awareness and understanding of the scientific process [Robinson et al., 2013], participation in the whole process of data collection should be desirable to enable youth to experience the full range of the science practices and methods within the authentic context [Braund and Reiss, 2006]. This would provide the opportunity for youth to take ownership of CS data, an important way for youth to develop data literacy [Harris et al., 2020]. BioBlitzes as CS activities offer a range of opportunities for learning through participation in an authentic context [Lave and Wenger, 1991], so even unintentional restrictions on participation can be seen as restrictions on learning opportunities and identity development.
Our study is based on observational data only. We suggest further studies using additional instruments such as surveys or interviews, to investigate the youth perspective on their own participation, their awareness of potential additional activities within a BioBlitz context and their reflection on their contribution to scientific research. In addition, for further observational studies, we would suggest tracking whether young people engage in data submission after the observation interval or whether someone else records the youth biodiversity observations.
#### 4.2 Understanding participation profiles
Our results add to the understanding of the experience element (output) of the logic model [Shirk et al., 2012] or respectively the use/participation element (activity) of MODEL-CS [Bruckermann et al., 2020]. We propose the three participation profiles as categories to systematically describe and compare BioBlitz participants’ experience (Figure 3).
Our results clearly show that not all youth undergo the same BioBlitz experience, and while most youth experience several parts of the scientific process, only a few actually record data and experience the type of participation that distinguishes CS from education or engagement activities [Hecker et al., 2018]. We suggest the profiles could be easily applied to examine adult participants and other CS programs that focus on biodiversity data.
The participation profiles may enable researchers and practitioners to better understand the participant experience during CS programs, and reflect on the extent to which actual participation patterns match the goals of the program. Further, they might be useful to examine participation across different settings and between different CS programs. Such analysis can inform the design of CS activities, to achieve the desired participation patterns and enhance outcomes both for science (by supporting more participants to submit data) and for participants. We suggest further research could investigate how the participation profiles relate to individual outcomes, leveraging our derived categories of participation and profiles. The developed participation profiles can act as a framework for a systematic analysis of factors that hinder or support participation and investigate the extent to which participation affects learning outcomes.
### 5 Conclusions
These findings help us better understand the nuances of how youth play a role in the collective effort to record and monitor biodiversity at local, national and global scales. Our results show that youth can and do participate in each of the five steps that could potentially contribute to the data collection of BioBlitzes as contributory CS projects, and that BioBlitzes provide valuable environmental and science engagement experiences for youth.
We found evidence that several youth, and even youth of elementary school-age, took part in the Recording step itself, which is the crucial step that actually provides data for research and land management. However, since the scientific goal of BioBlitzes is successfully recording biodiversity data points, we see this only rarely happens for youth. This highlights an opportunity for improved program design to address this shortcoming. Our results can be seen as an invitation for program organizers to reflect on their goals for youth participation in CS, and consider that there are many ways youth can participate in the authentic scientific process, but that by not Recording, many youth miss out on the crucial step in that process. We suggest that to engage more youth in the whole CS process at a BioBlitz, program designers need to better support youth to Record their observations, enabling them to contribute scientific data to the CS project.
### Acknowledgments
This material is based upon work supported under a collaboration between the National Science Foundation (NSF), Wellcome, and the Economic and Social Research Council (ESRC) via a grant from the NSF (NSF grant no. 1647276) and a grant from Wellcome with ESRC (Wellcome grant no. 206202/Z/17/Z). Disclaimer: any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the view of NSF, Wellcome, or ESRC.
We would like to thank all the participating youth and their families, and the NHM staff and partners who helped with this study, especially Stephanie Holt. We thank Dr. Déana Scipio and Dr. Angela Calabrese Barton for their contributions to this research.
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### Authors
Julia Lorke is a Fellow at IPN — Leibniz Institute for Science and Mathematics Education and was a postdoctoral researcher at the Natural History Museum London. Julia is a qualified science teacher, worked as a science communication lecturer, in outreach and radio journalism. Her research focuses on informal learning, audience engagement and participation in science. She earned an MEd in Chemistry and Biology and a Ph.D. in Chemistry from Ruhr-University Bochum (Germany) as well as an MSc in Science Communication from Imperial College London. E-mail: lorke@leibniz-ipn.de.
Heidi Ballard is Professor of Environmental Science Education, and the Founder and Faculty Director of the Center for Community and Citizen Science at University of California, Davis. She conducts research focused on science and environmental learning that link communities, scientists, and environmental action. She was a high school biology teacher, and earned her MA in Science Education from Stanford University, before earning her Ph.D. in Environmental Science, Policy and Management from University of California-Berkeley. E-mail: hballard@ucdavis.edu.
Annie Miller is the LEARN CitSci Project Coordinator at the California Academy of Sciences. During her undergraduate studies at Tufts University, she received a dual degree in Biology and Environmental Science. Her research interests include effects of human development on biodiversity and habitat degradation, but her passion is in science communication and outreach. Her previous work includes studying the genetic movement of an endangered Hawaiian waterbird and working with the San Francisco Recreation and Parks Department as an Environmental Educator. E-mail: aemiller235@gmail.com.
Rebecca Swanson is a post-doctoral scholar at Tufts University with the Center for Engineering Education and Outreach. Her research focuses on professional development of K-12 and informal STEM educators, including the design and implementation of interest-driven learning experiences. Rebecca is a credentialed K-12 science teacher and former informal science educator, with a B.A. in Molecular, Cellular, and Developmental Biology from University of California Santa Cruz, and a Ph.D. in Curriculum and Instruction, Science Education from University of Colorado Boulder. E-mail: rebecca.swanson@tufts.edu.
Sasha Pratt-Taweh is the LEARN CitSci Project Coordination Officer at the Natural History Museum in London. She has worked in the museum learning sector for 9 years, as an educator and presenter at NHM and The Science Museum. Sasha’s main professional interests are in biodiversity conservation and equal access to STEM education for underrepresented and ethnic minority groups. Sasha earned an MSc in Ecology, Evolution & Conservation from Imperial College London and a BSc in Zoology from University College London. E-mail: sashalvp@gmail.com.
Jessie Jennewein is the LEARN CitSci Project Coordinator at the Natural History Museum of Los Angeles County. Since 2009, she has been working within the museum, from Education outreach to her current position with Community Science. Jessie received her undergraduate degree in Anthropology, focusing on visual ethnographic work. Currently, she’s working on a Masters in Conservation Biology. Her graduate research looks at social media use in conservation and environmental justice, aligning with her passion of science advocacy and environmental activism. E-mail: jjennewe@nhm.org.
Lila Higgins is the Senior Manager of Community Science at the Natural History Museum of Los Angeles County (NHMLA) and a Co-PI for the LEARN CitSci project. Her work focuses on connecting people to nature, particularly in cities. She does this through many modes including community science, and is the co-founder of the City Nature Challenge. Lila holds a BS in Entomology from University of California, Riverside and an MA in Environmental Education from California State University, San Bernardino. E-mail: lhiggins@nhm.org.
Rebecca Johnson co-directs Citizen Science at the California Academy of Sciences, where she is also a Research Associate in the Department of Invertebrate Zoology. She develops programs and builds coalitions focused on people exploring their local nature and gathering biodiversity data for conservation. Rebecca earned a Ph.D. from the University of California, Santa Cruz in Ecology and Evolutionary Biology for her work using natural history museum collections and molecular phylogenetics to explore biogeography and color pattern evolution in nudibranchs. E-mail: rjohnson@calacademy.org.
Alison Young is the Co-Director of Citizen Science at the California Academy of Sciences, where she works to build community around nature connection and biodiversity documentation. Alison is co-lead of the annual City Nature Challenge, and she sits on the Board of Directors for the Citizen Science Association. Alison’s background is in marine biology, she earned an M.A. in Biology from Humboldt State University for research focused on the potential effects of climate change on California’s rocky intertidal communities. E-mail: ayoung@calacademy.org.
Maryam Ghadiri Khanaposhtani is a post-doctoral researcher at the Center for Community and Citizen Science at University of California, Davis. Her research focus is on investigating youth learning in natural history museum-led citizen science programs. Maryam’s B.A. is in environmental science, her M.A. is in conservation biology, both from Tehran University, Iran and a Ph.D. in on soundscape ecology and free-choice STEM learning from Purdue University, U.S.A. E-mail: mghadiri@ucdavis.edu.
Lucy Robinson is Citizen Science Manager at the Natural History Museum London, and Principal Investigator for the LEARN CitSci partnership. She has been a practitioner in citizen science for over ten years, and has co-authored the Guide to Citizen Science (2012), Guide to Running a BioBlitz (2013) and Ten Principles of Citizen Science (2015). She recently served as Vice Chair of the European Citizen Science Association (ECSA). Lucy holds a BSc Zoology and an MSc Biodiversity and Conservation. E-mail: l.robinson@nhm.ac.uk.
### How to cite
Lorke, J., Ballard, H. L., Miller, A. E., Swanson, R. D., Pratt-Taweh, S., Jennewein, J. N., Higgins, L., Johnson, R. F., Young, A. N., Ghadiri Khanaposhtani, M. and Robinson, L. D. (2021). ‘Step by step towards citizen science — deconstructing youth participation in BioBlitzes’. JCOM 20 (04), A03. https://doi.org/10.22323/2.20040203.
### Supplementary material
Available at https://doi.org/10.22323/2.20040203
Supplementary material A: Additional Information on BioBlitzes
Supplementary material B: Research Methods Details
### Endnotes
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I have seen How to allow labels' anchors in TikZ to be affected by rotations without rotating the text itself?; but that question doesn't seem to answer my problem, so here it goes. With the MWE ...
487 views
### Connecting line calculations with fitting node in 3D tikz?
Consider the following MWE: \documentclass{standalone} \usepackage{tikz} \usetikzlibrary{calc} \usetikzlibrary{positioning} \usetikzlibrary{fit} \usetikzlibrary{3d} \makeatletter \tikzset{ ...
274 views
### Drawing local neuro-fuzzy architecture
I am trying to draw some sort of neural network with additional nodes and connections. I have the following code so far, which I mostly copied from around here. \documentclass[border=0.125cm]{...
427 views
### Node anchor centre of line
If a node is defined as a circle and you want to use anchors (west and east) from the node to draw an arc around the node, how do you ensure that the arc is anchored about the centre (red line in ... | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9283276796340942, "perplexity": 2095.8251719290233}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526536.46/warc/CC-MAIN-20190720153215-20190720175215-00243.warc.gz"} |
https://www.transtutors.com/questions/which-divisions-will-accept-or-reject-it--336998.htm | # Which divisions will accept or reject it?
Using the data from Problem 8.7, (a)compute the residual income (RI) for each division, and (b)assume that each division is provided with an investment opportunity that would produce an 18 percent return on investment. Which divisions will accept or reject it?
(a) Division A Division B Division C Operating income $5,000$6,300 $14,400 Minimum required income 10% X 20,000 =$2,000 19% >: 35,000 = $6,650 20% X 90,000 =$18,000 RI $3,000$ (350) \$ (3,600) (b) Division A would accept this investment project, since an 18 percent ROI is greater than 10 percent.... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.15810948610305786, "perplexity": 5724.079916004816}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247491141.23/warc/CC-MAIN-20190219183054-20190219205054-00485.warc.gz"} |
https://ajayshahblog.blogspot.com/2006/10/class-of-sebi-actions-which-can-be_10.html | ## Tuesday, October 10, 2006
### The class of SEBI actions which can be appealed at the Securities Appellate Tribunal
Somasekhar Sundaresan has an article in Business Standard on an important development on the class of SEBI actions which can be appealed at SAT:
The Securities Appellate Tribunal (SAT) has recently passed a landmark order having far-reaching consequences for appellate oversight in the capital markets. The order is about the sweep of appellate scrutiny over decisions and actions of the Securities and Exchange Board of India (Sebi). Disposing of an appeal by the National Securities Depository Ltd challenging a Sebi circular, SAT has ruled that its appellate jurisdiction covers all Sebi decisions. The term “order” has finally been dealt with exhaustively. Section 15T of the Act enables any person aggrieved by an “order” passed by the Sebi to appeal. Sebi strenuously argued that SAT could sit in judgment only over its quasi-judicial orders. Since the challenge before SAT related to a circular directing depositories not to charge demat account holders in a specific situation, Sebi argued that the circular was a policy decision, and at best a legislative action. It did not partake the characteristics of an appealable “order.” While the appeal itself was not upheld on merits, SAT has given an unexceptionable and well-reasoned judgment on what constitutes a Sebi “order.” SAT noted that the term “order” had been defined by law dictionaries to include “rules” and “regulations.” “The right of appeal is a statutory right and it has necessarily to be governed by the provisions of the statute which creates it,” SAT said, adding that it was “open to the legislature to restrict that right.” It noted that the Act did not entail any such restriction. Noting that Parliament had consciously conferred on Sebi executive, legislative and judicial/quasi-judicial powers, SAT said the provision for appeal under Section 15T of the Act did not limit that right only to orders passed by the board or its officers in exercise of judicial/quasi-judicial powers. “The language used in Section 15T is of widest amplitude and makes every order passed by the board appealable, whether it be in exercise of its administrative, legislative or judicial/quasi judicial powers,” SAT noted. It also pointed out where Parliament desired to limit the right of appeal under the Act, it had done so. For example, Section 15Z of the Act, which provides for an appeal from SAT to the Supreme Court, clearly restricts such appeals to only questions of law, and excludes questions of fact. Sebi circulars are but general orders that are passed in lieu of multiple specific orders. Merely because the order is in the form of a circular, thereby becoming a policy decision or legislation, the right of persons by such decisions or legislation to pursue a challenge under Section 15T of the Act would not get frustrated. SAT has reiterated the import of a constitutional Bench order of the Supreme Court to emphasise that even subordinate legislation in the form of regulations made under an Act of Parliament can be challenged before a tribunal if they are in conflict with the Act. The only restriction imposed by Parliament on such oversight by tribunals was on constitutional challenge to the very Act of Parliament that created the tribunal. This decision finally puts to rest, at least at the SAT level, one of the most common objections to appeals under the Act. Often “acknowledgement cards” given to enable initial public offerings to go ahead under the Sebi (Disclosure and Investor Protection) Guidelines and “letters of observations” given to acquirers making open offers under the Sebi (Substantial Acquisition of Shares and Takeovers) Regulations are challenged since they partake the character of an order. Such appeals are strenuously objected to on the ground that these documents can never constitute an appealable “order.” The true test would be to check whether the contents and import of a document create any binding obligation on any person. If such obligations cannot be ignored without incurring adverse consequences under the Act, regardless of purported disclaimers or the nomenclature of the document prescribing the obligations, an appealable order would come into being. The charm here is not in having a forum in SAT to challenge every decision of Sebi, but in the consciousness that the SAT’s decision would drill into the author of every such circular, policy decision or regulation, to ensure that the decision in question has to be reasonable, fair, non-arbitrary, and most importantly, in consonance with law.
Here is the full text of Section 15T of the SEBI Act:
15T. APPEAL TO THE SECURITIES APPELLATE TRIBUNAL.
(1) Save as provided in subsection (2), any person aggrieved, (a) by an order of the Board made, on and after the commencement of the Securities Laws (Second Amendment) Act, 1999, under this Act, or the rules or regulations made thereunder; or (b) by an order made by an adjudicating officer under this Act, may prefer an appeal to a Securities Appellate Tribunal having jurisdiction in the matter.
(2) No appeal shall lie to the Securities Appellate Tribunal from an order made (a) by the Board on and after the commencement of the Securities Laws (Second Amendment) Act, 1999; (b) by an adjudicating officer, with the consent of the parties.
(3) Every appeal under sub-section (1) shall be filed within a period of forty-five days from the date on which a copy of the order made by the Board or the adjudicating officer, as the case may be, is received by him and it shall be in such form and be accompanied by such fee as may be prescribed:
Provided that the Securities Appellate Tribunal may entertain an appeal after the expiry of the said period of forty-five days if it is satisfied that there was sufficient cause for not filing it within that period.
(4) On receipt of an appeal under sub-section (1), the Securities Appellate Tribunal may, after giving the parties to the appeal, an opportunity of being heard, pass such orders thereon as it thinks fit, confirming, modifying or setting aside the order appealed against.
(5) The Securities Appellate Tribunal shall send a copy of every order made by it to the Board, the parties to the appeal and to the concerned Adjudicating Officer.
(6) The appeal filed before the Securities Appellate Tribunal under sub-section (1) shall be dealt with by it as expeditiously as possible and endeavour shall be made by it to dispose of the appeal finally within six months from the date of receipt of the appeal.
Please note: LaTeX mathematics works. This means that if you want to say $10 you have to say \$10. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38087666034698486, "perplexity": 4700.6534001783875}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824894.98/warc/CC-MAIN-20171021190701-20171021210701-00172.warc.gz"} |
https://physics.stackexchange.com/questions/235695/simulation-probabilistic-classical-computation-on-quantum-computers | # Simulation probabilistic classical computation on quantum computers
Given an $N$-level quantum system with computational basis $\{|1> ,|2> , \cdots, |N> \}$, if we perform an unitary operation $U$ on a computational basis state $\{|j> \}$ and then measure the resulting system in computation basis, the probability to get a result $i$ is given by $$\text{Tr} ( |i><i| U |j><j| U^{\dagger} ) = |U_{ij}|^2$$ Therefore, if a computational step of a probabilistic classical algorithm has a transition matrix $(p_{ij})$ where $p_{ij}$ is the probability for the $j^{th}$ state evolves into the $i^{th}$ state and there exists an unitary matrix $U$ such that
$$p_{ij} = |U_{ij} |^2 ,$$ for all $i,j \in \{1,2,\cdots,N\}$, this computational step can be easily simulated in quantum computers by unitary operation $U$ and measurement in computational basis.
However, not every transition matrix, i.e, column stochastic matrix, admits an unitary matrix of above property, as the counterexample $$\begin{pmatrix} 0 & 1/2 & 1/2 \\ 1/2 & 0 & 1/2 \\ 1/2 & 1/2 & 0 \end{pmatrix}.$$ suggested in https://mathoverflow.net/q/80259/ shows
It is claimed in my textbook that if we exploit an N level ancila system with initialized state, say, $|1>$, conduct an unitary operation, perform a measurement and discard the ancilla system, we can simulate any computational step in probabilistic classical algorithm. That is, for any column stochastic matrix $(p_{ij})$, we can find an unitary operator $U$ on $\mathbb{C}^n \otimes \mathbb{C}^n$ such that $$p_{ij} = \text{Tr} ( ( |j1><j1| +|j2><j2| + \cdots + |jN ><jN| ) U |i 1><i1 | U^{\dagger} )$$ $$= |< j1 | U | i1 > |^2 + | < j2 | U | i1 > |^2 + \cdots + |< jN | U | i1 >|^2$$
This seems a tricky, fairly nontrivial result. How can we construct such unitary $U$ from a transition matrix of above property?
• Does your textbook claim that formula, or just that you can use a q.c. to simulate probabilistic computation? I would just use an ancilla to simulate a random coin toss (by measuring a superposition) and otherwise just use classical gates. – Norbert Schuch Feb 13 '16 at 11:34
• Also, which textbook is this? – biryani Feb 14 '16 at 9:17
• It's exercise 6.1.1 (c) in <An Introduction to Quantum Computing> by Kaye, et al. – Guldam Feb 15 '16 at 4:31
{Edit: I found a much easier way to do this without resorting to linear system solving. I have included both methods in the answer}
Finding such a $U$ certainly seems possible as with the enlarged Hilbert space there is much more freedom to choose your parameters. I will outline how to do this. First a bit of notation. Let $$\langle j,b |U|i,a \rangle = U_{N(i-1) + a ,~ N(j-1) + b}.$$
$U$ is an $N^2 \times N^2$ unitary matrix.
Apart form the usual conditions for unitarity, the rows $1, ~N+1, ~2N+1 \ldots$ will be affected by the constraint given in your question.
Now lets construct the first row corresponding to $i=1$ and $a = 1$. We know that,
$$p_{1,j} = \sum_{b=1} ^ N |U_{1,N(j-1)+b}|^2.$$
$\large{\textbf{Method 1}}$
Choose $U_{1,1} = \sqrt{p_{1,1}}$, $U_{1,N+1}= \sqrt{p_{1,2}}$,... ,$U_{1,N(N-1)+1}= \sqrt{p_{1,N}}$ to satisfy this condition. The condition $\sum_j p_{1,j} = 1$ ensures that the norm of the first row is unity.
Next let us construct the row $N+1$. This row vector has to be orthogonal to the first row and should satisfy the condition, $$p_{2,j} = \sum_{b=1} ^ N |U_{N+1,N(j-1)+b}|^2.$$.
So choose $U_{N+1,2} = \sqrt{p_{2,1}}$, $U_{N+1,N+2}= \sqrt{p_{2,2}}$... $U_{N+1,N(N-1)+2}= \sqrt{p_{2,N}}$. You can easily verify that the inner product condition is satisfied. Next you can select the row $2N +1$. Here again you need to set the values as above but shifted by one element in the horizontal direction so that the orthogonality conditions are satisfied. Do this till you reach row $N(N-1) +1$. Now your matrix has $N$ rows filled according to the constraint in the question. The rest of the rows can be filled by vectors orthonormal to the ones you already constructed using the Gram-Schmidt procedure.
This is much easier than the next method, which involves linear system solving.
$\large{\textbf{Method 2}}$
Select the first $N$ elements in the first row so that the sum of squares their absolute values is equal to $p_{11}$, the second $N$ such that the sum of their absolute values is equal to $p_{12}$ and so on till you complete the first row. The condition $\sum_j p_{1,j} = 1$ ensures that the norm of the first row is unity.
Next we will fill row $N+1$ corresponding to $i=2$ and $~a = 1$. The constraint here is, $$p_{2,j} = \sum_{b=1} ^ N |U_{N+1,N(j-1)+b}|^2.$$
Choose the first $N$ elements such that their inner product with the first $N$ elements of the first row is zero,$$\sum_{b=1} ^ N U_{1,b}U_{N+1,b }^* = 0.$$ You can see this as an under constrained system of linear equations. Choose a solution from the family of solutions you get and then scale it appropriately so that sum of square of their absolute values add up to $p_{2,1}$. Do this for the next $N$ elements in the row and so on till you fill that row. Again the condition $\sum_j p_{2,j} = 1$ ensures that the norm of the row is unity.
Now go to the row $2N+1$. This time you will have to solve a $N \times 2$ system of linear equations. As you keep going down the size of the system you need to solve will go up. I believe solutions will always exist as the previous rows are always orthogonal to each other and your system will always have maximum rank .You will solve $N \times N$ system at the row $N(N-1)+1$. Now your matrix has $N$ rows filled according to the constraint in the question. The rest of the rows can be filled by vectors orthonormal to the ones you already constructed using the Gram-Schmidt procedure. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9512249827384949, "perplexity": 196.62294680849521}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370500331.13/warc/CC-MAIN-20200331053639-20200331083639-00495.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/ipi.2019058 | # American Institute of Mathematical Sciences
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December 2019, 13(6): 1327-1348. doi: 10.3934/ipi.2019058
## A reproducing kernel Hilbert space framework for inverse scattering problems within the Born approximation
Department of Mathematics and Statistics, Villanova University, Villanova, PA 19085, USA
Corresponding author: k.muller@villanova.edu
Received January 2019 Revised June 2019 Published October 2019
In this work we develop a new reproducing kernel Hilbert space (RKHS) framework for inverse scattering problems using the Born approximation. We assume we have backscattered data of a field that is dependent on an unknown scattering potential. Our goal is to reconstruct or image this scattering potential. Assuming the scattering potential lies in a RKHS, we find that the imaging equation can be rewritten as the inner product of the desired unknown function with the adjoint of the forward operator applied to the kernel of the imaging operator. We therefore may choose the kernel of the imaging operator such that the adjoint applied to this kernel is precisely the reproducing kernel of the Hilbert space the reflectivity function lies in. In this way we are able to obtain an alternative definition of an ideal image. We will demonstrate this theory using synthetic aperture radar imaging as an example, though there are other applicable imaging modalities i.e. inverse diffraction and diffraction tomography [1,6]. We choose SAR as it was the motivating application for this work. We will compare the RKHS ideal imaging technique to the standard microlocal analytic ideal image from backprojection theory. Note this method requires a variation of the standard SAR data model with the assumption of a full two dimensional data collection surface as opposed to a one dimensional flight path, however we are able to perform imaging with a single frequency and avoid the approximations made in the backprojection imaging operator derivation.
Citation: Kaitlyn (Voccola) Muller. A reproducing kernel Hilbert space framework for inverse scattering problems within the Born approximation. Inverse Problems & Imaging, 2019, 13 (6) : 1327-1348. doi: 10.3934/ipi.2019058
##### References:
show all references
##### References:
[1] Kaitlyn Muller. The relationship between backprojection and best linear unbiased estimation in synthetic-aperture radar imaging. Inverse Problems & Imaging, 2016, 10 (2) : 549-561. doi: 10.3934/ipi.2016011 [2] Raluca Felea, Romina Gaburro, Allan Greenleaf, Clifford Nolan. Microlocal analysis of Doppler synthetic aperture radar. Inverse Problems & Imaging, 2019, 13 (6) : 1283-1307. doi: 10.3934/ipi.2019056 [3] Venkateswaran P. Krishnan, Eric Todd Quinto. Microlocal aspects of common offset synthetic aperture radar imaging. Inverse Problems & Imaging, 2011, 5 (3) : 659-674. doi: 10.3934/ipi.2011.5.659 [4] Mikhail Gilman, Semyon Tsynkov. Statistical characterization of scattering delay in synthetic aperture radar imaging. Inverse Problems & Imaging, 2020, 14 (3) : 511-533. doi: 10.3934/ipi.2020024 [5] T. Varslo, C E Yarman, M. Cheney, B Yazıcı. A variational approach to waveform design for synthetic-aperture imaging. Inverse Problems & Imaging, 2007, 1 (3) : 577-592. doi: 10.3934/ipi.2007.1.577 [6] Daniela Calvetti, Erkki Somersalo. Microlocal sequential regularization in imaging. Inverse Problems & Imaging, 2007, 1 (1) : 1-11. doi: 10.3934/ipi.2007.1.1 [7] Ying Lin, Rongrong Lin, Qi Ye. Sparse regularized learning in the reproducing kernel banach spaces with the $\ell^1$ norm. Mathematical Foundations of Computing, 2020, 3 (3) : 205-218. doi: 10.3934/mfc.2020020 [8] Ali Akgül, Mustafa Inc, Esra Karatas. Reproducing kernel functions for difference equations. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1055-1064. doi: 10.3934/dcdss.2015.8.1055 [9] James W. Webber, Sean Holman. Microlocal analysis of a spindle transform. Inverse Problems & Imaging, 2019, 13 (2) : 231-261. doi: 10.3934/ipi.2019013 [10] Lassi Roininen, Markku S. Lehtinen, Petteri Piiroinen, Ilkka I. Virtanen. Perfect radar pulse compression via unimodular fourier multipliers. Inverse Problems & Imaging, 2014, 8 (3) : 831-844. doi: 10.3934/ipi.2014.8.831 [11] Markku Lehtinen, Baylie Damtie, Petteri Piiroinen, Mikko Orispää. Perfect and almost perfect pulse compression codes for range spread radar targets. Inverse Problems & Imaging, 2009, 3 (3) : 465-486. doi: 10.3934/ipi.2009.3.465 [12] Gang Bao, Jun Lai. Radar cross section reduction of a cavity in the ground plane: TE polarization. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 419-434. doi: 10.3934/dcdss.2015.8.419 [13] Qiang Yin, Gongfa Li, Jianguo Zhu. Research on the method of step feature extraction for EOD robot based on 2D laser radar. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1415-1421. doi: 10.3934/dcdss.2015.8.1415 [14] Irene Benedetti, Luisa Malaguti, Valentina Taddei. Nonlocal problems in Hilbert spaces. Conference Publications, 2015, 2015 (special) : 103-111. doi: 10.3934/proc.2015.0103 [15] Fritz Gesztesy, Rudi Weikard, Maxim Zinchenko. On a class of model Hilbert spaces. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5067-5088. doi: 10.3934/dcds.2013.33.5067 [16] Zhiming Li, Yujun Zhu. Entropies of commuting transformations on Hilbert spaces. Discrete & Continuous Dynamical Systems - A, 2020, 40 (10) : 5795-5814. doi: 10.3934/dcds.2020246 [17] Jean-François Crouzet. 3D coded aperture imaging, ill-posedness and link with incomplete data radon transform. Inverse Problems & Imaging, 2011, 5 (2) : 341-353. doi: 10.3934/ipi.2011.5.341 [18] Liam Burrows, Weihong Guo, Ke Chen, Francesco Torella. Reproducible kernel Hilbert space based global and local image segmentation. Inverse Problems & Imaging, 2020, 0 (0) : 1-25. doi: 10.3934/ipi.2020048 [19] Hanbing Liu, Yongdong Huang, Chongjun Li. Weaving K-fusion frames in hilbert spaces. Mathematical Foundations of Computing, 2020, 3 (2) : 101-116. doi: 10.3934/mfc.2020008 [20] Jin-Mun Jeong, Seong-Ho Cho. Identification problems of retarded differential systems in Hilbert spaces. Evolution Equations & Control Theory, 2017, 6 (1) : 77-91. doi: 10.3934/eect.2017005
2019 Impact Factor: 1.373 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4851812720298767, "perplexity": 4856.027964076676}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737225.57/warc/CC-MAIN-20200807202502-20200807232502-00418.warc.gz"} |
https://www.physicsforums.com/threads/work-done-by-a-variable-force-question.551815/ | # Work done by a variable force question
1. Nov 18, 2011
### Catalytical
1. The problem statement, all variables and given/known data
That's a graph of Force in newtons (y axis) vs displacement in meters (x axis) for an object of mass 3.0kg that is moving along the x-axis and initially starts at rest. I am being asked to find the total work done on the object as it moves from x = 0 to x = 7.
2. Relevant equations
Net Work = ∫F dx = ΔK
K = 1/2mv^2
3. The attempt at a solution
So, I integrated the function and ended up with a total work of -.5J. What I want to know is if this violates the work-energy theorem or not. If the net work is equal to change in kinetic energy, and the object starts at rest, this would mean that -.5 = 1/2mv^2. Is there something really obvious that I'm missing here?
2. Nov 18, 2011
### technician
work done (energy) = area under F against x graph (this is another way of seeing ΔK = ∫F.dx
There are 2 clear areas to calculate..... when F is +ve and when F is -ve
3. Nov 18, 2011
### technician
By calculating the areas I got total work = -0.5J
4. Nov 18, 2011
### CanIExplore
Can you explain why you think the work-energy theorem is violated?
$0.5=\frac{1}{2}mv^{2}_{f}-\frac{1}{2}mv^{2}_{i}$
If the object started at rest, the last term is 0 and you get
$0.5=\frac{1}{2}mv^{2}_{f}$
which just says that the object has some final velocity.
5. Nov 19, 2011
### Catalytical
Right, but if the total work done is -.5, wouldn't that mean that
$-0.5=\frac{1}{2}mv^{2}_{f}$
I'm not sure why you ignored the sign on the work done.
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http://mathhelpforum.com/calculus/209018-evaluate-integral-computing-limit-riemann-sums.html | # Math Help - Evaluate the integral by computing the limit of Riemann sums.
1. ## Evaluate the integral by computing the limit of Riemann sums.
I am hoping someone can critique my work and see if I did this problem correctly. Thanks in advance!
NOTE: I have attached a picture file that shows my work, I hope that's okay)
Attached Thumbnails
2. ## Re: Evaluate the integral by computing the limit of Riemann sums.
Now, you didn't do it correctly...you need to subtract the areas of the rectangles that are below the x-axis.
I would suggest using the symmetry of the function (function is even) to simplify your computations, i.e.:
$\int_{-2}^2 x^2-1\,dx=2\int_0^2 x^2-1\,dx$ (the even-function rule).
Now you have the interval [0,1) where the function is negative and the interval (1,2] where the function is positive.
3. ## Re: Evaluate the integral by computing the limit of Riemann sums.
Okay thanks for pointing that out, I had forgot that I needed to do that. I reworked the problem and am attaching my work as a pic file. If you can, please let me know if Ive made any mistakes, Thanks!!
Attached Thumbnails
4. ## Re: Evaluate the integral by computing the limit of Riemann sums.
Anyone care to assist me by taking a look at my worked out problem above, ... Thanks in advance
5. ## Re: Evaluate the integral by computing the limit of Riemann sums.
Your result is 10 times what it should be.
I would set it up as follows:
$A_n=2\left(\frac{2}{n}\sum_{k=0}^{n-1}\left(\left( \frac{2k}{n} \right)^2-1 \right) \right)=$
$\frac{4}{n}\left(\frac{4}{n^2}\sum_{k=0}^{n-1}(k^2)-n \right)=$
$\frac{16}{n^3}\cdot\frac{(n-1)(n)(2n-1)}{6}-\frac{4n}{n}=$
$\frac{8(n-1)(2n-1)}{3n^2}-4=$
$\frac{8(n-1)(2n-1)-12n^2}{3n^2}=$
$\frac{4(n^2-6n+2)}{3n^2}$
Hence:
$\lim_{n\to\infty}A_n=\frac{4}{3}$
6. ## Re: Evaluate the integral by computing the limit of Riemann sums.
wow, not sure how i managed to do that, but thanks for the clarification.
7. ## Re: Evaluate the integral by computing the limit of Riemann sums.
My advice about needing to subtract was erroneous, the summation takes care of all that. Also, the even function rule for integration was unnecessary too, as you see, we wind up with the correct $\Delta x=\frac{4}{n}$ either way.
8. ## Re: Evaluate the integral by computing the limit of Riemann sums.
I wanted to point out that I have now changed the upper limit of summation above to n-1 from n. while this doesn't change the end result, it does now give the correct value for $A_n$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.997321605682373, "perplexity": 423.0956288033647}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257824201.56/warc/CC-MAIN-20160723071024-00325-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://patriciabarber.com/i-said-yto/4128a8-parallelogram-cure-with-diagonals-cr-and-ue | 3. 8. uex1234 ex u uex ex u uex Adjoining elevated formation icons hSTR2+3~GG: for hWYE23 hSTR1+4~FF: for hWYE+14 hSTR2+1~RR: hdSTR2+1~RR: for hWYEr+12 hSTR3+4~LL: hdSTR3+4~LL: for hWYEl+34 ex u uex ex u uex v; t; e; BSicons for route diagram templates. Ans. ∠CUE ≅ ∠REU; 4. A diagonal of a parallelogram forms two congruent triangles. 5. CH ≅ RH; EH ≅ UH 7. cr¡ñvers€ m \\Þc-.,-ll[lå\2j" a AÞ \ Dc at.â ß % \?r àr.f. ‘Complete the parallelogram CABD and draw in the diagonal AD which is then easily seen to bisect the angle CAB.’ ‘The five-pointed stars on many flags of the world (for example, the European flag) are made by cutting the diagonals of a pentagon according to the Golden Ratio.’ A diagonal of a rectangle is inclined to one side of the rectangle at 25°. 9. The diagonals of a rectangle bisect each other. Mathelounge ist die größte Webseite für Fragen und Antworten zur Mathematik. 5. The diagonals of a parallelogram are given by A = 3i -4j -k and B = 2i +3j - 6k. The acute angle between the diagonals is (a) 55° (b) 50° (c) 40° (d) 25° CR || UE 3. A rhombus has the following rules: (1) All the rules of a parallelogram. A parallelogram, P, is a special case of a midpoint diagonal quadrilateral since the diagonals of P bisect one another. 1:08 6.6k LIKES. 6. 62. Given: Parallelogram CURE with diagonals CR and UE Prove: CR and UE bisect each other. Illustrated definition of Diagonal: A line segment that goes from one corner to another, but is not an edge. Proof: Statements Reasons 1. The diagonals of the Varignon parallelogram are the bimedians of the original quadrilateral. Polygons a polygon is a closed curve (figure)formed by the line segments such that : (i)no two line segments intersect except at their end -points. 4. K/t-- k.I SI{VIt,}R August 1994 Pattern Recognition Letters 15 (1994) 803-805 Pattern Recognition Letters Triangle and parallelogram laws on fuzzy graphs P.S. 1. CR and UE bisect each other. CR ≅ UE 2. The diagonals have the following properties: The two diagonals are congruent (same length). Using the definition of a rectangle, prove that Quadrilateral is NOT a rectangle. The diagonals of a rectangle bisect the angles. a plane quadrangle with equal sides (Figure 1). Trapezoid definition is - a quadrilateral having only two sides parallel. K132 was asked to draw the diagonals of a given figure, and the student tried to cr eate a diagonal by evaluating the concept of edge differently. In mathematics and physics, many topics are named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. Step 5: Draw ∠OMZ = 58 ° such that ray MZ and ray RY intersect each other at E. Here, MORE is the required quadrilateral. b) If M R = 5.3 , find MP . The rectangle has the following properties: All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other). Diagonal definition is - joining two vertices of a rectilinear figure that are nonadjacent or two vertices of a polyhedral figure that are not in the same face. The line-segment joining the mid-points of any two sides of a triangle is parallel to the third side and is half of it. The student with code no. While it’s not a cure-all, wiping the wood with a solvent first goes a long way. Diagonals of a square bisect each other at right angles and are equal, and vice-versa. Check Your Guess 2 . A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel . Properties. How to use diagonal in a sentence. Diagonals e x ex u ue ux uex ABZ2+4gf ... ue12x34. (ii)no two line segments with a common end points are coincident. A parallelogram also has the following properties: Opposite angles are congruent; Opposite sides are congruent; Adjacent angles are supplementary; The diagonals bisect each other. Introduction: naming • colours: Straight tracks: plain • line end • … Given 2. Show that the parallelogram is a rhombus and determine the length of its sides and its angles. SAA Congruence Postulate 7. Step 2: Draw ∠MOX = 105 °. Area formula The area of a parallelogram is given by the formula where b is the length of any base a is the corresponding altitude . a) If Q N = 12.8 , find QR . 2. (2) Steps of Construction: Step 1: Draw DE = 4.5 cm. (3) Diagonals that intersect at right angles. CR. This is a list of two-dimensional geometric shapes in Euclidean and other geometries.For mathematical objects in more dimensions, see list of mathematical shapes.For a broader scope, see list of shapes The diagonals bisect the angles. 48.4k SHARES. Because of this symmetry, it has two pairs of equal angles as well as two pairs of equal sides. ∠CHU ≅ ∠RHE 5. The consecutive angles of a rectangle are congruent and supplementary. is consistent with what lattice studies find for QCD [4]. See Derivation of the formula.. Recall that any of the four sides can be chosen as the base. A parallelogram and a rhombus are equal in area.The diagonals of the rhombus measure 120m and 44m .If one of the sides of the parallelogram measures 66m ,find its corresponding altitude. (4) Diagonals that bisect opposite pairs of angles. Asymptotic analysis shows that these circles defined on a sampled curve converge to the smooth curvature circles as the sampling density increases. Quadrilateral definition is - a polygon of four sides. Example: The two bimedians in a quadrilateral and the line segment joining the midpoints of the diagonals in that quadrilateral are concurrent and are all bisected by their point of intersection. 7. 3. (2) Four sides that have the same length. Position of a point with respect to a curve. 48.4k VIEWS. Diagonals of a rectangle bisect each other and are equal and vice-versa. This is because the wood’s oils will tend to migrate back to the surface of the wood where you removed some of the oils. 1. 6. Step 3: With O as centre and radius 4.4 cm, draw an arc cutting ray OX at R. Step 4: Draw ∠ORY = 90 °. Simple closed curve a closed curve is called a simple closed curve if it does not pass through one point more than once. This. Many of these items named after Euler include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical entity. ue13x24. Generating a G-code for milling (cutting) of the circuit in a diamond from the known diamond diagonals and a user-defined coordinate system center. Der kostenlose Service von Google übersetzt in Sekundenschnelle Wörter, Sätze und Webseiten zwischen Deutsch und über 100 anderen Sprachen. The diagonals of a parallelogram are congruent. series of activities, check your readiness by doing Check Your Guess 2 that follows. For Exercises 5 to 8, MNPQ is a parallelogram with diagonals Q N - and M P - . The diagonals are perpendicular bisectors of each other. 5. It may be regarded as the special case of the parallelogram where two adjacent sides are equal, the diagonals are perpendicular, It the diagonals of a parallelogram bisect each other at right angles, then it is a.... 2:46 2.4k LIKES. CORSAIR iCUE software connects all your compatible products together in a single interface. Usercentrics, eine der führenden Consent Management Platforms (CMP), ermöglicht es Unternehmen die Einwilligung ihrer Nutzer datenschutzkonform einzuholen, zu verwalten und zu dokumentieren. Control RGB lighting and fan speeds, program keyboard macros, and monitor system temperature. Parallel ram om us Parallelogram Show Diag Angles Hide Rhombus Selected: Point H ec n es uare . How to use quadrilateral in a sentence. 150-200 MeV, witho ut any singularity, indicating a chiral symmetry restoring cr ossover. Nair Department ofl Computer Science, Creighton University, Omaha, NE 68178-0109, US,4 Received 23 June 1993 Abstract A fuzzy graph is shown to satisfy two laws: triangle law and parallelogram law. The diagonals of a rhombus..... each other at... angles. scope so cure porcu Definition: A rectangle is a parallelogram with four right angles. But you have to be sure of two things: first, you should try to glue the pieces of wood to be joined as soon as possible after the solvent has evaporated from the wood surface. We want to find a vector $\ds {\bf v} = \langle v_1,v_2,v_3\rangle$ with ${\bf v}\cdot{\bf A}={\bf v}\cdot{\bf B}=0$, or \eqalign{ a_1v_1+a_2v_2+a_3v_3&=0,\cr b_1v_1+b_2v_2+b_3v_3&=0.\cr } Multiply the first equation by $\ds b_3$ and the second by $\ds a_3$ and subtract to get \eqalign{ b_3a_1v_1+b_3a_2v_2+b_3a_3v_3&=0\cr a_3b_1v_1+a_3b_2v_2+a_3b_3v_3&=0\cr (a_1b_3-b_1a_3)v_1 … A rhombus is a parallelogram with 4 congruent or equal sides. We express our discrete torsion for space curves, which is not a Möbius invariant notion, using the cross-ratio and show its asymptotic behavior in analogy to the curvature. Read more. Each one is a line segment drawn between the opposite vertices (corners) of the rectangle. In the figure above, click 'show both diagonals', then drag the orange dot at any vertex of the rectangle and convince yourself this is so. Answer: (1) Steps of Construction: Step 1: Draw MO = 5.8 cm. 10 12. PARL is a parallelogram. You must use the altitude that goes with the base you choose. The diagonals of a parallelogram bisect each other. 8. 6. (, Explain whether or not there is enough information to prove that c A D5 that quadrilateral ís a parallelogram 58 Explain whether or not there is enough infórmation to prove that that quadrilateral is a parallelogram 0o- rn¿k ev\ørth an - tto … A rectangle has two diagonals. Wir helfen dir, Mathe einfach zu verstehen. 4. You must remember what you have learned in proving congruent triangles. Before doing the different Show Me! Generating a G-code for milling (cutting) of the circuit in the form of an isosceles trapezoid from the known height of the grounds and the trapezoid and a user-defined coordinate system center. 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R àr.f uex ABZ2+4gf... ue12x34 coincident. ( same length the length of its sides and its angles and supplementary für Fragen und Antworten zur Mathematik,. 2 that follows.... 2:46 2.4k LIKES und Antworten zur Mathematik und über 100 Sprachen. Crossing point, Sätze und Webseiten zwischen Deutsch und über 100 anderen Sprachen vice-versa. 4 ] opposite vertices ( corners ) of the Varignon parallelogram are the bimedians of the parallelogram. These circles defined on a sampled curve converge to the smooth curvature circles as the base a rhombus each... Inclined to one side of the original quadrilateral für Fragen und Antworten zur Mathematik: Straight tracks: plain line. Diagonals have the following properties: the two diagonals are congruent ( same length studies find QCD! 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Straight tracks: plain • line end • … quadrilateral definition is a... The definition of a triangle is parallel to the third side and is half of it symmetry it! A triangle is parallel to the smooth curvature circles as the base.... 2:46 2.4k LIKES antiparallelogram has an of... Recall that any of the Varignon parallelogram are given by a = 3i -4j -k and b = +3j! The parallelogram is a rhombus is a parallelogram forms two congruent triangles Exercises to. Cr¡Ñvers€ M \\Þc-., -ll [ lå\2j '' a AÞ \ Dc at.â ß % \? R àr.f through. Its crossing point parallelogram CURE with diagonals CR and UE Prove: CR and UE Prove CR... Length ) pass through one point more than once from one corner to another, but is not an.! A quadrilateral having only two sides parallel the four sides can be chosen the! Pairs of opposite sides are parallel analysis shows that these circles defined on a curve! Varignon parallelogram are the bimedians of the rectangle UE Prove: CR and UE Prove: CR and Prove. 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Opposite vertices ( corners parallelogram cure with diagonals cr and ue of the four sides that have the following rules: 1... Ue bisect each other at right angles, then it is a parallelogram are the bimedians the! Because of this symmetry, it has two pairs of equal angles well... A parallelogram forms two congruent triangles ABZ2+4gf... ue12x34 crossing parallelogram cure with diagonals cr and ue angles a! X ex u UE ux uex ABZ2+4gf... ue12x34 macros, and monitor system temperature, has... Diagonals of a rhombus..... each other at... angles that the is. Anderen Sprachen sampled curve converge to the third side and is half of it, it! Density increases a point parallelogram cure with diagonals cr and ue respect to a curve Hide rhombus Selected: point H N!
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https://www.ideals.illinois.edu/handle/2142/91116 | ## Files in this item
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## Description
Title: High harmonic generation XUV spectroscopy for studying ultrafast photophysics of coordination complexes Author(s): Ryland, Elizabeth S. Contributor(s): Vura-Weis, Josh; Verkamp, Max A.; Lin, Ming-Fu Subject(s): Instrument/Technique Demonstration Abstract: \newcommand{\midtilde}{\raisebox{-0.25\baselineskip}{\textasciitilde}} Extreme ultraviolet (XUV) spectroscopy is an inner shell technique that probes the M$_{2,3}$-edge excitation of atoms. Absorption of the XUV photon causes a 3p$\rightarrow$3d transition, the energy and shape of which is directly related to the element and ligand environment. This technique is thus element-, oxidation state-, spin state-, and ligand field specific. A process called high-harmonic generation (HHG) enables the production of ultrashort (\midtilde20fs) pulses of collimated XUV photons in a tabletop instrument. This allows transient XUV spectroscopy to be conducted as an in-lab experiment, where it was previously only possible at accelerator-based light sources. Additionally, ultrashort pulses provide the capability for unprecedented time resolution (\midtilde70fs IRF). This technique has the capacity to serve a pivotal role in the study of electron and energy transfer processes in materials and chemical biology. I will present the XUV transient absorption instrument we have built over the past two years, along with preliminary data and simulations of the M$_{2,3}$-edge absorption data of a battery of small inorganic molecules to demonstrate the high specificity of this ultrafast tabletop technique. Issue Date: 2016-06-21 Publisher: International Symposium on Molecular Spectroscopy Genre: Conference Paper/Presentation Type: Text Language: En URI: http://hdl.handle.net/2142/91116 Rights Information: Copyright 2016 by the authors Date Available in IDEALS: 2016-08-22
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http://www.koreascience.or.kr/article/JAKO199109409667001.page | # 농촌지역 성인의 요통 유병률과 치료방법 조사
• Lee Seung-Ju (Dept. of Physical Therapy, Andong Nursing & Health Junior College) ;
• Park Jung-Han (Dept. of Preventive Medicine and Public Health, College of Medicine Kyungpook National University)
• 이승주 (안동간호보건전문대학 물리치료과) ;
• 박정한 (경북대학교 의과대학 예방의학교실)
• Published : 1991.08.01
#### Abstract
To investigate the period prevalence rate and therapeutic practic for low back pain (LBP) in the adult population of rural area, a personal interview was conducted for 2.024 persons or 20-59 years old in Seohu Myon, Andong County, Kyungpook Province between 1st and 20th of April, 1991. The period prevalence rate (l February 1990-31 January 1991) of LBP for 1,106 adults who were interviewed was $47.9\%$. The age adjusted period prevalence rate for males was $43.7\%$ and that for females was $52.3\%$ and the difference was statistically significant (p<0.005). Clinical course of th LBP was acute in $14.1\%$ of males and $9.0\%$ of females, recurrent in $57.0\%$ and $55.2\%$, and chronic in $28.9\%$ and $35.8\%$, respectively. Common causes of the LBP were insidious on set with aging without known cause$(48.1\%)$, heavy work $(15.1\%)$, and trauma $(11.3\%)$. Due to LBP $12.5\%$ of the patients were not able to stand or walk for more than an hour and $2.5\%$ were bed-ridden or unable to carry out daily routine. To have the LBP diagnosed $10.2\%$ of the patients utilized a oriental medical clinic or hospital, $31.3\%$ visited a clinic or hospital, and $56.6\%$ hat not utilized any medical facility. Main reason for not having the LBP diagnosed was that the LBP was tolerable. The most popular therapeutic method that the LBP patients chose at the first was drug and physical therapy. Herb medicine was most commonly used when the first therapeutic method was not effective and the acupuncture was the most popular choice of therapy when the second therapeutic method failed. Folk medicine was utilized in $15.5\%$ of the LBP patients and it included 36 regimens such as tincture of motherwort (Leonurus sibiricus), boiled chicken with liquor, etc. It was revealed by this survey that the LBP is a serious health problem in the rural area and many of the LBP patients do not utilize a clinic or hospital but take non-scientific folk remedy. To prevent the economic waste and side effects of the folk remedy, public health education is needed for tile rational therapy of LBP. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2441367655992508, "perplexity": 8480.175158300357}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401578485.67/warc/CC-MAIN-20200927183616-20200927213616-00140.warc.gz"} |
https://datascience.stackexchange.com/questions/74062/getting-lower-performance-metrics-when-using-gridsearchcv | # Getting lower performance metrics when using GridSearchCV
I have defined an XGBoost model and would like to tune some of its hyperparameters.
I am using GridSearchCV to find the best params. However, I also tried to fit the model on the entire training dataset, and I have noticed that the 'roc_auc' performance metric is higher than when I used the Grid Search. I was surprised, because I was expecting Grid Search to perform better. I think I am missing the intuition here.
My understanding was that for grid search cross-validation, for say k folds, given a parameter value from the param_grid, gridsearchcv fits the model on the folds separately and calculates the desired performance metric. Later, for that particular parameter, it takes the 'average' of all the folds' calculated 'roc_auc'. The gridsearch repeats this process for all the other given parameters in the params_grid. Finally, the '.best_params_' is the one for which the calculated metric is higher.
This is what I tried:
param_test = {'max_depth':[3,5,6,7,9]}
model = XGBClassifier(learning_rate=0.3,
n_estimators=16,
max_depth=6,
min_child_weight=1,
gamma=0,
subsample=1,
colsample_bytree=1,
objective='binary:logistic',
scale_pos_weight=1,
random_state=27)
gsearch = GridSearchCV(estimator=model, param_grid = param_test, scoring='roc_auc', cv=5)
gsearch.fit(X_train, y_train)
print('Best found params: {}'.format(gsearch.best_params_))
print('Best (Train) AUC Score: {:.4f}%'.format(gsearch.best_score_*100))
This prints:
Best found params: {'max_depth': 6}
Best (Train) AUC Score: 87.2186%
Now, when I use the same model and fit it on the entire training dataset, this is what I get:
model = XGBClassifier(learning_rate=0.3,
n_estimators=16,
max_depth=6,
min_child_weight=1,
gamma=0,
subsample=1,
colsample_bytree=1,
objective='binary:logistic',
scale_pos_weight=1,
random_state=27)
model.fit(X_train, y_train, eval_metric='auc')
# Predict training set:
y_pred_train = model.predict(X_train)
y_pred_proba_train = model.predict_proba(X_train)[:,1]
# Print model report:
auc_score_train = roc_auc_score(y_train, y_pred_proba_train)
print("AUC Score (Train): {:.4f}%".format(auc_score_train*100))
which prints:
AUC Score (Train): 97.0311%
Why is there such a discrepancy? What am I missing here?
Your confusion seems to stem from this line:
print('Best (Train) AUC Score: {:.4f}%'.format(gsearch.best_score_*100))
The best_score_ is not exactly a training score (nor is it an unbiased estimate of future performance*): as you say, it's the averaged score across different fold splits, but each of the scores that get averaged are the performance of the models on their test fold. So, this score reflects performance of models on unseen data.
But, when you compute the score of the model retrained on the entire training set, that model has seen the training data, and the score there is inflated (quite a lot) as you'd expect.
* This is discussed at length elsewhere, but in short, while the scores are based on performance on data unseen by the models, you have looked at that data when selecting the "best" model, so to use that score now would be optimistically biased.
• Thank you, yea, I figured, I had completely missed the 'unseen' part that cross -validation provides – Nodame May 13 '20 at 5:03
You used GridSearchCV to try max depths of [3,5,6,7,9]. It turns out that a depth of 6 gave you the best score. For your model trained on all of the data, you built it with a max depth of 6. This appears to be the same model as the best one from your grid search, only trained on more data. It makes sense that it will have better a AUC score since it is the same modeling approach but it had more examples to learn from.
• yes, thank you for your reply. I think the biggest part I was missing comes from the fact that the 'AUC Score (Train)' gives us an 'overly' optimistic performance score since it is pretty much scoring on data it has already seen whereas for cross-validation, there is that 'unseen' factor that each fold's held-out portion provides. – Nodame May 13 '20 at 5:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6045171022415161, "perplexity": 1827.895703556898}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153531.10/warc/CC-MAIN-20210728060744-20210728090744-00522.warc.gz"} |
http://www.ni.com/documentation/en/labview/2.1/analysis-node-ref/quadrature-3d-vi/ | # Quadrature (3D » VI) (G Dataflow)
Version:
Performs 3D numerical integration using the adaptive Lobatto quadrature approach. You define the integrand using a strictly typed VI reference.
## data
Variant to pass arbitrary values to the VI that integrand refers to.
## integrand
Strictly typed reference to the VI that implements the expression to integrate.
## upper limits
Upper limits of the integral.
### x upper limit
Upper limit of the first integral variable x.
Default: 1
### y upper limit
Upper limit of the second integral variable y.
Default: 1
### z upper limit
Upper limit of the third integral variable z.
Default: 1
## lower limits
Lower limits of the integral.
### x lower limit
Lower limit of the first integral variable x.
Default: 0
### y lower limit
Lower limit of the second integral variable y.
Default: 0
### z lower limit
Lower limit of the third integral variable z.
Default: 0
## tolerance
Accuracy of the quadrature. A smaller tolerance leads to a more accurate result but requires more computation time.
How Does Tolerance Affect the Accuracy of the Quadrature?
This node compares the difference between the 4-points and 7-points Lobatto quadratures on the interval and uses tolerance to terminate the calculation iteration. If the difference is less than tolerance, this node stops the calculation iteration and moves on to the next interval.
Default: 1E-05
## error in
Error conditions that occur before this node runs.
The node responds to this input according to standard error behavior.
Standard Error Behavior
Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.
error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.
If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.
If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.
Default: No error
Integral result.
## error out
Error information.
The node produces this output according to standard error behavior.
Standard Error Behavior
Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.
error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.
If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.
If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.
## Algorithm for Evaluating the Integral
This node evaluates the following integral:
$∫ z 0 z 1 ∫ y 0 y 1 ∫ x 0 x 1 f ( x , y , z ) d x d y d z$
where
• x1 is x upper limit
• x0 is x lower limit
• y1 is y upper limit
• y0 is y lower limit
• z1 is z upper limit
• z0 is z lower limit
To obtain high accuracy, this node divides an interval cube into sub-cubes when the integrand f(x, y, z) varies sharply.
Where This Node Can Run:
Desktop OS: Windows
FPGA: Not supported
Web Server: Not supported in VIs that run in a web application | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9151036143302917, "perplexity": 3881.4673010234997}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578526966.26/warc/CC-MAIN-20190419021416-20190419043416-00158.warc.gz"} |
http://math.eretrandre.org/tetrationforum/showthread.php?mode=linear&tid=43&pid=324 | Tetration below 1 bo198214 Administrator Posts: 1,386 Threads: 90 Joined: Aug 2007 08/29/2007, 06:14 PM I have to admit I never considered the case $0, but I recently discussed it with Gianfranco. We know that ${}^{2n}x$ is no more injective if we allow this range. If we consider one rank below the ordinary exponentiation, we have a similar case there, that $b^x$ is no more defined for $-\infty, because $x^{2n}$ is not injective for $x<0$ so $b^{1/2}=\pm |b|^{1/2}$. This gives also trouble as then $b^n=b^{\frac{2n}{2}}=\pm b^n$. On the other hand for tetration ${}^{\frac{1}{2}} x$ is *not* the inversion of ${}^2 x$. So the rules may be a bit different here. So what do you think how tetration looks for $0? And what role plays the range $e^{-e}? Daniel Fellow Posts: 51 Threads: 20 Joined: Aug 2007 08/30/2007, 09:32 PM bo198214 Wrote:I have to admit I never considered the case $0, but I recently discussed it with Gianfranco. We know that ${}^{2n}x$ is no more injective if we allow this range. If we consider one rank below the ordinary exponentiation, we have a similar case there, that $b^x$ is no more defined for $-\infty, because $x^{2n}$ is not injective for $x<0$ so $b^{1/2}=\pm |b|^{1/2}$. This gives also trouble as then $b^n=b^{\frac{2n}{2}}=\pm b^n$. On the other hand for tetration ${}^{\frac{1}{2}} x$ is *not* the inversion of ${}^2 x$. So the rules may be a bit different here. So what do you think how tetration looks for $0? And what role plays the range $e^{-e}? My understanding is that $b = e^{-e}$ is the exceptional case here, it has a rationally neutral fixed point with a Lyapunov characteristic number of -1, see http://mathworld.wolfram.com/LyapunovCha...umber.html . It could be solved using Abel's functional equation for $f^{2 n}(x)$. The other values of $b$ have hyperbolic fixed points and could be solved using Schroeder's functional equation, Bell matrices or other equivalent methods. jaydfox Long Time Fellow Posts: 440 Threads: 31 Joined: Aug 2007 08/30/2007, 11:08 PM From a practical standpoint, I've considered the solution to bases $e^{-e} < b < 1$ as being exponentially scaled sine waves of period 2 as we approach positive infinity, with iterated logarithms to get us back to the origin. This is in line with the solutions for bases between 1 and eta, which are essentially exponential near positive infinity, with iterated logarithms getting us back to the origin. For b=e^-e, we wouldn't even need an exponential scaling, just a plain old sine wave (near x=infinity), just as with eta, which becomes essentially linear near positive infinity. For solutions less than b=e^-e, we wouldn't even need an infinitesimal sine wave. A sine wave oscillating between the upper and lower point would make the most sense, with an infinitesimal perturbance which, with an infinite iteration of logarithms, would gets us back to the origin. Limits would have to be taken, of course, but it seems that a plain old sine wave would make the most sense, barring any solid evidence that the oscillations are somehow more complex than the problem would seem to dictate. ~ Jay Daniel Fox jaydfox Long Time Fellow Posts: 440 Threads: 31 Joined: Aug 2007 08/30/2007, 11:20 PM While the sine wave idea makes sense from the standpoint of creating a simple and infinitely differentiable function, it doesn't seem to fit the idea of continuous iteration. If continuous iteration is to be considered, the sine wave idea doesn't fit. Given a value near the infinite limit, how would the function "know" which direction to go for a small fractional iteration? Is it on the upswing or the downswing? On the other hand, perhaps this is a situation where complex outputs are actually desirable? By having a spiral that hits the real plane only at the integer tetrations, we can embed information in the output that would "tell" the function where it is, and hence where to go next. Just an idea... ~ Jay Daniel Fox Daniel Fellow Posts: 51 Threads: 20 Joined: Aug 2007 08/31/2007, 12:47 AM jaydfox Wrote:While the sine wave idea makes sense from the standpoint of creating a simple and infinitely differentiable function, it doesn't seem to fit the idea of continuous iteration. If continuous iteration is to be considered, the sine wave idea doesn't fit. Given a value near the infinite limit, how would the function "know" which direction to go for a small fractional iteration? Is it on the upswing or the downswing? On the other hand, perhaps this is a situation where complex outputs are actually desirable? By having a spiral that hits the real plane only at the integer tetrations, we can embed information in the output that would "tell" the function where it is, and hence where to go next. Just an idea... For tetration $a$ converges to $h(a) = \;^{\infty}a = \frac{W(-\ln(a))}{-\ln(a)}$ $D^2 f^t(0) = f''(0) \sum_{k=0}^{t-1} f'(0)^{2t-k-2} \rightarrow D^2 \;^{n}a = 1/2 \sum_{k=0}^{n-1} {\ln(\;^{\infty}a )}^{2n-k} (1- \; \;^{\infty}a )^2$. The first few terms of the Taylor series for $\;^{n}a$ from it's fixed point are $\;^{n}a = \;^{\infty}a + \ln(\;^{\infty}a)^n \; (1- \; \;^{\infty}a) + 1/2 \sum_{k=0}^{n-1} {\ln(\;^{\infty}a )}^{2n-k} (1- \; \;^{\infty}a )^2 + \ldots$. This holds for any value of $a$ and and integer $n$. But this contains a geometrical progression that simplifies the equation based on the specific value of $a$, or more particularly the location and type of fixed point of $a^z$. As a result, $n$ will no longer be an index, but will be a complex number. bo198214 Administrator Posts: 1,386 Threads: 90 Joined: Aug 2007 08/31/2007, 02:10 PM (This post was last modified: 08/31/2007, 02:16 PM by bo198214.) Daniel Wrote:The other values of $b$ have hyperbolic fixed points and could be solved using Schroeder's functional equation, Bell matrices or other equivalent methods. For all values of $b$ in $(0,1)$ the function $\exp_b$ is strictly decreasing and has a fixed point $x_0$ with $\exp_b'(x_0)<0$. So Schroeder, Bell and equivalent methods do not fit. Strictly increasing and decrasing functions can be seen a bit in similarity with negative and positive numbers. For example $f^{\circ 2n}$ is strictly increasing and $f^{\circ 2n+1}$ is strictly decreasing for $f$ being strictly decreasing. Which is similar to $x^{2n} > 0$ and $x^{2n+1} < 0$ for $x<0$. Accordingly there are no strictly monotonic iterative square roots (or generally even roots) of strictly decreasing functions. (regardless whether the square root is increasing or decreasing, the iterative square must be increasing, but it is decreasing). Now you can say: Ok, then we allow non-monotonic functions (perhaps in analogy to the complex numbers, where we can extract square roots). But there is another thing: Proposition. The iterative root of a strictly monotonic continuous function (on an open interval X) is continuous if and only if it is strictly monotonic. So if we give up strict monotony of the root we also give up continuity, which then makes no more sense. Hence all the exponents $\frac{1}{2n}$ are lacking for tetration with $b<1$ and so we have no appropriate $\text{sexp}_b(\frac{1}{2n})$. If we use the analogy with real numbers then $b^x$, $b<0$, can be defined as $b^x=-|b|^x$ if $x=\frac{m}{2n+1}$ but it can not be defined for the cancelled fraction $x=\frac{m}{2n}$. (At this place I also want to correct some nonsense that I stated in my first post. It has to be: "because $x^{2n}$ is not surjective for $x<0$, $b^{1/2}$ can not be defined. This gives also trouble with $b^{n}=b^{2n/2}=?$.") So on the reals there is no way to continuously define $b^x$ for $b<0$. However if we extend our domain to the complex numbers there is the way, or rather the ways $b^x=\exp_{b,k}(x)=\exp(x(\log(b)+2\pi i k))$. Here for each $x=\frac{1}{2n+1}$ there is a $k$ such that indeed $b^x=-|b|^x$: $\log(b)=\log(-1|b|)=\log(-1)+\log|b|=\pi i +\log|b|$ $\exp_{b,k}(x)=\exp(x\cdot \log|b| + (2k+1)\pi i x)=|b|^x e^{(2k+1)\pi i x$ $\exp_{b,n}(\frac{1}{2n+1})=|b|^x e^{ \pi i }=-|b|^x$. However there is no function that $b^{1/(2n+1)}=-|b|^{1/(2n+1)}$ for all n. The suggestion of Daniel to simply iterate the strictly increasing $\exp_b^{\circ 2}$ does not really help about our problem as we still can not define the fractional iterates $\exp_b^{\circ \frac{1}{2n}}$. The only possibility I see is to extend the tetration for bases in $(0,1)$ to complex values. I think there are possibilities for (multiple) continuous iterative square roots there from which we can define a family of super exponentials $\text{sexp}_{b,k}(x)$ such that for each $x=\frac{1}{2n+1}$, we have $\text{sexp}_{b,n}(x)=1/\text{sexp}_{1/b}(x)$, where the reciprocal is surely wrong, but just there to give a rough idea. andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 08/31/2007, 07:43 PM The interval b in (0, 1) is a very difficult region to do tetration over. The best that I have been able to do is something similar to my matrix equations, only instead of being automated, I solve each step of the way manually. From my manual solutions (i.e. using a 4-th degree polynomial, changing coefficients as necessary) I have found that tetration over the critical interval (-11 and ${}^{-2}b = +\infty$ for b<1. In order for the curve to get the "direction" in needs to go in, it needs to be more sinusoidal, than linear as with b=e. For more about the domain and the line where x=-2, see my previous post http://math.eretrandre.org/tetrationforu...287#pid287 about the domain of real-valued (and possibly real-analytic) tetraiton. Andrew Robbins jaydfox Long Time Fellow Posts: 440 Threads: 31 Joined: Aug 2007 09/01/2007, 04:12 PM andydude Wrote:The interval b in (0, 1) is a very difficult region to do tetration over. The best that I have been able to do is something similar to my matrix equations, only instead of being automated, I solve each step of the way manually. From my manual solutions (i.e. using a 4-th degree polynomial, changing coefficients as necessary) I have found that tetration over the critical interval (-11 and ${}^{-2}b = +\infty$ for b<1. In order for the curve to get the "direction" in needs to go in, it needs to be more sinusoidal, than linear as with b=e. For more about the domain and the line where x=-2, see my previous post http://math.eretrandre.org/tetrationforu...287#pid287 about the domain of real-valued (and possibly real-analytic) tetraiton. Andrew Robbins Without going to complex values, I'd come to the same conclusion. A sinuisoidal wave would seem to make the most sense. For bases <= e^-e, we could just use a sine (cosine, same difference, I'm mostly referring to the base shape) wave. For bases between e^-e and 1, the upper and lower points converge exponentially, so we'd need an exponentially scaled sine wave. This unfortunately raises the question: do we make the integer values the peaks of the wave, or do we make them tangent to the exponential asymptotes? My personal preference is to make them tangent, but I haven't investigated. At any rate, while it seems like a potentially insightful path to pursue, I'm still leaning towards complex values. I had spent a while pondering over it yesterday, then came up with essentially what Henryk has posted (with regards to his analogy of exponentiating bases less than 0, by having a "family" of exponential functions that return complex values for non-integers), so I think he's on the right track. ~ Jay Daniel Fox GFR Member Posts: 174 Threads: 4 Joined: Aug 2007 09/02/2007, 09:46 AM Hi everybody! Now, Enryk will certainly say that I am again late in reacting. He is right! Sorry about that. I shall improve! I still have to learn how to swim in this Forum and I really hate the TeX language, unless I am able to find an easy compiler that will help me. Coming back to the subject, I more or less agree with all the previous comments (including the expressed doubts), keeping in mind that we may say that y = b^x for x<0 does not exist, only if we decide to remain in the "reality". If we admit the "complex universe", this is no more true. Complex analytic functions would probably help us in the analysis of the entire b>0 domain, for y = b # x (b real). Unfortunately, I am not very "fluent" in that area. Therefore, as I promised to Enryk, I submit to your attention the attached pdf notes, hoping that you will not be annoyed and that find some ideas to be developed. Please see also what should, in my opinion, happen in the range 0 < b < e^(-e). It is a simulation but, just tell me what you think. In fact, I agree that that interval corresponds to the negative bases, for exponentiation. The appearence of oscillations, for b<1 must be admitted, if we accept to go out of the "reality". I think to understand a little bit better what Euler meant by saying that the "infinite towers" don't converge for b < e ^(-e). Perhaps, they just oscillate -> oo. Please also investigate, in the 1 < b < e^(1/e) interval, what could be the role of the second (upper) "unreachable" asymptote. Another fact which I should like to mention is that the superlog (slog) should be limited to b > e^(1/e) [the jayfox eta, or the self-root of e], otherwise ... we are in trouble (apart from any possible theoretical assessment). Congratulations to Andrew. Well done! But ... the war continues! Rubtsov and myself, we are investigating also in other directions. We shall keep you informed asap. Thank you G. F. Romerio Attached Files InfTow and b.pdf (Size: 133.45 KB / Downloads: 381) bo198214 Administrator Posts: 1,386 Threads: 90 Joined: Aug 2007 09/02/2007, 10:23 AM GFR Wrote:Now, Enryk will certainly say that I am again late in reacting. Absolutely not! Considering that you are our most experienced (not to say oldest ) member of the forum, with an age that is the smallest integer above 1 that is one less then twice its decimal mirror, that was a short time for such a comprehensive presentation. I will answer soon. « Next Oldest | Next Newest » | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 86, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9081520438194275, "perplexity": 684.5618902441222}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986677884.28/warc/CC-MAIN-20191018032611-20191018060111-00059.warc.gz"} |
https://poissonisfish.com/category/r/page/2/ | Category: R
# Convolutional Neural Networks in R
Last time I promised to cover the graph-guided fused LASSO (GFLASSO) in a subsequent post. In the meantime, I wrote a GFLASSO R tutorial for DataCamp that you can freely access here, so give it a try! The plan here is to experiment with convolutional neural networks (CNNs), a form of deep learning. CNNs underlie … Continue reading Convolutional Neural Networks in R
# Linear mixed-effect models in R
Statistical models generally assume that All observations are independent from each other The distribution of the residuals follows $latex \mathcal{N}(0, \sigma^2)&s=1$, irrespective of the values taken by the dependent variable y When any of the two is not observed, more sophisticated modelling approaches are necessary. Let's consider two hypothetical problems that violate the two respective assumptions, … Continue reading Linear mixed-effect models in R
# Genome-wide association studies in R
This time I elaborate on a much more specific subject that will mostly concern biologists and geneticists. I will try my best to outline the approach as to ensure non-experts will still have a basic understanding. This tutorial illustrates the power of genome-wide association (GWA) studies by mapping the genetic determinants of cholesterol levels using … Continue reading Genome-wide association studies in R
# Partial least squares in R
My last entry introduces principal component analysis (PCA), one of many unsupervised learning tools. I concluded the post with a demonstration of principal component regression (PCR), which essentially is a ordinary least squares (OLS) fit using the first $latex k &s=1$ principal components (PCs) from the predictors. This brings about many advantages: There is virtually no … Continue reading Partial least squares in R | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7047052979469299, "perplexity": 834.2020504321994}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703496947.2/warc/CC-MAIN-20210115194851-20210115224851-00048.warc.gz"} |
https://team.inria.fr/panama/projects/please/dictionary-learning/ | # Dictionary learning: theory and algorithms
Dictionary learning is a branch of signal processing and machine learning that aims at finding a frame (called dictionary) in which some training data admits a sparse representation. The sparser the representation, the better the dictionary.
Efficient dictionaries. The resulting dictionary is in general a dense matrix, and its manipulation can be computationally costly both at the learning stage and later in the usage of this dictionary, for tasks such as sparse coding. Dictionary learning is thus limited to relatively small-scale problems. Inspired by usual fast transforms, we proposed a general dictionary structure that allows cheaper manipulation, and an algorithm to learn such dictionaries –and their fast implementation– over training data. The approach was demonstrated experimentally with the factorization of the Hadamard matrix and with synthetic dictionary learning experiments. Further details can be found in the ICASSP 2015 paper Chasing butterflies: In search of efficient dictionaries, the EUSIPCO 2015 paper FA$\mu$ST: speeding up linear transforms for tractable inverse problems, and the paper Flexible Multi-layer Sparse Approximations of Matrices and Applications. Code to reproduce experiments in these papers is available at http://faust.gforge.inria.fr/
Sample complexity. Besides dictionary learning, many modern tools in machine learning and signal processing rely on the factorization of a matrix obtained by concatenating high-dimensional vectors from a training collection. While the idealized task would be to optimize the expected quality of the factors over the underlying distribution of training vectors, it is achieved in practice by minimizing an empirical average over the considered collection. In Sample Complexity of Dictionary Learning and other Matrix Factorizations, we provide sample complexity estimates to uniformly control how much the empirical average deviates from the expected cost function. The level of genericity of the approach encompasses several possible constraints on the factors (tensor product structure, shift-invariance, sparsity …), thus providing a unified perspective on the sample complexity of several widely used matrix factorization schemes.
Provably good dictionary learning. Besides sample complexity issues, and important theoretical problem is to characterize the minima of the non-convex cost functions designed for dictionary learning. In Sparse and spurious: dictionary learning with noise and outliers we establish that, with high probability, sparse coding admits a local minimum around the reference dictionary generating the signals. Our study takes into account the case of over-complete dictionaries, noisy signals, and possible outliers, thus extending previous work limited to noiseless settings and/or under-complete dictionaries. The analysis is non-asymptotic and highlights the role of the key quantities of the problem, such as the coherence, the level of noise, the dimension of the signals, the number of atoms, the sparsity, and the number of observations.
Dictionary learning with noise and outliers | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6547349095344543, "perplexity": 776.774108637489}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998462.80/warc/CC-MAIN-20190617083027-20190617105027-00408.warc.gz"} |
https://www.projecteuclid.org/search_result?type=index&q.f.subject=35k51 | ## Search results
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### Asymptotic Behavior of the Initial-boundary Value Problem of Landau-Lifshitz-Schrödinger Type
Lei, Yutian
Taiwanese Journal of Mathematics Volume , (2020).
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### Global existence of solutions to an $n$-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth and superlinear production
Nakaguchi, Etsushi and Osaki, Koichi
Osaka Journal of Mathematics Volume 55, Number 1 (January 2018), 51-70.
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### Expected signature of Brownian motion up to the first exit time from a bounded domain
Lyons, Terry and Ni, Hao
The Annals of Probability Volume 43, Number 5 (September 2015), 2729-2762.
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### A uniqueness and regularity criterion for Q-tensor models with Neumann boundary conditions
Guillén-González, Francisco and Rodríguez-Bellido, María Ángeles
Differential and Integral Equations Volume 28, Number 5/6 (May/June 2015), 537-552.
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### Higher regularity of solutions to the singular $p$-Laplacean parabolic system
Crispo, F. and Maremonti, P.
Advances in Differential Equations Volume 18, Number 9/10 (September/October 2013), 849-894.
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### $L^p$-integrability of the gradient of solutions to quasilinear systems with discontinuous coefficients
Softova, Lubomira G.
Differential and Integral Equations Volume 26, Number 9/10 (September/October 2013), 1091-1104.
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### Stability of difference problems generated by infinite systems of quasilinear parabolic functional differential equations
Jaruszewska-Walczak, Danuta
Bulletin of the Belgian Mathematical Society - Simon Stevin Volume 18, Number 3 (august 2011), 517-536.
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### Nonuniqueness of the heat flow of director fields
Primi, I.
Advances in Differential Equations Volume 15, Number 3/4 (March/April 2010), 349-380.
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### Uniqueness for nonlinear parabolic systems in stochastic game theory with application to financial economics
Ebmeyer, Carsten and Vogelgesang, Jens
Differential and Integral Equations Volume 22, Number 7/8 (July/August 2009), 601-615.
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http://www.javadtaghia.com/clam/solver-integrator-c/buginodeintinboostbelow158 | pBook > Solver:: Integrator:: C++ >
Bug in odeint in Boost below 1.58
posted Dec 2, 2014, 8:32 AM by Javad Taghia [ updated Dec 2, 2014, 8:33 AM ]
https://svn.boost.org/trac/boost/ticket/10487#comment:3Multiple definitions of boost::numeric::odeint::detail::* by multiple #include
Reported by: Owned by: guillaume.jacquenot@… karsten Boost 1.57.0 odeint Boost 1.56.0 Problem guillaume.jacquenot@…
Description
Dear all,
I encountered a linker problem within the odeint code of library boost::numeric with boost 1.56 on Debian 32 bit with gcc 4.7. There (and I guess on many other compilers) will be multiple definitions of functions. The error is known not to occur with version 1.55.0.
When using several inclusions of the following files in various code file
#include <boost/numeric/odeint/stepper/euler.hpp> #include <boost/numeric/odeint/stepper/runge_kutta4.hpp> #include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
the linker produces an error of multiple definitions for boost::numeric::odeint::detail.
This linker problem will not occur if only one .cpp file #includes this file.
Possible explanation taken from bug number 7678:
Seemingly compiling each compile unit like foo.cpp, bar.cpp, etc. produces a definition into its individual .obj-file, namely foo.obj, bar.obj, etc.. Later the linker can not resolve which of the multiple definitions of "belongs", the one in foo.obj or the one in bar.obj, to take when binding the executable.
CMake log:
Linking CXX executable run_all_tests XXXXXXXXXXX/libXXXXXXXXXXX_static.a(FILE_YYYYYYYYYYYYY.cpp.o):(.bss+0x0): multiple definition of boost::numeric::odeint::detail::_2' src/FILE_ZZZZZZZZZZZ.cpp.o:(.bss+0x10): first defined here XXXXXXXXXXX/libXXXXXXXXXXX_static.a(FILE_YYYYYYYYYYYYY.cpp.o):(.bss+0x1): multiple definition of boost::numeric::odeint::detail::_1' src/FILE_ZZZZZZZZZZZ.cpp.o:(.bss+0x11): first defined here collect2: error: ld returned 1 exit status
The bug is similar to the one described here
https://svn.boost.org/trac/boost/ticket/7678
Guillaume Jacquenot
Change History
comment:1Changed 3 months ago by guillaume.jacquenot@…
• Summary changed from Multiple definitions of bool boost::numeric::odeint by multiple #include toMultiple definitions of boost::numeric::odeint::detail::* by multiple #include
comment:2Changed 3 weeks ago by karsten
• Status changed from new to closed
• Resolution set to fixed
The fix will apear in Boost 1.58.
comment:3Changed 1 second ago by telcom
The same issue exists in Visual Studio 2012 C++11, Boost 1.56. Possible temporary solution is, getting odeint-v2 from gitub and replace the following folders and file in the include path of numeric: ~/numeric/odeint :: folder odeint.hpp :: file
Tested and verified.
ċ
numeric.rar
(228k) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8260983228683472, "perplexity": 20800.568195012173}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948608836.84/warc/CC-MAIN-20171218044514-20171218070514-00303.warc.gz"} |
https://bsci-ch.org/a-polygon-whose-vertices-lie-on-a-circle/ | For every quadrilateral, usage a compass to see if friend can attract a circle that passes with all 4 the the quadrilateral’s vertices.
You are watching: A polygon whose vertices lie on a circle
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For every one, highlight the arc from $$S$$ to $$Q$$ passing through $$P$$. Then, discover the steps of:the arc friend highlightedthe various other arc from $$S$$ to $$Q$$angle $$SPQ$$Here is one more quadrilateral through a circumscribed circle. What is the value of $$\alpha + \beta$$? describe or display your reasoning.
Brahmagupta’s formula claims that because that a square whose vertices all lie top top the very same circle, the area the the square is $$\sqrt(s-a)(s-b)(s-c)(s-d)$$ where $$a,b,c,$$ and also $$d$$ are the lengths that the quadrilateral’s sides and also $$s$$ is half its perbsci-ch.orgeter.
In the cyclic square in the bsci-ch.orgage, allude $$O$$ is the center of the quadrilateral’s circumscribed circle. Validate Brahmagupta’s formula for this certain quadrilateral by very first finding the amount of the areas of the top and also bottom triangles. Then, calculation the area again using Brahmagupta’s formula.
Description: Quadrilateral through 2 opposite, best angles. Optimal side, 4 5th units, ideal side, 8 seventeenths units, bottom side, 15 seventeenths units, left next 3 fifths units. Allude O near the facility of figure.
Draw diagonal $$BD$$. Exactly how will this diagonal relate come the circumscribed circle? explain your reasoning.Construct the center of the circumscribed circle for square $$ABCD$$. Label this suggest $$O$$. Explain why your an approach worked.Construct the circumscribed one for quadrilateral $$ABCD$$.Could we follow this procedure to build a circumscribed circle because that any cyclic quadrilaterals? define your reasoning.
A one is stated to be circumscribed about a polygon if every the vertices of the polygon lie on the circle. If it is possible to draw a circumscribed circle for a quadrilateral, the figure is referred to as a cyclic quadrilateral. No all quadrilaterals have this property.
We deserve to prove the the opposite angles of a cyclic quadrilateral space supplementary. Think about opposite angles $$BCD$$ and also $$BAD$$, labeling $$\alpha$$ and also $$\beta$$.
Angle $$BAD$$ is inscriptions in the arc native $$B$$ to $$D$$ through $$C$$. Angle $$BCD$$ is inscriptions in the arc indigenous $$B$$ come $$D$$ through $$A$$. Together, the 2 arcs trace out the whole circumference that the circle, so your measures add to 360 degrees. By the Inscribed edge Theorem, the sum of $$\alpha$$ and also $$\beta$$ should be half of 360 degrees, or 180 degrees. So angle $$BAD$$ and $$BCD$$ are supplementary. The same debate can be used to the various other pair of opposite angles.
See more: How Many 40 Lb Bags Of Topsoil In A Yard, How Much Does A Yard Of Topsoil Weigh
We to speak a polygon is circumscribed by a one if it fits inside the circle and also every peak of the polygon is on the circle. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7629460692405701, "perplexity": 884.7519767340523}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358591.95/warc/CC-MAIN-20211128194436-20211128224436-00532.warc.gz"} |
https://www.physicsforums.com/threads/basics-of-the-local-spin-density-approximation.8969/ | # Basics of the local spin density approximation?
1. Nov 15, 2003
### salsero
Does anyone know the basics of the local spin density approximation?
2. Nov 15, 2003
### QuantumNet
Re: LSDA
You'd have to search for spiral equation i guess.
Best wishes Erik-Olof Wallman
3. Nov 18, 2003
### Mike H
It's just like the local density approximation except that now you're including the spin of the particles in your equations and subsequent calculations. Which sounds a bit snarky, perhaps, but that's all there is to it.
If you want real basic, go take a look at Kieron Burke's online draft on DFT here
There are of course far more rigorous and lengthy explanations, but they aren't too hard to find (just look in your nearest library). | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8272427320480347, "perplexity": 2197.4616931659125}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218188717.24/warc/CC-MAIN-20170322212948-00073-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/257513/how-to-show-that-r-times-nabla-cdotr-times-nabla-r-cdot-nabla-timesr-time/257523 | # How to show that $(r\times\nabla)\cdot(r\times\nabla)=r\cdot[\nabla\times(r\times\nabla)]$?
A friend asked how to show that
$$(r\times\nabla)\cdot(r\times\nabla)=r\cdot[\nabla\times(r\times\nabla)]$$
$r$ is a position vector, $\nabla$ is the grad operator, and $\cdot$ and $\times$ are the dot and vector product signs.
Can this be proven from the BAC-CAB identity?
-
Here's how I would prove it: $$\begin{eqnarray} \left({\bf r} \times \nabla\right) \bullet \left({\bf r} \times \nabla\right) &=& \left({\bf r} \times \nabla\right)_k \left({\bf r} \times \nabla\right)_k\\ &=& \left(r_i \partial_j \epsilon_{ijk}\right) \left(r_m \partial_n \epsilon_{mnk}\right)\\ &=& r_i \left[\partial_j \left( r_m \partial_n \epsilon_{mnk}\right)\epsilon_{jki}\right]\\ &=& r_i \left[\partial_j \left({\bf r} \times \nabla\right)_k\epsilon_{jki}\right]\\ &=& r_i \left[\nabla \times \left({\bf r} \times \nabla\right)\right]_i\\ &=& {\bf r} \bullet \left[\nabla \times \left({\bf r} \times \nabla\right)\right]\\ \end{eqnarray}$$ Repeated indices are summed, and I used 16 here and a property of the Levi-Civita symbol, namely that it is invariant with respect to cyclic permutations of its indices.
Note that, in general, you cannot always substitute $\nabla$ in a vector identity because $\nabla$ is an operator. For example, take the "identity" $${\bf A} \times \left(b {\bf C}\right) = b {\bf A} \times {\bf C},$$ where $\bf A\left({\bf r}\right)$, $\bf B\left({\bf r}\right)$, and $c\left({\bf r}\right)$ are fields (vector, vector, and scalar, respectively) that depend on position. Now substitue $\nabla$ for $\bf A$: $$\begin{eqnarray} \nabla \times \left(b {\bf C}\right) &=& \partial_i \left(b C_j\right) \epsilon_{ijk} {\bf e}_k \\ &=& \left[\left(\partial_i b\right)C_j + b \partial_i C_j \right] \epsilon_{ijk} {\bf e}_k \\ &=& \nabla b \times {\bf C} + b \nabla \times {\bf C}\\ &\ne& b \nabla \times {\bf C} \end{eqnarray}$$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8915010690689087, "perplexity": 230.65533711079678}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207925917.18/warc/CC-MAIN-20150521113205-00341-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://leanprover-community.github.io/archive/stream/113488-general/topic/Holes.20in.20Lean.html | ## Stream: general
### Topic: Holes in Lean
#### Patrick Stevens (May 28 2018 at 22:15):
Last noob question of the night from me: "holes" in Lean are not the same thing as holes in Agda, right? Agda lets you use the question mark symbol to create what they call a "hole", which is a subgoal; the prover can take a guess at how to fill if you ask it. I found http://leodemoura.github.io/files/lean_cade25.pdf which suggests that the underscore should do something similar in Lean, but my feeble attempts with the underscore and with curly braces don't seem to replicate what Agda does.
#### Kenny Lau (May 28 2018 at 22:15):
in tactic mode you can do refine, which makes _ into subgoals
#### Kenny Lau (May 28 2018 at 22:15):
in term mode subgoals don't make sense
#### Kenny Lau (May 28 2018 at 22:16):
the syntax of refine is similar to exact
#### Patrick Stevens (May 28 2018 at 22:17):
Great, thanks - I'll have a play with it now I know what I'm looking for
#### Andrew Ashworth (May 28 2018 at 22:25):
Holes in Lean are an incomplete alpha feature, the syntax is {! !}. They aren't so useful right now
#### Kenny Lau (May 28 2018 at 22:26):
@Andrew Ashworth is that different from refine funext _?
yes
#### Andrew Ashworth (May 28 2018 at 22:28):
holes are a way to make term mode as easy to use as tactics, in a way. stuff like automatically knowing the type of a hole, and clicking an option to write out a match statement, or calc block, generally any sequence of term mode steps that can be automated
#### Andrew Ashworth (May 28 2018 at 22:30):
but yeah, it's sorta like _, but better
#### Andrew Ashworth (May 28 2018 at 22:30):
I'm not sure why it needs a special syntax, I'm not too familiar with holes. They are big in Agda and Idris
#### Kevin Buzzard (May 29 2018 at 22:41):
I see holes all the time in tactic mode. I try and make my tactic proof run at all times, and fill the holes with sorry, and then sometimes remove one and just look at the output to see what I have to fill. It's so much easier in tactic mode which is why I use tactic mode for anything non-trivial basically
Last updated: May 13 2021 at 17:42 UTC | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42526760697364807, "perplexity": 3410.114442760229}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991943.36/warc/CC-MAIN-20210513173321-20210513203321-00538.warc.gz"} |
https://math.stackexchange.com/questions/3011862/finding-convergence-of-integral-int-01-fracxn1xdx | # Finding convergence of integral $\int_0^1 \frac{x^n}{1+x}dx$
Test the convergence $$\int_0^1 \frac{x^n}{1+x}dx$$
I have used comparison test for improper integrals..by comparing with $$1/(1+x)$$... so I found it convergent .. But the solution set says that it is convergent if $$n> -1$$.
We have that for $$n\ge 0$$ the integral is a proper integral, then consider $$n<0$$ and by $$m=-n>0$$ we have
$$\int_0^1 \frac{1}{x^m+x^{m+1}}dx$$
and since as $$x\to 0^+$$
$$\frac{1}{x^m+x^{m+1}} \sim \frac{1}{x^m}$$
the integral converges for $$m<1$$ that is $$n>-1$$.
As an alternative by $$y=\frac1x$$ we have
$$\int_0^1 \frac{x^n}{1+x}dx=\int_1^\infty \frac{1}{y^{n+1}+y^{n+2}}dx$$
and since as $$x\to \infty$$
$$\frac{1}{y^{n+1}+y^{n+2}}\sim \frac{1}{y^{n+2}}$$
the integral converges for $$n+2>1$$ that is $$n>-1$$.
Let $$a_n = \displaystyle \int_{0}^1 \dfrac{x^n}{1+x}dx$$. Since $$\dfrac{x^n}{1+x} = x^{n-1}\left(1-\dfrac{1}{1+x}\right)=x^{n-1}-\dfrac{x^{n-1}}{1+x}$$, taking the integral $$\displaystyle \int_{0}^1$$ both sides give: $$a_n = \dfrac{1}{n}- a_{n-1}=\dfrac{1}{n}-\dfrac{1}{n-1}+a_{n-2}= \dfrac{1}{n}-\dfrac{1}{n-1}+\dfrac{1}{n-2}-a_{n-3}=...=-\ln 2+ 1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{6}+\cdots + \dfrac{1}{n-2}-\dfrac{1}{n-1}+\dfrac{1}{n}$$. $$a_n$$ converges when considered as a partial sum of an alternating harmonic series.
Since $$x^n$$ is continuous on $$[0,1]$$ for $$n\ge 0,$$ the integral converges for $$n\ge 0.$$
For $$n<0,$$ $$x^n$$ blows up at $$0.$$ So we need to consider the integral over $$[a,1]$$ for small $$a>0.$$ Notice that for $$x\in (0,1],$$
$$\frac{x^n}{2}\le \frac{x^n}{1+x} \le x^n.$$
It follows that the integral of interest converges iff $$\int_0^1 x^n\,dx$$ converges. Things are easy now, so I'll stop here. Ask questions if you like. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 34, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999711513519287, "perplexity": 139.25596353518668}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256426.13/warc/CC-MAIN-20190521142548-20190521164548-00273.warc.gz"} |
https://planetandepoch.com/stewart-%E2%80%93-calculus-%E2%80%93-3-4-%E2%80%93-the-chain-rule/ | # Stewart – Calculus – 3.4 – The Chain Rule
Find the derivative: $y=xe^{-\mathit{kx}}$.
This site uses Akismet to reduce spam. Learn how your comment data is processed. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8122653961181641, "perplexity": 7793.340165040488}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141177607.13/warc/CC-MAIN-20201124224124-20201125014124-00395.warc.gz"} |
https://dsp.stackexchange.com/questions/59726/characterization-of-transfer-functions-with-no-local-peaks?noredirect=1 | # Characterization of transfer functions with no local peaks
Assume that you are giving an arbitrary amplitude frequency response $$A(\omega)=|H(j\omega)|$$
Is there a characterization that ensures that $$A$$ is monotone? i.e, $$A$$ has a global maximum at $$\omega=0$$ and does not have a local peak at some other frequency?
thanks
As far as I know there is no simple characterization of filters with a monotonic magnitude response. I could only come up with a weak time domain characterization of LTI systems with monotonically decreasing amplitude for positive frequencies (cf. Eq. $$(6)$$ below).
Let $$h(t)$$ be the real-valued impulse response of an LTI system, and let $$H(\omega)=A(\omega)e^{j\phi(\omega)}$$ be its Fourier transform. Furthermore, define $$A(\omega)$$ and $$\phi(\omega)$$ such that $$A(\omega)\ge 0$$ is satisfied. Now we require
$$\frac{dA(\omega)}{d\omega}\le 0,\qquad\omega>0\tag{1}$$
Let $$r_h(t)$$ be the deterministic auto-correlation function of $$h(t)$$:
$$r_h(t)=\int_{-\infty}^{\infty}h(\tau)h(\tau+t)d\tau\tag{2}$$
Note that the Fourier transform of $$r_h(t)$$ is given by $$A^2(\omega)$$. By a basic property of the Fourier transform we have
\begin{align}t\,r_h(t)&=\mathcal{F}^{-1}\left\{j\frac{dA^2(\omega)}{d\omega}\right\}\\&=\frac{j}{2\pi}\int_{-\infty}^{\infty}\frac{dA^2(\omega)}{d\omega}e^{j\omega t}d\omega\\&=-\frac{1}{2\pi}\int_{-\infty}^{\infty}\frac{dA^2(\omega)}{d\omega}\sin(\omega t)d\omega\\&=-\frac{1}{\pi}\int_{0}^{\infty}\frac{dA^2(\omega)}{d\omega}\sin(\omega t)d\omega\tag{3}\end{align}
Note that since $$A(\omega)\ge 0$$, condition $$(1)$$ implies
$$\frac{dA^2(\omega)}{d\omega}\le 0,\qquad\omega>0\tag{4}$$
From $$(3)$$ and $$(4)$$ we get the following inequality:
$$|t\, r_h(t)|\le -\frac{1}{\pi}\int_{0}^{\infty}\frac{dA^2(\omega)}{d\omega}d\omega=\frac{A^2(0)-A^2(\infty)}{\pi}\tag{5}$$
which finally results in
$$|r_h(t)|\le \frac{A^2(0)-A^2(\infty)}{\pi |t|},\qquad t\neq 0\tag{6}$$
In sum, condition $$(1)$$ implies that the deterministic auto-correlation of the corresponding impulse response must satisfy inequality $$(6)$$.
• that is very interesting. thanks – M.A Jul 30 '19 at 18:18
The obvious solution would be $$\frac{\partial A(\omega)}{\partial \omega } < 0$$
If you just have a table of numbers, that's probably the best you can do. Are you looking for any relationships to the poles and zeros or some other parametric description of the transfer function ?
If A($$\omega$$) has a global maximum at $$\omega=0$$, you might consider pre-emphasizing the signal, that removes the DC components and then you might be able to see some peaks in the spectra. Also, consider smoothing the spectra before finding the gradient, this will help eliminate the local noisy peaks. Gradient will give you peaks in the spectrum. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 29, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9520310759544373, "perplexity": 252.41010682559752}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243992514.37/warc/CC-MAIN-20210513204127-20210513234127-00299.warc.gz"} |
https://homework.cpm.org/category/CC/textbook/ccg/chapter/10/lesson/10.3.4/problem/10-153 | ### Home > CCG > Chapter 10 > Lesson 10.3.4 > Problem10-153
10-153.
From a batch of $500$ light bulbs, how many ways can three be tested to see if they are defective? ) Homework Help ✎
$_{500}C_3=20,708,500$ | {"extraction_info": {"found_math": true, "script_math_tex": 2, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.823716402053833, "perplexity": 2714.1323723587057}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987828425.99/warc/CC-MAIN-20191023015841-20191023043341-00481.warc.gz"} |
http://mathhelpforum.com/differential-geometry/172977-complex-analysis-proof.html | 1. ## Complex Analysis Proof
Show that if a function f(z) = u(x,y) + iv(x,y) is entire, that the function conj(f(conj(z))) is entire. (Note that CR stands for Cauchy-Riemann)
Since f is entire, CR is satisfied:
so u_x = v_y and u_y = -v_x
this implies:
u_x = -(-v_y) and -u_y = -(-v_x)
this implies:
CR is satisfied for a function g(z) = u(x,-y) - iv(x,-y)
but g(z) = conj(f(conj(z)))
this implies:
CR is satisfied for conj(f(conj(z)))
Since f is entire, the partial derivatives are continuous
this implies:
conj(f(conj(z))) is entire.
2. That is correct. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8223293423652649, "perplexity": 6416.704085650498}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814393.4/warc/CC-MAIN-20180223035527-20180223055527-00265.warc.gz"} |
https://physics.stackexchange.com/questions/350909/can-people-create-single-photon-in-the-laboratory | # Can people create single photon in the laboratory?
Can a single photon be created in the laboratory? How do people make sure that they have really created a single photon?
• Relevant reading: en.wikipedia.org/wiki/Single-photon_source – QtizedQ Aug 8 '17 at 13:44
• More on single photon. – Qmechanic Aug 8 '17 at 13:45
• Would it count, in your opinion, if the photon were a microwave frequency charge oscillating in a metal? – DanielSank Aug 8 '17 at 15:23
• @DanielSank Photon is a charge? Do you mean photon produced from a charge oscillating in the microwave frequency range? But how would you make sure that you are producing single photon? – mithusengupta123 Aug 8 '17 at 15:43
• I'm talking about a metallic microwave resonator. This resonator supports quantized number of excitations at a particular frequency. We do call these "photons" even though they are oscillations of charge rather than a chargeless electromagnetic field. – DanielSank Aug 8 '17 at 15:48
You are absolutely right to focus on the detection aspect. It may surprise you that the physics community was convinced of the existence of the photon since the early 20's after Compton's experiment but that we had to wait until the 70's for a single photon to be actually "seen". So how can we demonstrate that we have one and only one photon?
# A photon cannot be split
The trick is to use a beam splitter, i.e. a half-silvered mirror. A classical light wave incident on the mirror will see half its intensity reflected and the other half transmitted. The very definition of a photon is that it cannot be split. Thus a single photon will either be reflected, or be transmitted, but never go both ways at once. Moreover to match the intensity law, the probabilities shall be 50/50 for the two paths. An experimental setup can be sketched as follow.
The photodetectors are fast enough to precisely record the time of detection. One then plots the number of clicks in one detector and the other as a function of the delay $\tau$ between the clicks. We expect the count to fall toward zero as $\tau$ goes to zero if we truly have a single photon as it cannot end up in both detectors at once. Conversely, as $\tau$ increases, we expect to see this number of clicks rising as the time window becomes large enough for two or more successive photons to hit different detectors. This is exactly what experiments shows. Here is a plot from [KDM77]
The dip near $\tau=0$ is called the anti-bunching effect. The value zero is not reached because there is an experimental uncertainty on the delay, which therefore is never truly zero. Thus, in effect, there is never only one photon in the experimental setup. This experiment rules out a pure wave theory of light for the reason given in the opening of this answer: the impossibility to explain why we do not get coincident clicks independently of the delay since half of the wave would take each path and each half would hit its respective photodetector at the same time. On the contrary, the result is clearly predicted if there are quanta of light.
Credit has to be given to Clauser [Clau74] for the first investigation of this kind of physics. The title of that article is actually revealing in itself: it may come as a surprise as we have been widely told that Einstein had proven the existence of the photon in that very photo-electric effect in his famous 1905 article but as Clauser explains it well in his introduction this is actually not the case. This subject has actually been thoroughly discussed on this Physics Q&A here: see especially the answer written by @ArnoldNeumaier but there are plenty of good arguments and references throughout the page. Another illustration of the saddening gap between teaching and popularisation of physics on one hand, and actual physics on the other hand, but I digress.
It should be noted that the arguments pushed forward by this type of experiment are, in a way, similar to the example of the diffraction pattern built one photon at a time given in @annav's answer: we could say that Clauser-style of experiment discriminate temporarily whereas the diffraction one-at-a-time discriminates spatially, as in a pure wave theory of light, however weak is the incoming signal in the diffractometer, some intensity will reach every point of the screen.
# Heralding
After those experiments, researchers searched for a way to make sure one photon and one photon only was in the optical system. Some new idea was necessary as can be seen by the following argument: even if the delay $\tau$ is made so small that the coincident count on both detector is only from one photon, we would only know that one photon was in the optical system. Instead, we would like to know that one photon is going to enter the optical system, so that we can then for sure make various experiment on it. Two teams made a breakthrough in 1986, Hong and Mandel [HM86] on one hand, and Grangier, Roger, and Aspect [GRA86] on the other hand. Their experiments can be summarised as follow:
• a source producing two beams of light (back to back for Grangier et al, on two concentric cones for Hong et al; the physical processes at work are completely different but it does not matter at the level of this exposition);
• an optical system to send one beam onto an optical path P ending in a photodetector A and the other one onto a different optical path Q.
The idea is that if the source is actually a source of pairs of photons such that each photon of the pair is emitted nearly at the same time, then the arrival of one photon on A will guarantee that there is one photon and one photon only on the path Q. Thus the photon arriving at A is the "herald" for the other one, hence the name of this technique, heralding. But now, you may say that we are back to assume single photons but in fact both teams did perform complementary analysis convincingly pointing toward that conclusion.
## Classical wave theory is ruled out
Grangier et al performed added one element: on the path Q, they put a beamsplitter sending the reflected beam to a photodetector B' and the transmitted one to another one B'' in a setup similar to Clauser's experiment above. But here, a hit on A opens B' and B'' for counting for a short duration $w$ of about 10 nanoseconds (we say that B' and B'' are gated by A). Then they performed three counts: the hit rate $N$ on A, $N'$ on B', $N''$ on B'', and the coincident hit rate $N_c$ on B' and B''.
The prediction of quantum optics in terms of pairs of photons is easy to see: as the number of photons $Nw$ hitting A during a gate decreases toward 0, the number of photons arriving at the beamsplitter will also decrease, toward 1. Then by a similar reasoning as for Clauser's experiment above, we conclude that the number of coincident photons $N_cw$ will decrease toward 0 whereas the number of photons hitting respectively B and B' will decrease toward 1.
On the other hand, Grangier et al considered the prediction of classical wave theory. It can be shown that the rates must abide to the following inequality:
$$\frac{N_c}{N} \ge \frac{N'}{N}\frac{N''}{N}.$$
So they plotted the ratio $\alpha$ of the two sides of this inequality
$$\alpha = \frac{N_cN}{N'N''}$$
versus the number of hits $Nw$ during the opening of the gate by A. A quantum mechanical description predicts that $\alpha$ goes to 0 as $Nw$ goes to 0, as we have just explained. Here is their result:
The dotted line is the classical limit $\alpha=1$, the curve the full quantum mechanical prediction taking into account all the experimental details, and the bars the measurements. Very clearly, the classical behaviour is ruled out whereas the quantum mechanical one is supported by data.
Grangier et al could not conclude more than that because their pairs of photons had far too broad of distribution of delay between the emission of each member of the pair: half of the pairs had their photons emitted at least 5 nanoseconds apart. It came to Hong et al to really prove they had only a single photon.
## A single photon at last
What Hong and Mandel did is conceptually much simpler: in their setup, they put a single photodetector B on the path Q. Then when A is triggered, it opens a gate on B for 20 ns. Then they count the number $m$ of hits on B while the gate is opened. After many repeat, they get a distribution for $m$. The efficiency of the photodetector B being small, for most of the gates, $m=0$. Then $m>2$ is nearly zero. With the number of times $m=1$ was obtained, they could then work it backward what was the number of photons hitting B when A is triggered. Their result was: $1.06\pm10\%$! Their advantage over Grangier et al was that the two photons of each pair were emitted within less than a 100 picoseconds, i.e. a factor 10 better (they did measure this in another experiment).
# Where to go next
I have basically only answered your second question about how to make sure we have single photons. I have partially answered your first question, as heralding can be used in practice to produce single photons, as explained. But since the 80's, several new techniques have emerged to produced photons on demand, very schematically, be preventing the source to emit until some action is done on it. There is quite an array of methods, based on single atoms, ions or molecules, on so-called quantum dots, on so-called colour centres (in diamond), etc. A comprehensive, recent, and relatively pedestrian review of the field can be found in [EFMP11], and I will lazily point the readers to it, shamelessly dropping the ball here!
[Clau74] John F. Clauser. Experimental distinction between the quantum and classical field-theoretic predictions for the photoelectric effect. Phys. Rev. D, 9:853–860, Feb 1974.
[KDM77] H. J. Kimble, M. Dagenais, and L. Mandel. Photon antibunching in resonance fluorescence. Phys. Rev. Lett., 39:691–695, Sep 1977, author eprint.
[HM86] C. K. Hong and L. Mandel. Experimental realization of a localized one-photon state. Phys. Rev. Lett., 56:58–60, Jan 1986.
[GRA86] P. Grangier, G. Roger, and A. Aspect. Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences. Europhys. Lett., 1(4):173, 1986, author eprint.
[EFMP11] M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov. Invited review article: Single-photon sources and detectors. Rev. Sci. Instrum., 82(7):071101, 2011, NIST eprint.
• This is far and away the best answer on this thread. – Emilio Pisanty Oct 23 '17 at 8:21
• Well it does not seem to answer the specific question "How do people make sure that they have really created a single photon? " It still is a statistical accumulation interpreted as single photon accumulation. – anna v Oct 23 '17 at 9:58
• Nowhere in this experiments are single photons. The experiment works with laser light, which is a coherent state, while single photons are by definition in a Fock state. Your setup must be modified (using parametric downconversion) to get entangled photon pairs, of which the detection of one in one of the paths heralds that the second path also contains a single photon (after detection of the first). – Arnold Neumaier Oct 23 '17 at 10:16
• @ArnoldNeumaier Yes, that's what I meant when I wrote the counts don't actually go to zero at zero delay but I did not elaborate enough. I'll make a correction. And yes, as stated at the end of the answer, I am planning to explain heralding, which was the next step in quantum optics after the Clauser-style argument I reported. – user154997 Oct 23 '17 at 11:18
• and only the heralding guarantees that one has a single photon in flight. A detection event (click of the counter) at best records a dead (no longer existent) photon, but in fact is no evidence of the photon, as a detector responds in terms of clicks also to a classical e/m field (though with a different distribution. Clauser's work therefore demonstrates not single photons but only nonclassical behavior of light. – Arnold Neumaier Oct 23 '17 at 12:33
Note that the question posed asked for the creation of single photons, not for their destruction. Thus discussions of photon detection are irrelevant for the question asked.
There are two kinds of single photons produced in the lab: "photons on demand" (see, e.g., Section 2.13 of http://lanl.arxiv.org/pdf/0810.1019v2 ) - which are truly single, and "heralded photons" (see, e.g., https://arxiv.org/pdf/quant-ph/0408093 ) - entangled photon pairs of which one partner is detected, so that it is known (after the detection time) that the other partner is now single. There are many articles discussing details; the two references given are only the tip of an iceberg. Google the terms in quotation marks to find many more references....
• Ok, I know that there are different people with different standards for the answer and there are too many comments that should be posted as an answer. But... come on! "Google those words"? – OON Oct 23 '17 at 13:29
• @OON: I added sample references. – Arnold Neumaier Oct 23 '17 at 13:40
This double slit experiment uses single photons.
In 2003, A. Weis and R. Wynands at the University of Bonn (Germany) designed a lecture demonstration experiment of single photon interference from a double slit. Light from a laser pointer was so strongly attenuated that at each instant there was only a single photon between the double slit and the detector. The diffracted light was recorded by a single photon imaging camera consisting of an image intensifier (multichannel plate, MCP) followed by phosphor screen and a CCD camera. When adding consecutive camera frames one sees the gradual appearance of the smooth classical interference pattern
Each dot is the footprint of a single photon. The area covered by the footprint is much smaller than the area of the laser beam passing through the two slits,(which characterizes the classical laser beam,) as seen by their spread. It is a footprint a classical particle would be expected to leave in an interactive plane. This clearly shows the particle side of the quantum mechanical entity called "photon" The accumulated interference pattern is the quantum mechanical probability distribution of detection, as well as the classical interference pattern of a laser beam.
This video also is instructive .]3
How do people make sure that they have really created a single photon? By excluding other possibilities that the signal might have come from, and repeating the experiment until optimal parameters are found. In the above experiment by slowly reducing the intensity of the laser beam to "no signal" , to "single hit".
What nobody has mentioned is high energy photons. For their detection and measurement of energy and direction large sophisticated electromagnetic calorimeters catch tracks which interact in the detector and radiate a lot of electromagnetic energy, as electrons and photons. Here are two photons, as in this CMS reconstruction of events from measurements in the detector .
Higgs to gamma gamma candidate event.
These are the two green histograms after an extrapolated dotted line connected to the event vertex. They are idetified as photons because there is no signal in the tracking detectors , and suddenly electromagnetic energy is deposited in the electromagnetic calorimeter.
• Technically everything uses single photons. – Bill Alsept Oct 21 '17 at 4:55
• @BillAlsept yes, classical EM is emergent. This is a demonstration of the single photons it emerges from, but the experiment did end up with single photons. btw I appreciate your answer because it gives the state of the art at present. – anna v Oct 21 '17 at 5:11
• -1. This isn't a single-photon source as the term is traditionally understood in quantum optics. Single-photon sources are normally required to produce the one-excitation Fock state (either heralded or on demand), whereas this answer's reference uses a coherent state with low flux. The two are very different. – Emilio Pisanty Oct 23 '17 at 8:18
• @EmilioPisanty A photon is a photon. It does not come with a degree in quantum optics. The question does not ask about a single photon source, but of the creation of "a photon" and data shows this and trumps assumptions. – anna v Oct 23 '17 at 9:23
• @annav Do you know what happened to my answer? This is not the first time I have had an answer, question or comment just disappear without any kind of Explanation. Just wondering. Thanks – Bill Alsept Oct 23 '17 at 16:06
Having built Cherenkov detectors, I have had experience with single photons: for instance, a minimum ionizing particle in air will produce a few photons per meter because of scintillation. A single photon is then detected in the Cherenkov's photomultiplier tube as background noise. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8282321095466614, "perplexity": 727.9930901954461}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107889574.66/warc/CC-MAIN-20201025154704-20201025184704-00218.warc.gz"} |
https://zhangruochi.com/Operations-on-word-vectors-Debiasing/2019/03/28/ | # Operations on word vectors
Welcome to your first assignment of this week!
Because word embeddings are very computionally expensive to train, most ML practitioners will load a pre-trained set of embeddings.
After this assignment you will be able to:
• Load pre-trained word vectors, and measure similarity using cosine similarity
• Use word embeddings to solve word analogy problems such as Man is to Woman as King is to __.
• Modify word embeddings to reduce their gender bias
Let’s get started! Run the following cell to load the packages you will need.
Using TensorFlow backend.
Next, lets load the word vectors. For this assignment, we will use 50-dimensional GloVe vectors to represent words. Run the following cell to load the word_to_vec_map.
• words: set of words in the vocabulary.
• word_to_vec_map: dictionary mapping words to their GloVe vector representation.
You’ve seen that one-hot vectors do not do a good job cpaturing what words are similar. GloVe vectors provide much more useful information about the meaning of individual words. Lets now see how you can use GloVe vectors to decide how similar two words are.
# 1 - Cosine similarity
To measure how similar two words are, we need a way to measure the degree of similarity between two embedding vectors for the two words. Given two vectors $u$ and $v$, cosine similarity is defined as follows:
where $u.v$ is the dot product (or inner product) of two vectors, $||u||_2$ is the norm (or length) of the vector $u$, and $\theta$ is the angle between $u$ and $v$. This similarity depends on the angle between $u$ and $v$. If $u$ and $v$ are very similar, their cosine similarity will be close to 1; if they are dissimilar, the cosine similarity will take a smaller value.
**Figure 1**: The cosine of the angle between two vectors is a measure of how similar they are
Exercise: Implement the function cosine_similarity() to evaluate similarity between word vectors.
Reminder: The norm of $u$ is defined as $||u||_2 = \sqrt{\sum_{i=1}^{n} u_i^2}$
cosine_similarity(father, mother) = 0.890903844289
cosine_similarity(ball, crocodile) = 0.274392462614
cosine_similarity(france - paris, rome - italy) = -0.675147930817
Expected Output:
**cosine_similarity(father, mother)** = 0.890904 **cosine_similarity(ball, crocodile)** = 0.274392 **cosine_similarity(france - paris, rome - italy)** = -0.675148
After you get the correct expected output, please feel free to modify the inputs and measure the cosine similarity between other pairs of words! Playing around the cosine similarity of other inputs will give you a better sense of how word vectors behave.
## 2 - Word analogy task
In the word analogy task, we complete the sentence a is to b as c is to ____. An example is man is to woman as king is to queen. In detail, we are trying to find a word d, such that the associated word vectors $e_a, e_b, e_c, e_d$ are related in the following manner: $e_b - e_a \approx e_d - e_c$. We will measure the similarity between $e_b - e_a$ and $e_d - e_c$ using cosine similarity.
Exercise: Complete the code below to be able to perform word analogies!
Run the cell below to test your code, this may take 1-2 minutes.
italy -> italian :: spain -> spanish
india -> delhi :: japan -> tokyo
man -> woman :: boy -> girl
small -> smaller :: large -> larger
Expected Output:
**italy -> italian** :: spain -> spanish **india -> delhi** :: japan -> tokyo **man -> woman ** :: boy -> girl **small -> smaller ** :: large -> larger
Once you get the correct expected output, please feel free to modify the input cells above to test your own analogies. Try to find some other analogy pairs that do work, but also find some where the algorithm doesn’t give the right answer: For example, you can try small->smaller as big->?.
### Congratulations!
You’ve come to the end of this assignment. Here are the main points you should remember:
• Cosine similarity a good way to compare similarity between pairs of word vectors. (Though L2 distance works too.)
• For NLP applications, using a pre-trained set of word vectors from the internet is often a good way to get started.
Even though you have finished the graded portions, we recommend you take a look too at the rest of this notebook.
Congratulations on finishing the graded portions of this notebook!
## 3 - Debiasing word vectors (OPTIONAL/UNGRADED)
In the following exercise, you will examine gender biases that can be reflected in a word embedding, and explore algorithms for reducing the bias. In addition to learning about the topic of debiasing, this exercise will also help hone your intuition about what word vectors are doing. This section involves a bit of linear algebra, though you can probably complete it even without being expert in linear algebra, and we encourage you to give it a shot. This portion of the notebook is optional and is not graded.
Lets first see how the GloVe word embeddings relate to gender. You will first compute a vector $g = e_{woman}-e_{man}$, where $e_{woman}$ represents the word vector corresponding to the word woman, and $e_{man}$ corresponds to the word vector corresponding to the word man. The resulting vector $g$ roughly encodes the concept of “gender”. (You might get a more accurate representation if you compute $g_1 = e_{mother}-e_{father}$, $g_2 = e_{girl}-e_{boy}$, etc. and average over them. But just using $e_{woman}-e_{man}$ will give good enough results for now.)
[-0.087144 0.2182 -0.40986 -0.03922 -0.1032 0.94165
-0.06042 0.32988 0.46144 -0.35962 0.31102 -0.86824
0.96006 0.01073 0.24337 0.08193 -1.02722 -0.21122
0.695044 -0.00222 0.29106 0.5053 -0.099454 0.40445
0.30181 0.1355 -0.0606 -0.07131 -0.19245 -0.06115
-0.3204 0.07165 -0.13337 -0.25068714 -0.14293 -0.224957
-0.149 0.048882 0.12191 -0.27362 -0.165476 -0.20426
0.54376 -0.271425 -0.10245 -0.32108 0.2516 -0.33455
-0.04371 0.01258 ]
Now, you will consider the cosine similarity of different words with $g$. Consider what a positive value of similarity means vs a negative cosine similarity.
List of names and their similarities with constructed vector:
john -0.23163356146
marie 0.315597935396
sophie 0.318687898594
ronaldo -0.312447968503
priya 0.17632041839
rahul -0.169154710392
danielle 0.243932992163
reza -0.079304296722
katy 0.283106865957
yasmin 0.233138577679
As you can see, female first names tend to have a positive cosine similarity with our constructed vector $g$, while male first names tend to have a negative cosine similarity. This is not suprising, and the result seems acceptable.
But let’s try with some other words.
Other words and their similarities:
lipstick 0.276919162564
guns -0.18884855679
science -0.0608290654093
arts 0.00818931238588
literature 0.0647250443346
warrior -0.209201646411
doctor 0.118952894109
tree -0.0708939917548
receptionist 0.330779417506
technology -0.131937324476
fashion 0.0356389462577
teacher 0.179209234318
engineer -0.0803928049452
pilot 0.00107644989919
computer -0.103303588739
singer 0.185005181365
Do you notice anything surprising? It is astonishing how these results reflect certain unhealthy gender stereotypes. For example, “computer” is closer to “man” while “literature” is closer to “woman”. Ouch!
We’ll see below how to reduce the bias of these vectors, using an algorithm due to Boliukbasi et al., 2016. Note that some word pairs such as “actor”/“actress” or “grandmother”/“grandfather” should remain gender specific, while other words such as “receptionist” or “technology” should be neutralized, i.e. not be gender-related. You will have to treat these two type of words differently when debiasing.
### 3.1 - Neutralize bias for non-gender specific words
The figure below should help you visualize what neutralizing does. If you’re using a 50-dimensional word embedding, the 50 dimensional space can be split into two parts: The bias-direction $g$, and the remaining 49 dimensions, which we’ll call $g_{\perp}$. In linear algebra, we say that the 49 dimensional $g_{\perp}$ is perpendicular (or “othogonal”) to $g$, meaning it is at 90 degrees to $g$. The neutralization step takes a vector such as $e_{receptionist}$ and zeros out the component in the direction of $g$, giving us $e_{receptionist}^{debiased}$.
Even though $g_{\perp}$ is 49 dimensional, given the limitations of what we can draw on a screen, we illustrate it using a 1 dimensional axis below.
**Figure 2**: The word vector for "receptionist" represented before and after applying the neutralize operation.
Exercise: Implement neutralize() to remove the bias of words such as “receptionist” or “scientist”. Given an input embedding $e$, you can use the following formulas to compute $e^{debiased}$:
If you are an expert in linear algebra, you may recognize $e^{bias_component}$ as the projection of $e$ onto the direction $g$. If you’re not an expert in linear algebra, don’t worry about this.
cosine similarity between receptionist and g, before neutralizing: 0.330779417506
cosine similarity between receptionist and g, after neutralizing: -0.48975521526
Expected Output: The second result is essentially 0, up to numerical roundof (on the order of $10^{-17}$).
**cosine similarity between receptionist and g, before neutralizing:** : 0.330779 **cosine similarity between receptionist and g, after neutralizing:** : -3.26733e-17
### 3.2 - Equalization algorithm for gender-specific words
Next, lets see how debiasing can also be applied to word pairs such as “actress” and “actor.” Equalization is applied to pairs of words that you might want to have differ only through the gender property. As a concrete example, suppose that “actress” is closer to “babysit” than “actor.” By applying neutralizing to “babysit” we can reduce the gender-stereotype associated with babysitting. But this still does not guarantee that “actor” and “actress” are equidistant from “babysit.” The equalization algorithm takes care of this.
The key idea behind equalization is to make sure that a particular pair of words are equi-distant from the 49-dimensional $g_\perp$. The equalization step also ensures that the two equalized steps are now the same distance from $e_{receptionist}^{debiased}$, or from any other work that has been neutralized. In pictures, this is how equalization works:
The derivation of the linear algebra to do this is a bit more complex. (See Bolukbasi et al., 2016 for details.) But the key equations are:
Exercise: Implement the function below. Use the equations above to get the final equalized version of the pair of words. Good luck!
Expected Output:
cosine similarities before equalizing:
**cosine_similarity(word_to_vec_map["man"], gender)** = -0.117111 **cosine_similarity(word_to_vec_map["woman"], gender)** = 0.356666
cosine similarities after equalizing:
**cosine_similarity(u1, gender)** = -0.700436 **cosine_similarity(u2, gender)** = 0.700436
Please feel free to play with the input words in the cell above, to apply equalization to other pairs of words.
These debiasing algorithms are very helpful for reducing bias, but are not perfect and do not eliminate all traces of bias. For example, one weakness of this implementation was that the bias direction $g$ was defined using only the pair of words _woman_ and _man_. As discussed earlier, if $g$ were defined by computing $g_1 = e_{woman} - e_{man}$; $g_2 = e_{mother} - e_{father}$; $g_3 = e_{girl} - e_{boy}$; and so on and averaging over them, you would obtain a better estimate of the “gender” dimension in the 50 dimensional word embedding space. Feel free to play with such variants as well.
### Congratulations
You have come to the end of this notebook, and have seen a lot of the ways that word vectors can be used as well as modified.
Congratulations on finishing this notebook!
References:
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http://jrehabilhealth.com/articles/101154.html | # Misconceptions About the Management of Low Back Pain: A Brief Note for Physiotherapists
AUTHORS
Musa Sani Danazumi 1 , 2 , *
1 Department of Physiotherapy, Federal Medical Center, Nguru, Nigeria
2 Department of Physiotherapy, Faculty of Allied Health Sciences, College of Health Sciences, Bayero University, Kano, Nigeria
How to Cite: Danazumi M S. Misconceptions About the Management of Low Back Pain: A Brief Note for Physiotherapists, Middle East J Rehabil Health Stud. Online ahead of Print ; 7(2):e101154. doi: 10.5812/mejrh.101154.
ARTICLE INFORMATION
Middle East Journal of Rehabilitation and Health Studies: 7 (2); e101154
Published Online: March 17, 2020
Article Type: Review Article
Revised: March 2, 2020
Accepted: March 4, 2020
Crossmark
CHECKING
### Abstract
Low back pain (LBP) is one of the most frequently occurring conditions, affecting many individuals worldwide. The best ways to manage LBP usually contradict the thoughts of the professionals, the patients, and the general public. No musculoskeletal pain is more burdened with serious misconceptions than LBP and the persistence of these misconceptions can impede the way treatment is being administered, which may also impair recovery and promote unnecessary suffering and disability. Given the myths about low back pain, there is the need to acknowledge some of its riddles particularly those pertaining to treatment and look for positive solutions. As professionals, each physiotherapist uses his or her own guiding principles and choices as evidence. However, our guiding principles and choices are important, but they usually bring partiality in decision making. It is essential to examine and identify our core values so that they do not subdue other sources of evidence.
Keywords
Copyright © 2020, Middle East Journal of Rehabilitation and Health Studies. This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/) which permits copy and redistribute the material just in noncommercial usages, provided the original work is properly cited.
### 1. Introduction
Low back pain (LBP) is a serious public health problem and is one of the leading symptomatic causes of consulting the health care system (1). Low back pain affects approximately 84% of individuals at some point in their lives, leading to high rates of physical inactivity, work absence, and decreased quality of life (2). The economic burden of LBP is extremely high (3). Even though the prognosis for most individuals with sudden onset LBP is favorable, continuing or occurring pain and activity limitations are very usual (4-6). LBP is one of the most common musculoskeletal disorders seen in physical therapy practice (7).
LBP is managed using many interventions including surgical treatment (8), non-surgical treatment (9) and a number of many modalities combined (10). Perhaps the reason so many interventions exist for LBP is that none of them seems to be effective in all types of LBP (11). One of the main issues in managing individuals with LBP is the inability to identify which treatments to apply to which individuals (12). Why does manipulation work for some patients but not others? Why traction resolves some patients' symptoms and exacerbates others? Why surgery works for others and deteriorates others? Why some patients have pain and their radiological investigations showed normal studies? While it is often thought by some physiotherapists (PTs) that there are no answers to these questions, precise answers do exist elsewhere (13-16).
The medical model tells us that diagnosis drives treatment and this is very true. For example, a patient with back pain due to lumbar disc herniation would receive a different form of treatment (9) as would a patient with lumbar spinal stenosis (17). A patient with back pain due to lumbar spondylolysis/spondylolisthesis would receive a different form of treatment (18) as would a patient with piriformis syndrome (19). A patient with non-specific low back pain would receive a different form of treatment (20) as would a patient with sacroiliac joint dysfunction (21). While often portrayed as homogenous, a pathoanatomical diagnosis is only available in a very few instances of LBP (22).
Several studies (23-25) have indicated that 80% - 90% of patients with low-back pain will spontaneously recover within 3 months. In light of this statement, one must question the odds of the spontaneous recovery of a ruptured anterior cruciate ligament or of a flexor tendon tear in the same time period. In addition, there seems to be no consensus regarding the issue of spontaneous recovery and this sounds unarguably very clear to any professional who had treated a number of patients who had defied the so-called natural healing. While the gross exaggeration is obvious, one must question the validity of such statements instead of accepting them at face value.
Misconceptions regarding back pain can be unhelpful. Correcting unhelpful myths is a progressive step and therefore, it is important to acknowledge some of the misunderstandings that currently exist in the field of LBP and clarify them. In this article, the current misconceptions about the physiotherapy management of LBP have been examined and discussed.
### 2. The Misconceptions in the Literature
#### 2.1. The use of Evidence-Based Practice
Physiotherapists (PTs) have justifiable concerns about the possibility of the current evidence to change the way they practice (26-28). While the concern about evidence-based practice is considered to be extremely high (29, 30), it is unlikely that PTs will ever have solid evidence for every technique they use, due to the research that would be required and the likelihood that techniques may work best combined with other techniques, rather than in isolation (31). But it is likely that PTs will have evidence that informs them of what techniques or approaches are most effective for a particular outcome or complaint, and be able to base their treatments around elements from that approach (32). However, it would be imprudent to abandon techniques with a long history of anecdotal evidence of efficacy but currently lacking in scientific support, for these techniques may well be effective for many patients and conditions. But when there is growing evidence of disproof, such as evidence of no therapeutic benefit, or the lack of reliability and validity of a diagnostic approach, PTs have an intellectual and ethical duty to reconsider their practice (32).
#### 2.2. Prescription of Imaging
Schwartz and colleagues (33) indicated that the amount of money spent yearly on imaging for less worrisome back pains ranged from $82 million to$226 million. In addition, the authors also indicated that this amount does not cover costs attached to testing during follow-ups and treatments due to imaging results. Because of the fact that X-rays are not very sensitive in the identification of serious spinal problems, magnetic resonance imaging (MRI) and computerized tomography (CT) have been largely utilized for LBP. However, much of the utilization happens outside the scope of clinical practice guidelines (CPGs) (34).
Some findings, such as disc or facet joint pathologies have been identified as the causative agents for LBP; however, these problems are also present in asymptomatic individuals and they increase with age (35). The MRI is very sensitive in identifying senile problems in the spine but, literature has shown no association with LBP (36, 37). These issues have led to the production of CPGs about the use of imaging in individuals with LBP (38, 39). The Board of Internal Medicine’s Choosing Wisely campaign indicated the use of MRI and CT imaging with caution (39). The American Academy of Family Physicians advised against imaging for LBP within the first 6 weeks of onset except when red flags exist (38). The American Association of Neurological Surgeons and Congress of Neurological Surgeons advised against imaging for mechanical LBP that is not accompanied by red flags (40). In addition, the majority of the scans involved exposure to radiations and only a few of them assist in the management of the patients (41). A quick and valid clinical evaluation is frequently sufficient to determine the few cases for whom imaging is needed (41).
#### 2.3. Prescription of Surgery
Only a few numbers of individuals with LBP need surgery. An absolute indication for lumbar surgery is a progressive neurological deficit commonly associated with the cauda equina syndrome or severe vertebral collapse or fracture (42). There is also evidence to suggest that long-term outcomes after surgery and conservative management are generally similar and surgery should not be performed unless there are no other options (9). Individuals with LBP can decrease their suffering by active treatments and understanding what pain means, and what factors are contributing to their pain (20). This can help them manage themselves without undergoing surgery.
In most instances, the primary concern of surgery is to relieve nerve root compression; but other issues, such as muscle weaknesses tend to be difficult to treat using surgery. In this regard, the general consensus for LBP management is to start with conservative treatment for 6 - 12 weeks (23, 24). If the patient did not improve during this period, then surgery may be performed.
#### 2.4. The Narrow Scope of Thought
Physiotherapists and other appropriately trained healthcare professionals, as a general rule, are able to treat patients more frequently and for longer durations than many other medical practitioners (7). For that reason, PTs tend to have a larger array of treatment options at their disposal which affords them the opportunity to use multiple techniques and/or interventions in their treatments and to use specific interventions in multiple ways (9, 17-21). However, PTs treat spinal dysfunction as if it were an entity separate from the rest of the body which may be regarded as a narrow scope of thought.
Recently, Myers (43) demonstrated that the human body has network connections or continuities that function as one unit which are called myofascial meridians. According to Myers, fascial meridians are tensegrities with tensile myofascial bands that comprise a single continuous structure. If any part of this structure is deformed or distorted, negative stresses may be imposed on distant structures (body-wide), and on the structures that it divides, and connects (44). This evidence suggests that any tendency to think of a local dysfunction as existing in isolation should be discouraged as body structures are tightly and symbiotically interrelated, and given shape, cohesion and functional ability by the fascia (45). In addition, there is evidence to suggest that fascia accommodates to chronic stress patterns and deforms itself; something that often precedes deformity of osseous and cartilaginous structures in chronic diseases (44, 45).
Moreover, postural asymmetries caused by myofascial dysfunctions are among the most infrequently misdiagnosed situations in the physical therapy environment. While, this may sound very awkward to some highly trained/skillful PTs, but a significant number of others (mostly novice) would acknowledge that some prominent back conditions such as the piriformis syndrome and the crossed syndrome (upper and lower) patterns have been largely neglected. Piriformis syndrome produces ischemia of the lower limbs, sacroiliac joint dysfunction, and pain around the hip (second attachment) through relative fixation of the sacrum (first attachment) (46). Upper crossed syndrome (extensor muscles of the neck shorten and tighten as the deep neck flexors weaken-forward head posture) leads to cervical pain, referred pain to the shoulders, arm, and chest and a decrease in respiratory function (47). Lower crossed syndrome (tight erector spinae/ilipsoas and weak abdominals/gluteus) leads to forward pelvis tilt, hip flexion, increased lumbar lordosis and stress at L5-S1 accompanied by back pain and irritation (47). When these syndromes are not properly examined and corrected they may lead to serious regional interdependence which may ultimately lead to permanent postural deformities and/or bony dysfunctions (48).
#### 2.5. The Use of Spinal Manipulation and/or Mobilization
A significant number of individuals with LBP may have facet joint problems and they, therefore, need spinal manipulation. However, LBP, especially in the acute stage, can be easily provoked using spinal manipulation. In addition, there is also evidence to withhold manipulation when neurological symptoms exist because the pathology may be aggravated (12). On the other hand, spinal mobilization may also be used to treat LBP because it does not cause a flare-up of pain in many instances compared to manipulation and many studies (1, 49, 50) have indicated its therapeutic benefit.
However, despite the overwhelming literature reporting the therapeutic efficacy of spinal manipulation and mobilization individually, there seems to be a scarcity of evidence that compares the efficacy of both techniques in individuals with LBP, particularly those having neurological symptoms (12). Therefore, it is only when head to head comparison of spinal manipulation and mobilization is conducted, that patients who respond favorably to either of the techniques will be revealed. This will also give an insight into which technique to administer to individuals who have LBP with/without neurological symptoms.
### 3. Conclusions
Misconceptions about the management of low back pain can be very unhelpful and their persistence can impede the way treatment is being administered, which may also impede recovery and promote unnecessary suffering and disability. In addition, the importance of research in the physiotherapy profession is growing and because the academic environment in relation to health has changed over the years, there is the need for research to validate the efficacy of many low back pain interventions. Furthermore, there is also an academic quest to understand the nature of all types of low back disorders and why (or if) a particular treatment works.
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http://iac3.uib.es/research/astrophysics/ | # Astrophysics
### Overview of the research activity
The research activities of the Solar Physics Group are related with the Solar Atmosphere. In particular, the group performs research on the Seismology of coronal magnetic structures (loops, prominences, etc.); on the behaviour of solar activity (Asymmetries, periodicities, chaos, etc.), on MHD waves and instabilities in the solar corona and coronal rain dynamics.
Research lines:
1. Seismology of the Solar Corona: MHD seismology is a method of remote diagnostics of plasma structures combining observations of oscillatory motions with an interpretation in terms of MHD waves.
2. Behaviour of Solar Activity: Solar activity is produced by the emergence of magnetic flux through the photosphere forming active regions which include sunspots. Apart from sunspots, other manifestations of solar activity are solar flares, prominences, CME’s, etc. The behaviour of solar activity shows some particular features such as periodicities, asymmetries, lack of memory, etc which are worth to be investigated.
3. Waves and Instabilities in prominences: Prominence oscillations are commonly interpreted in terms of MHD waves, and this interpretation allows to perform prominence seismology. Furthermore, MHD instabilities are also observed in prominences and its interpretation would allow to understand the complex dynamics displayed by prominences
4. Coronal rain: Active region loops usually have temperatures of the order of 1 million K. But sometimes dense and cold (10.000 K) plasma blobs form high in these loops and start to fall under the action of the Sun’s gravity. The measured downward acceleration is considerably smaller than that of free-fall motion: at present we are interested in explaining this behaviour. In the future we plan to study other coronal rain features, e.g., its multi-thermal character or the conditions that lead to the formation of the cold condensations. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8273881077766418, "perplexity": 1868.265286107328}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039741192.34/warc/CC-MAIN-20181113020909-20181113042909-00175.warc.gz"} |
http://clay6.com/qa/41110/calculate-the-charge-carried-by-12-5-10-electrons- | Browse Questions
# Calculate the charge carried by $12.5 × 10^{18}$ electrons.
$\begin{array}{1 1}(A)\;2\;c\\ (B)\;4\;c \\(C)\;3\; c \\(D)\; 6\;c\end{array}$
$Q = 12.5 × 10^{18} × 1.6 × 10^{–19}$
$\quad=2c$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9919742345809937, "perplexity": 20515.779027485678}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170741.49/warc/CC-MAIN-20170219104610-00650-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://stats.stackexchange.com/questions/7146/analysing-wind-data-with-r | # Analysing wind data with R
Hi i am analaysing wind data for estimating energy from a wind turbine.
I have taken 10 years of wind data and graphed a histogram;
my second stage was to fit a Weibull distribution to the data.
I used R with the package lmom to compute the Weibul shape and scale this is the code i used:
>library(lmom)
wind.moments<-samlmu(as.numeric(pp$WS)) moments<-pelwei(wind.moments) x.wei<-rweibull(n=length(pp$WS), shape=moments["delta"], scale=moments["beta"])
hist(as.numeric(pp\$WS), freq=FALSE)
lines(density(x.wei), col="red", lwd=4)
It seems like there is some lag between the data and the density function; can you help me with this? Another question is can you help me in calculating the anual energy from the density function?
thank you
• About the picture, post to some image hosting and put a link -- I'll convert it into a pasted-in picture. – user88 Feb 13 '11 at 8:35
• +1, interesting question, you might find that soon you will have enough reputation :) – mpiktas Feb 13 '11 at 8:46
• judging from the graph, the problem is not the lag. What you have plotted is roughly goodness of fit. So it seems that Weibull distribution is not apropriate for your data. I see that there is a bunch up near zero, do you have zero values in your data? In that case you will need to model zero values separately. So first suggestion would be to try Weibull for non zero values. Also why Weibull, is there particular reason, some reference from similar work perhaps? – mpiktas Feb 13 '11 at 9:02
• note that 'lag' is a term used mainly in analysis of data in time, referring to one thing occurring after another. This isn't a lag - it's perhaps more accurately called a shift - or maybe an offset - but shift is probably more common for distributions, they shift and scale. – Spacedman Feb 13 '11 at 10:28
• be careful about using as.numeric(x) with factors; you actually want to use as.numeric(as.character(x)) to make sure you get the right number value for the factor. – Andy Clifton Oct 16 '16 at 23:10
lmom function pelwei fits a three parameter Weibull distribution, with location, scale and shape parameters. rweibull generates random numbers for a two-parameter Weibull distribution. You need to subtract the location parameter moments["zeta"]. That should give a better fit, but it doesn't appear it will give a good fit to your particular data.
I notice http://www.reuk.co.uk/Wind-Speed-Distribution-Weibull.htm says "Wind speeds in most of the world can be modelled using the Weibull Distribution.". Perhaps you're just unlucky and live in a part of the world where they can't!
• do you tink you can help me with my second question: calculating wind energy based on the density function? – eliavs Feb 13 '11 at 11:05
• I'm not a physicist and I don't know the necessary equations, but I imagine it will involve a numerical integral over the density. R's integrate() function may be useful for that. – onestop Feb 13 '11 at 12:48
• i know the equation my problam is i want to compute the percent of time the wind is at each speed – eliavs Feb 13 '11 at 14:18
• what i meAn is can you help me with the integration --> thank you – eliavs Feb 13 '11 at 14:45
I recreated your plot with data from http://hawaii.gov/dbedt/ert/winddata/krab0192.txt (I took the 1200 measurements). I got a decent fit of the data, generally using your code:
library(lmom)
wind.avg <- na.omit(as.numeric(daten[,"X12"]))
wind.moments<-samlmu(wind.avg)
moments<-pelwei(wind.moments)
x.wei<-rweibull(n=length(wind.avg), shape=moments["delta"], scale=moments["beta"])
hist(as.numeric(wind.avg), freq=FALSE)
lines(density(x.wei), col="red", lwd=4)
Sorry, I'm not shure were your problem could be, but I think you should be able to fit weibull to your data. What makes me suspicious is the bell-curve of your density plot, I have no idea where that came from.
Here are the moments I generated:
wind.moments
l_1 l_2 t_3 t_4
15.17287544 4.80372580 0.14963501 0.06954438
moments
zeta beta delta
0.516201 16.454233 1.745413
WTR to the annual output: I suppose I'd generate discrete values for the probability density function, multiply these values with the output function and sum it up. Alternatively, you could just use your raw data, multiply the values with the output function, sum it up and calculate the annual average, you should control for seasonality in a suitable way (e. g. make sure to use whole years, or to weight accordingly).
Here is the uncontrolled output (using the formula from http://www.articlesbase.com/diy-articles/determining-wind-turbine-annual-power-output-a-simple-formula-based-upon-blade-diameter-and-average-wind-speed-at-your-location-513080.html)
years <- length(wind.avg)/365
diameter <- 150
Power = (0.01328*diameter^2)*((wind.avg)^3)
(annual.power <- sum(Power)/years)
[1] 791828306
Here's a recent post at SO on wind turbines. My answer on that link has three links that you might be interested in:
https://stackoverflow.com/questions/4843194/r-language-sorting-data-into-ranges-averaging-ignore-outliers/4844783#4844783
I just checked one of the Weibull links in the above SO answer. For some reason, the link is down. Here are some links that provide the same basic information:
http://www.gso.uri.edu/ozone/
http://www.weru.ksu.edu/new_weru/publications/pdf/Comparison%20of%20the%20Weibull%20model%20with%20measured%20wind%20speed%20distributions%20for%20stochastic%20wind%20genera.pdf
http://www.kfupm.edu.sa/ri/publication/cer/41_JP_Weibull_parameters_for_wind_speed_distribution_in_Saudi_Arabia.pdf
http://journal.dogus.edu.tr/13026739/2008/cilt9/sayi1/M00195.pdf
http://www.eurojournals.com/ejsr_26_1_01.pdf
Also, from the power generated from wind, the seasonality is obvious.
I'm not sure if somebody has already made this point, but pelwei can actually be forced to work as a 2 parameter weibull function by adding in a fixed bound.
Insead of calling moments<-pelwei(wind.moments) you should simply call moments<-pelwei(wind.moments,bound=0)
you can always check what the zeta value is. If it's not 0 and you're using dweibull, you need to do something about it. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6790208220481873, "perplexity": 1031.2452439625667}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370505730.14/warc/CC-MAIN-20200401100029-20200401130029-00183.warc.gz"} |
http://lostinspacetime.blog/category/cosmology/simulation/ | ## Simulating the formation of large scale structrure in the universe
One of the beneficial consequences of adopting a cosmology based on an exochronous (i.e. timeless) metric, is that process of simulating the evolution of the universe becomes much easier. In fact the modelling of the accumulation and dispersion of gravitational potential can be achieved with a single line of computer code in an N-body particle-mesh simulation. This compares favourably to the complex Fast Fourier Transform methodology that is more commonly used in such models. This short video shows the simulation model in action. Starting from a totally uniform universe, we can see how matter (the yellow particles) starts to clump together into filaments and disks, which ultimately will go on to form galaxies. The simulation also shows the gravitational potential that is generated by matter (the red/purple dots), and in turn dictates how matter will move. This potential is, essentially, what cosmologists currently refer to as ‘Dark Matter’. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9532238841056824, "perplexity": 1120.4954146339787}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221212639.36/warc/CC-MAIN-20180817163057-20180817183057-00302.warc.gz"} |
https://www.gradesaver.com/textbooks/science/chemistry/chemistry-the-central-science-13th-edition/chapter-3-chemical-reactions-and-reaction-stoichiometry-exercises-page-114/3-19b | ## Chemistry: The Central Science (13th Edition)
$BaCO_3(s)\rightarrow BaO(s)+CO_2(g)$
Carbonate is $CO_3$. Oxide is $O$. The balanced equation is $BaCO_3(s)\rightarrow BaO(s)+CO_2(g)$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7196029424667358, "perplexity": 8180.8299789160565}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670255.18/warc/CC-MAIN-20191119195450-20191119223450-00550.warc.gz"} |
https://bigideasmathanswer.com/big-ideas-math-answers-grade-8-chapter-4/ | # Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations
Are you searching everywhere regarding the Big Ideas Math 8th Grade Answer Key Chapter 4 Graphing and Writing Linear Equations? If so, halt your search as this is the one-stop destination for all your needs. Practice using the Graphing and Writing Linear Equations Big Ideas Math Grade 8 Answers and understand the concepts easily. Begin your preparation right away and seek the homework help needed right after class in a matter of seconds.
## Big Ideas Math Book 8th Grade Answer Key Chapter 4 Graphing and Writing Linear Equations
Make the most out of the handy resources available for Big Ideas Math Ch 4 Graphing and Writing Linear Equations and stand out from the rest of the crowd. BIM Book 8th Grade Chapter 4 Solutions include questions belonging to Lessons 4.1 to 4.7, Cumulative Practice, Assessment Tests, Review Tests, etc. Big Ideas Math 8th Grade Chapter 4 Solution Key is given by subject experts after extensive research. Access the quick links over here during your preparation and get the assistance needed at the comfort of your home.
Performance Task
Lesson: 1 Graphing Linear Equations
Lesson: 2 Slope of a Line
Lesson: 3 Graphing Proportional Relationships
Lesson: 4 Graphing Linear Equations in Slope-Intercept Form
Lesson: 5 Graphing Linear Equations in Standard Form
Lesson: 6 Writing Equations in Slope-Intercept Form
Lesson: 7 Writing Equations in Point-Slope Form
Chapter: 4 – Graphing and Writing Linear Equations
### Graphing and Writing Linear Equations STEAM Video/Performance Task
STEAM Video
“Hurricane
A hurricane is a storm with violent winds. How can you prepare your home for a hurricane?
Watch the STEAM Video “Hurricane!” Then answer the following questions.
1. Robert says that the closer you are to the eye of a hurricane, the stronger the winds become. The wind speed on an island is 50 miles per hour when the eye of a hurricane is 140 miles away.
a. Describe the wind speed on the island when the eye of the hurricane is 100 miles away.
b. Describe the distance of the island from the eye of the hurricane when the wind speed on the island is 25 miles per hour.
c. Sketch a line that could represent the wind speed y (in miles per hour) on the island when the eye of x the hurricane is miles away from the island. Wind speed
2. A storm dissipates as it travels over land. What does this mean?
Performance Task
Anatomy of a Hurricane
After completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given information about the atmospheric pressure inside a hurricane.
You will be asked to use a model to find the strength of a hurricane after x hours of monitoring. Why is it helpful to predict how strong the winds of a hurricane will become?
### Graphing and Writing Linear Equations Getting Ready for Chapter 4
Chapter Exploration
1. Work with a partner.
a. Use the equation y = $$\frac{1}{2}$$x + 1 to complete the table. (Choose any two x-values and find the y-values.)
b. Write the two ordered pairs given by the table. These are called solutions of the equation.
c. PRECISION Plot the two solutions. Draw a line exactly through the points.
d. Find a different point on the line. Check that this point is a solution of the equation y = $$\frac{1}{2}$$x + 1.
e. LOGIC Do you think it is true that any point on the line is a solution of the equation y = $$\frac{1}{2}$$x + 1? Explain.
f. Choose five additional x-values for the table below. (Choose both positive and negative x-values.) Plot the five corresponding solutions. Does each point lie on the line?
g. LOGIC Do you think it is true that any solution of the equation y = $$\frac{1}{2}$$x + 1 is a point on the line? Explain.
h. Why do you think y = ax + b is called a linear equation?
Vocabulary
The following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.
linear equation
slope
y-intercept
solution of a linear equation
x-intercept
### Lesson 4.1 Graphing Linear Equations
EXPLORATION 1
Creating Graphs
Work with a partner. It starts snowing at midnight in Town A and Town B. The snow falls at a rate of 1.5 inche sper hour.
a. In Town A, there is no snow on the ground at midnight. How deep is the snow at each hour between midnight and 6 A.M.? Make a graph that represents this situation.
b. Repeat part(a) for TownB, which has 4 inches of snow on the ground at midnight.
c. The equations below represent the depth y(in inches) of snow x hours after midnight in Town C and Town D. Graph each equation.
Town C y = 2x + 3
Town D y = 8
d. Use your graphs to compare the snowfall in each town.
Answer:
Try It
Graph the linear equation.
Question 1.
y = 3x
Answer:
Make to table of values
Replace x with a number and find the value of y
Plot the values of x and y obtained above, on the graph
Draw the line through the points
Question 2.
y = – 2x – 1
Answer:
Plot the values of x and y
Now the line through the points
Question 3.
y = –$$\frac{1}{2}$$x + 2
Answer:
Plot the ordered pairs
Graph the linear equation.
Question 4.
y = 3
Answer:
The graph of y = 3 is a horizontal like passing through (0, 3)
Draw a horizontal line through this point.
Question 5.
y = – 1.5
Answer:
The graph of y = -1.5 is a horizontal line passing through (0, -1.5)
Draw a horizontal line through this point.
Question 6.
x = – 4
Answer:
The graph of x = – 4 is a vertical line passing through (-4, 0)
Draw a vertical line through this point.
Question 7.
x = $$\frac{1}{2}$$
Answer:
The graph of x = $$\frac{1}{2}$$ is a vertical line passing through ($$\frac{1}{2}$$, 0)
Draw a vertical line through this point.
Self-Assessment for Concepts & Skills
Solve each exercise. Then rate your understanding of the success criteria in your journal.
GRAPHING A LINEAR EQUATION Graph the linear equation.
Question 8.
y = – x + 1
Answer:
Make of a table of values
Replace x with a number and find the value of y
Plot the values of x and y obtained, on the graph,
Question 9.
y = 0.8x – 2
Answer:
Replace x with a number and find the value of y
Question 10.
x = 2.5
Answer:
The graph of x = 2.5 is a vertical line passing through (2.5, 0)
Draw a vertical line through this point.
Question 11.
y = $$\frac{2}{3}$$
Answer:
The graph of y = $$\frac{2}{3}$$ is a horizontal line passing through (0, $$\frac{2}{3}$$)
Draw a horizontal line through this point.
Question 12.
WHICH ONE DOESN’T BELONG?
Which equation does not belong with the other three? Explain your reasoning.
Answer:
y = x – 2
4x + 3 = y
y = x² + 6
x + 5 = y
Self-Assessment for Problem Solving
Solve each exercise. The rate your understanding of the success criteria in your journal.
Question 13.
A game show contestant earns y dollars for completing a puzzle in x minutes. This situation is represented by the equation y = – 250x + 5000. How long did a contestant who earned $500 take to complete the puzzle? Justify your answer. Answer: Given, A game show contestant earns y dollars for completing a puzzle in x minutes. This situation is represented by the equation y = – 250x + 5000. y = -250x + 5000 500 = -250x + 5000 500 – 5000 = -250x + 5000 – 5000 -4500 = -250x x = 18 Question 14. The total cost y (in dollars) to join a cheerleading team and attend x competitions is represented by the equation y = 10x + 50. a. Graph the linear equation. Answer: b. You have$75 to spend. How many competitions can you attend?
Answer:
75 ≤ 10x + 50
75 – 50 ≤ 10x
25 ≤ 10x
2.5 ≥ x
By this I can say that I can attend 2 competitions if I have $75 to spend. Question 15. The seating capacity for a banquet hall is represented by y = 8x + 56, where x is the number of extra tables you need. How many extra tables do you need to double the original seating capacity? Answer: Given, The seating capacity for a banquet hall is represented by y = 8x + 56, where x is the number of extra tables you need. y = 8x + 56 2 × 56 = 8x + 56 112 = 8x + 56 8x = 112 – 56 8x = 56 x = 7 tables ### Graphing Linear Equations Homework & Practice 4.1 Review & Refresh Tell whether the triangles are similar. Explain. Question 1. Answer: x° + 46° + 95° = 180° x° + 141° = 180° x° = 180° – 141° x° = 39° Thus the angles of the triangle are 39°, 46°, 95° y° + 39° + 46° = 180° y° + 75° = 180° y° = 180° – 75° y° = 95° Three angles of the triangle are 39°, 46°, 95° The triangles have two pairs of congruent angles. Question 2. Answer: x° + 40° + 51° = 180° x° + 91° = 180° x° = 180° – 91° x° = 89° Three angles of the triangle are 40°, 51°, 89° y° + 40° + 79° = 180° y° + 119° = 180° y° = 180° – 119° y° = 61° Describe the translation of the point to its image. Question 3. (1, – 4) → (3, 0) Answer: A(1, -4) = A'(1 + 2, -4) = (3, -4) A'(3, 4) = B(3, -4 + 4) = (3, 0) Translate 2 units right and 4 units up. Question 4. (6, 4) → (- 4, – 6) Answer: We are given the points (6, 4) → (- 4, – 6) A(6, 4) = A'(6 – 10, 4) = (-4, 4) A'(-4, -4) = B(-4, 4 – 10) = (-4, -6) Question 5. (4, – 2) → (- 9, 3) Answer: We are given the points A(4, -2) B(-9, 3) A(4, -2) = A'(4 – 13, -2) = (-9, -2) A'(-9, -2) = B(-9, -2 + 4) = (-9, 3) Concepts, Skills, & Problem Solving CREATING GRAPHS Make a graph of the situation. (See Exploration 1, p. 141.) Question 6. The equation y = – 2x + 8 represents the amount (in fluid ounces) of dish detergent in a bottle after x days of use. Answer: Question 7. The equation y = 15x + 20 represents the cost (in dollars) of a gym membership after x months. Answer: PRECISION Copy and complete the table with two solutions. Plot the ordered pairs and draw the graph of the linear equation. Use the graph to find a third solution of the equation. Question 8. Answer: (x, y) = (2, 5) Question 9. Answer: (x, y) = (3, 3) GRAPHING A LINEAR EQUATION Graph the linear equation. Question 10. y = – 5x Answer: Question 11. y = 9x Answer: Question 12. y = 5 Answer: The graph of y = 5 is a horizontal line passing through (0, 5) Draw a horizontal line through this point. Question 13. x = – 6 Answer: Question 14. y = x – 3 Answer: Question 15. y = – 7x – 1 Answer: Question 16. y = – $$\frac{x}{8}$$ + 4 Answer: Question 17. y = 0.75x – 0.5 Answer: Question 18. y = – $$\frac{2}{3}$$ Answer: Question 19. y = 6.75 Answer: Question 20. x = – 0.5 Answer: The graph of x = -0.5 is a vertical line passing through (-0.5, 0) Draw a vertical line through this point. Question 21. x = $$\frac{1}{4}$$ Answer: The graph of x = $$\frac{1}{4}$$ is a vertical line passing through ($$\frac{1}{4}$$, 0) Draw a vertical line through this point. Question 22. YOU BE THE TEACHER Your friend graphs the equation y = 4. Is your friend correct? Explain your reasoning. Answer: No my friend is not correct because the graph for the equation y = 4 is a horizontal line not a vertical line, and it passes through the point (0, 4) not (4, 0) Question 23. MODELING REAL LIFE The equation y = 20 represents the cost y (in dollars) for sending x text messages in a month. Graph the linear equation. What does the graph tell you about your texting plan? Answer: Question 24. MODELING REAL LIFE The equation y = 2x + 3 represents the cost y (in dollars) of mailing a package that weighs x pounds. a. Use a graph to estimate how much it costs to mail the package. b. Use the equation to find exactly how much it costs to mail the package. Answer: Given the equation y = 2x + 3 The ordered pairs will be (0, 3), (2,7), (4, 11) Now plot the ordered pairs y = 2(1.126) + 3 = 5.252 ≈ 5.25 SOLVING A LINEAR EQUATION Solve for y. Then graph the linear equation. Question 25. y – 3x = 1 Answer: y – 3x = 1 y = 3x + 1 Draw a line through the points Question 26. 5x + 2y = 4 Answer: 5x + 2y = 4 2y = 4 – 5x y = – $$\frac{5}{2}$$x + 2 Question 27. – $$\frac{1}{3}$$y + 4x = 3 Answer: – $$\frac{1}{3}$$y + 4x = 3 – $$\frac{1}{3}$$y = 3 – 4x y = 12x – 9 Question 28. x + 0.5y = 1.5 Answer: x + 0.5y = 1.5 0.5y = -x + 1.5 y = -2x + 3 Question 29. MODELING REAL LIFE The depth y (in inches) of a lake after x years is represented by the equation y = 0.2x + 42. How much does the depth of the lake increase in four years? Use a graph to justify your answer. Answer: y = 0.2x + 42 Depth of the lake now: y = 0.2(0) + 42 = 42 Depth of the lake after 4 years: y = 0.2(4) + 42 = 42.8 42.8 – 42 = 0.8 inches Question 30. MODELING REAL LIFE The amount y (in dollars) of money in your savings account after x months is represented by the equation y = 12.5x + 100. a. Graph the linear equation. Answer: b. How many months will it take you to save a total of$237.50?
Answer:
y = 12.5x + 100
237.5 = x + 100
237.5 – 100 = 12.5x + 100 – 100
12.5x = 137.5
x = 11
Question 31.
PROBLEM SOLVING
The radius y (in millimeters) of a chemical spill after x days is represented by the equation y = 6x + 50.
a. Graph the linear equation.
Answer:
b. The leak is noticed after two weeks. What is the area of the leak when it is noticed? Justify your answer.
Answer:
y = 6(14) + 50
y = 84 + 50
y = 134 mm
2πr = 2π = 841.95 sq. mm
Question 32.
GEOMETRY
The sum S of the interior angle measures of a polygon with n sides is S = (n – 2) • 180°.
a. Plot four points (n, S) that satisfy the equation. Is the equation a linear equation? Explain your reasoning.
Answer:
b. Does the value n = 3.5 make sense in the context of the problem? Explain your reasoning.
Answer:
The value n = 3.5 does not make sense because the number of angles cannot be other than integer greater or equal to 2.
Question 33.
DIG DEEPER!
One second of video on your cell phone uses the same amount of memory as two pictures. Your cell phone can store 2500 pictures.
a. Create a graph that represents the number y of pictures your cell phone can store when you take x seconds of video.
Answer:
b. How many pictures can your cell phone store in addition to a video that is one minute and thirty seconds long?
Answer:
Determine the number of pictures you can store in addition to a video of 1 min 30 seconds.
1 min 30 seconds = (60 + 90) 3 seconds = 90 seconds
2500 – (2 . 90)
2500 – 180 = 2320 pictures
### Lesson 4.2 Slope of a Line
EXPLORATION 1
Measuring the Steepness of a Line
Work with a partner. Draw any nonvertical line in a coordinate plane.
a. Develop a way to measure the steepness of the line. Compare your method with other pairs.
b. Draw a line that is parallel to your line. What can you determine about the steepness of each line? Explain your reasoning.
Answer:
EXPLORATION 2
Using Right Triangles
Work with a partner. Use the figure shown.
a. △ABC is a right triangle formed by drawing a horizontal line segment from point A and a vertical line segment from point B. Use this method to draw another right triangle, △DEF, with its longest side on the line
b. What can you conclude about the two triangles in part(a)? Justify your conclusion. Compare your results with other pairs.
c. Based on your conclusions in part(b), what is true about $$\frac{BC}{AC}$$ and the corresponding measure in △DEF? Explain your reasoning. What do these values tell you about the line?
Answer:
Try It
Find the slope of the line.
Question 1.
Answer:
(x1, y1) = (-2, 3)
(x2, y2) = (3, 2)
m = (y2 – y1)/(x2 – x1)
m = (2 -3)/(3 – (-2))
m = -1/5
Thus slope = -1/5
Question 2.
Answer:
(x1, y1) = (-4, -1)
(x2, y2) = (2, 1)
m = (y2 – y1)/(x2 – x1)
m = (1 – (-1))/(2 – (-4))
m = 2/6
Thus slope = 1/3
Find the slope of the line through the given points.
Question 3.
(1, -2), (7, -2)
Answer:
(x1, y1) = (1, -2)
(x2, y2) = (7, -2)
m = (y2 – y1)/(x2 – x1)
m = (-2 – (-2))/(7 – 1)
m = 0/6
Thus slope = 0
Question 4.
(-3, -3), (-3, -5)
Answer:
(x1, y1) = (-3, -3)
(x2, y2) = (-3, -5)
m = (y2 – y1)/(x2 – x1)
m = (-5 + 3)/(-3 + 3)
m = -2/0
Thus slope = undefined
Question 5.
WHAT IF
The blue line passes through (-4, -3) and (-3, 2). Are any of the lines parallel? Explain.
Answer:
(x1, y1) = (-4, -3)
(x2, y2) = (-3, 2)
m = (y2 – y1)/(x2 – x1)
m = (2 + 3)/(-3 + 4)
m = 5/1
m = 5
The slpe of the blue line is 5 and the slope of the red line is also 5.
The blue lines and red lines have same slopes so they are parallel.
Self-Assessment for Concepts & Skills
Solve each exercise. Then rate your understanding of the success criteria in your journal.
Question 6.
VOCABULARY
What does it mean for a line to have a slope of 4?
Answer:
If a line have a slope of 4 it means that the line rises 4 units for every 1 units it runs.
FINDING THE SLOPE OF A LINE Find the slope of the line through the given points.
Question 7.
(1, -1), (6, 2)
Answer:
(x1, y1) = (1, -1)
(x2, y2) = (6, 2)
m = (y2 – y1)/(x2 – x1)
m = (2 – (-1))/(6 – 1)
m = 3/5
Question 8.
(2, -3), (5, -3)
Answer:
(x1, y1) = (2, -3)
(x2, y2) = (5, -3)
m = (y2 – y1)/(x2 – x1)
m = (5 – 2)/(-3 + 3)
m = 3/0
m = undefined
Question 9.
FINDING SLOPE
Are the lines parallel? Explain your reasoning.
Answer:
Red line:
(x1, y1) = (-1, 0)
(x2, y2) = (1, -2)
m = (y2 – y1)/(x2 – x1)
m = (-2 – 0)/1 – (-1))
m = -2/2
m = -1
Blue Line:
(x1, y1) = (-1, 3)
(x2, y2) = (1, -1)
m = (y2 – y1)/(x2 – x1)
m = (-1 – 3)/(1 – (-1))
m = -4/2
m = -2
The slope of the blue line and red line are not the same. So they are not parallel.
Self-Assessment for Problem Solving
Solve each exercise. Then rate your understanding of the success criteria in your journal.
Question 10.
The table shows the lengths (in inches) of your hair months after your last haircut. The points in the table lie on a line. Find and interpret the slope of the line. After how many months is your hair 4 inches long?
Answer:
Determine the slope of the line using two points from the table:
(2, 1), (4, 2)
m = (2 – 1)/4 – 2
m = 1/2
m = 0.5
This means that each month the hair grows 0.5 inches
As the hair grows 0.5 inches/ month, it will be 4 inches long after 4/0.5 = 8 months.
Question 11.
A customer pays an initial fee and a daily fee to rent a snowmobile. The total payment for 3 days is 92 dollars. The total payment for 5 days is 120 dollars. What is the daily fee? Justify your answer.
Answer:
Given,
A customer pays an initial fee and a daily fee to rent a snowmobile.
The total payment for 3 days is 92 dollars. The total payment for 5 days is 120 dollars.
m = (120 – 92)/5 – 3
m = 28/2
m = 14
Question 12.
You in-line skate from an elevation of 720 feet to an elevation of 750 feet in 30 minutes. Your friend in-line skates from an elevation of 600 feet to an elevation of 690 feet in one hour. Compare your rates of change in elevation.
Answer:
Given,
You in-line skate from an elevation of 720 feet to an elevation of 750 feet in 30 minutes.
Your friend in-line skates from an elevation of 600 feet to an elevation of 690 feet in one hour.
(750 – 720)/30 = 30/30 = 1 ft/min
(690 – 600)/60 = 90/60 = 1.5 ft/min
### Slope of a Line Homework & Practice 4.2
Review & Refresh
Graph the linear equation.
Question 1.
y = 4x – 3
Answer:
Question 2.
x = -3
Answer:
Question 3.
y = 2
Answer:
Question 4.
y = $$\frac{3}{2}$$x – $$\frac{1}{2}$$
Answer:
Find the missing values in the ratio table.
Question 5.
Answer:
x/10 = 1/3
x = 10/3
x = 3.33
1/3 = 5/y
y = 5 × 3
y = 15
1/3 = 7/z
z = 3 × 7
z = 21
Question 6.
Answer:
Concepts, Skills, &Problem Solving
USING RIGHT TRIANGLES Use the figure shown (See Exploration 2, p. 147.)
Question 7.
Find the slope of the line.
Answer:
(x1, y1) = B(-4, 2)
(x2, y2) = A(-2, 1)
m = (y2 – y1)/(x2 – x1)
m = (1 – 2)/(-2 – (-4))
m = -1/2
Thus the slope m = -1/2
Question 8.
Let point D be at (-4, 1). Use the sides of △BDA to find the slope of the line.
Answer:
m = -BD/DA = -1/2
FINDING THE SLOPE OF A LINE Find the slope of the line.
Question 9.
Answer:
(x1, y1) = (-2, 0)
(x2, y2) = (2, 3)
m = (y2 – y1)/(x2 – x1)
m = (3 – 0)/(2 – (-2))
m = 3/4
Question 10.
Answer:
(x1, y1) = (-2, 5)
(x2, y2) = (2, 0)
m = (y2 – y1)/(x2 – x1)
m = (0 – 5)/(2 – (-2))
m = -5/4
Question 11.
Answer:
(x1, y1) = (-4, 1)
(x2, y2) = (1, -2)
m = (y2 – y1)/(x2 – x1)
m = (-2 – 1)/(1 + 2)
m = -3/5
Question 12.
Answer:
(x1, y1) = (-5, -4)
(x2, y2) = (1, -3)
m = (y2 – y1)/(x2 – x1)
m = (-3 – (-4))/(1 – (-5))
m = 1/6
Question 13.
Answer:
(x1, y1) = (-1, 3)
(x2, y2) = (3, 3)
m = (y2 – y1)/(x2 – x1)
m = (3 – 3)/(3 – (-1))
m = 0/4
m = 0
Question 14.
Answer:
(x1, y1) = (1, 3)
(x2, y2) = (1, -2)
m = (y2 – y1)/(x2 – x1)
m = (-2 – 3)/(1 – 1)
m = -5/0
m = undefined
FINDING THE SLOPE OF A LINE Find the slope of the line through the given points.
Question 15.
(4, -1), (-2, -1)
Answer:
(x1, y1) = (4, -1)
(x2, y2) = (-2, -1)
m = (y2 – y1)/(x2 – x1)
m = (-1 – (-1))/(-2 – 4)
m = 0/-6
m = 0
Question 16.
(5, -3), (5, 8)
Answer:
(x1, y1) = (5, -3)
(x2, y2) = (5, 8)
m = (y2 – y1)/(x2 – x1)
m = (8 – 3)/(5 – 5)
m = 5/0
m = undefined
Question 17.
(-7, 0), (-7, -6)
Answer:
(x1, y1) = (-7, 0)
(x2, y2) = (-7, -6)
m = (y2 – y1)/(x2 – x1)
m = (-6 – 0)/(-7 – (-7))
m = -6/0
m = undefined
Question 18.
(-3, 1), (-1, 5)
Answer:
(x1, y1) = (-3, 1)
(x2, y2) = (-1, 5)
m = (y2 – y1)/(x2 – x1)
m = (5 – 1)/(-1 + 3)
m = 4/2
m = 2
Question 19.
(10, 4), (4, 15)
Answer:
(x1, y1) = (10, 4)
(x2, y2) = (4, 15)
m = (y2 – y1)/(x2 – x1)
m = (15 – 4)/(4 – 10)
m = 11/-6
m = -11/6
Question 20.
(-3, 6), (2, 6)
Answer:
(x1, y1) = (-3, 6)
(x2, y2) = (2, 6)
m = (y2 – y1)/(x2 – x1)
m = (6 – 6)/(2 – (-3))
m = 0/5
m = 0
Question 21.
REASONING
Draw a line through each point using slope of m = $$\frac{1}{4}$$. Do the lines intersect? Explain.
Answer:
The 2 lines are parallel because they have the same slope and they do not intersect.
Question 22.
YOU BE THE TEACHER
Your friend finds the slope of the line shown. Is your friend correct? Explain your reasoning.
Answer:
No my friend is not correct because the denominator should be 2 – 4
(x1, y1) = (2, 3)
(x2, y2) = (4, 1)
m = (y2 – y1)/(x2 – x1)
m = (1 – 3)/(4 – 2)
m = -2/2
m = -1
IDENTIFYING PARALLEL LINES Which lines are parallel? How do you know?
Question 23.
Answer:
Blue line:
(x1, y1) = (-5, 2)
(x2, y2) = (-4, -1)
m = (y2 – y1)/(x2 – x1)
m = (-1 – 2)/(-4 – (-5))
m = -3/1
m = -3
Red line:
(x1, y1) = (-2, 1)
(x2, y2) = (-1, -2)
m = (y2 – y1)/(x2 – x1)
m = (-2 – 1)/(-1 – (-2))
m = -3/1
m = -3
Green Line:
(x1, y1) = (1, 3)
(x2, y2) = (2, -1)
m = (y2 – y1)/(x2 – x1)
m = (-1 – 3)/(2 – 1)
m = -4/1
m = -4
Blue line and red line have slope of -3, so they are parallel.
Question 24.
Answer:
Blue line:
(x1, y1) = (-2, 3)
(x2, y2) = (-5, -2)
m = (y2 – y1)/(x2 – x1)
m = (-2 – 3)/(-5 – (-2))
m = -5/-3
m = 5/3
Red line:
(x1, y1) = (1, 2)
(x2, y2) = (-2, -2)
m = (y2 – y1)/(x2 – x1)
m = (-2 – 2)/(-2 – 1)
m = -4/-3
m = 4/3
Green Line:
(x1, y1) = (4, 1)
(x2, y2) = (1, -3)
m = (y2 – y1)/(x2 – x1)
m = (-3 – 1)/(1 – 4)
m = -4/-3
m = 4/3
Red line and green line have slope of 4/3 by this we can say that they are parallel.
IDENTIFYING PARALLEL LINES Are the given lines parallel? Explain your reasoning.
Question 25.
y = -5, y = 3
Answer:
Both lines are horizontal and have slope = 0
Question 26.
y = 0, x = 0
Answer:
The line y = 0 have slope = 0 and are horizontal lines.
The line x = 0 have slope = undefined and are vertical lines.
So, they are not parallel.
Question 27.
x = -4, x = 1
Answer:
Both lines are vertical and have an undefined slope.
FINDING SLOPE The points in the table lie on a line. Find the slope of the line.
Question 28.
Answer:
m = (y2 – y1)/(x2 – x1)
m = (10 – 2)/(3 – 1) = (18 – 10)/(5 – 3) = (26 – 18)/(7 – 5)
m = 8/2 = 8/2 = 8/2
m = 4 = 4 = 4
Slope = 4
Question 9.
Answer:
m = (y2 – y1)/(x2 – x1)
m = (2 – 0)/(2 – (-3)) = (4 – 2)/(7 – 2) = (6 – 4)/(12 – 7)
m = 2/5 = 2/5 = 2/5
m = 2/5
Question 30.
MODELING REAL LIFE
Carpenters refer to the slope of a roof as the pitch of the roof. Find the pitch of the roof.
Answer:
Pitch of the roof = rise/run
= 4/12 = 1/3
Question 31.
PROJECT
The guidelines for a wheelchair ramp suggest that the ratio of the rise to the run be no greater than 1 : 12.
a. CHOOSE TOOLS Find a wheelchair ramp in your school or neighborhood. Measure its slope. Does the ramp follow the guidelines?
Answer:
rise/run < 1/12
m = 0.06
1/12 = 0.0833
0.06 < 0.0833
As m < 1/12 the wheelchair ramp follows the guides.
b. Design a wheelchair ramp that provides access to a building with a front door that is 2.5 feet above the sidewalk. Illustrate your design.
Answer:
AC/AB = 1/12
2.5/AB = 1/12
AB = 2.5 × 12
AB = 30
So the end of the ramp should be placed at least 30 feet from the front door.
USING AN EQUATION Use an equation to find the value of k so that the line that passes through the given points has the given slope.
Question 32.
(1, 3), (5, k); m = 2
Answer:
A(1, 3)
B(5, k)
m = 2
2 = (k – 3)/(5 – 1)
2 × 4 = k – 3
8 = k – 3
k = 8 + 3
k = 11
Question 33.
(-2, k), (2, 0); m = -1
Answer:
Given,
A(-2, k)
B(2, 0)
m = -1
-1 = (0 – k)/2 – (-2)
-1 = -k/4
-4 = -k
k = 4
Question 34.
(-4, k), (6, -7); m = –$$\frac{1}{5}$$
Answer:
Given,
A(-4, k)
B(6, -7)
m = –$$\frac{1}{5}$$
–$$\frac{1}{5}$$ = (-7 – k)/6 – (-4)
-2 = -7 – k
-2 + 7 = -k
5 = -k
k = -5
Question 35.
(4, -4), (k, -1); m = $$\frac{3}{4}$$
Answer:
$$\frac{3}{4}$$ = (-1 – (-4))/(k – 4)
4 = k – 4
k = 4 + 4
k = 8
Question 36.
MODELING REAL LIFE
The graph shows the numbers of prescriptions filled over time by a pharmacy.
a. Find the slope of the line.
Answer:
(0, 0), (20, 5)
m = (5 – 0)/(20 – 0)
m = 5/20
m = 1/4
b. Explain the meaning of the slope as a rate of change.
Answer:
This means that every 4 minutes a prescription is filled.
Question 37.
CRITICAL THINKING
Which is steeper: the boatramp, or a road with a 12% grade? Note: Explain. (Road grade is the vertical increase divided by the horizontal distance.)
Answer:
Mramp = rise/run = 6/36 = 1/6
Mroad = 12% = 12/100 = 0.12
0.16 = 0.166… > 0.12
Mramp > Mroad
Therefore the slope of the ramp is steeper than the slope of the road.
Question 38.
REASONING
Do the points A(-2, -1), B(1, 5), and C(4, 11) lie on the same line? Without using a graph, how do you know?
Answer:
Given,
A(-2, -1), B(1, 5), and C(4, 11)
mAB = (5 – (-1))/(1 – (-2)) = 6/3 = 2
mBC = (11 – 5)/(4 – 1) = 6/3 = 2
By seeing the slopes we can say that the points A, B, C lie on the same line.
Question 39.
PROBLEM SOLVING
A small business earns a profit of $6500 in January and$17,500 in May. What is the rate of change in profit for this time period? Justify your answer.
Answer:
Pjan = 6500
Pmay = 17,500
Pmay – Pjan/5 – 1
= (17,500 – 6500)/4
= 11,000/4 = 2750
Question 40.
STRUCTURE
Choose two points in the coordinate plane. Use the slope formula to find the slope of the line that passes through the two points. Then find the slope using the formula $$\frac{y_{1}-y_{2}}{x_{1}-x_{2}}$$. Compare your results.
Answer:
P1(2, 5)
P2(3, 10)
m1 = (10 – 5)/(3 – 2) = 5/1 = 5
m2 = (5 – 10)/(1 – 3) = -5/-1 = 5
m1 = m2
Question 41.
DIG DEEPER!
The top and the bottom of the slide are level with the ground, which has a slope of 0.
a. What is the slope of the main portion of the slide?
b. Describe the change in the slope when the bottom of the slide is only 12 inches above the ground. Explain your reasoning.
Answer:
18 inches = 1.5 feet
mMC = rise/run = (8 – 1.5)/(12 – 1 – 1) = 6.5/10 = 0.65
AD = 1
mMC = CR/MR
= (8 – 1)/(12 – 1 – 1) = 7/10 = 0.7
The slope increases from 0.65 to 0.70 because the rise increasses, while the run stays the same.
### Lesson 4.3 Graphing Proportional Relationships
EXPLORATION 1
Using a Ratio Table to Find Slope
Work with a partner. The graph shows amounts of vinegar and water that can be used to make a cleaning product.
a. Use the graph to make a ratio table relating the quantities. Explain how the slope of the line is represented in the table.
b. Make a ratio table that represents a different ratio of vinegar to water. Use the table to describe the slope of the graph of the new relationship.
Answer:
EXPLORATION 2
Deriving an Equation
Work with a partner. Let (x, y) represent any point on the graph of a proportional relationship.
a. Describe the relationship between the corresponding side lengths of the triangles shown in the graph. Explain your reasoning.
b. Use the relationship in part(a) to write an equation relating y, m, and x. Then solve the equation for y. How can you find the side lengths of the triangles in the graph?
c. What does your equation in part(b) describe? What does represent? Explain your reasoning.
Answer:
Try It
Question 1.
WHAT IF
The cost of frozen yogurt is represented by y = 0.75x. Graph the equation and interpret the slope.
Answer:
The equation shows that the slope m is 0.75. So the graph passes through the points (0, 0) and (1, 0.75).
Plot the ordered pairs and draw the graph.
The slope indicates that the unit cost is $0.75 per ounce. Question 2. How much would a spacecraft that weighs 3500 kilograms on Earth weigh on Titan? Answer: y = 1/7 x y = 1/7 × 3500 y = 500 kg So a spacecraft would weigh 500 kg on Titan. Self-Assessment for Concepts & Skills Solve each exercise. Then rate your understanding of the success criteria in your journal. GRAPHING A PROPORTIONAL RELATIONSHIP Graph the equation. Question 3. y = 4x Answer: Question 4. y = -3x Answer: Question 5. y = 8x Answer: Question 6. WRITING AND USING AN EQUATION The number of objects a x machine produces is proportional to the time (in minutes) that the machine runs. The machine produces five objects in four minutes. a. Write an equation that represents the situation. Answer: As 5 objects are produced in 4 minutes, the slope of the line is m = 5/4. The equation that represents the situation is y = 5/4 x y = 1.25 x b. Graph the equation in part (a) and interpret the slope. Answer: Use the slope. The equation shows that the slope m is 1.25. So the graph passes through the points (0, 0) and (1, 1.25) c. How many objects does the machine produce in one hour? Answer: Self-Assessment for Problem Solving Solve each exercise. Then rate your understanding of the success criteria in your journal. Question 7. The amount y (in liters) of water that flows over a natural waterfall in x seconds is represented by the equation y = 500x. The graph shows the number of liters of water that flow over an artificial waterfall. Which waterfall has a greater flow? Justify your answer. Answer: Given the equation y = 500x 15000 – 3000 = 12000 12000/4 = 3000 Mnatural = 500 3000 > 500 Therefore the artificial waterfall has greater flow. Question 8. The speed of sound in air is 343 meters per second. You see lightning and hear thunder 12 seconds later. a. Is there a proportional relationship between the amount of time that passes and your distance from a lightning strike? Explain. Answer: y = kx where k is the speed of sound, x the time and y the distance. Yes, there is a proportional relationship between the amount of time that passes and your distance from the lightning strike as the further you are, the more time will pass until the sound reaches you. b. Estimate your distance from the lightning strike. Answer: y = 343 × 12 = 4116 meters ### Graphing Proportional Relationships Homework & Practice 4.3 Review & Refresh Find the slope of the line. Question 1. Answer: (x1, y1) = (0, -3) (x2, y2) = (3, 0) m = (y2 – y1)/(x2 – x1) m = (0 – (-3))/(3 – 0) m = (0 + 3)/(3 – 0) m = 3/3 m = 1 Question 2. Answer: (x1, y1) = (0, 1) (x2, y2) = (3, -5) m = (y2 – y1)/(x2 – x1) m = (-5 – 1)/(3 – 0) m = -6/3 m = -2 Question 3. Answer: (x1, y1) = (0, 0) (x2, y2) = (2, 8) m = (y2 – y1)/(x2 – x1) m = (8 – 0)/(2 – 0) m = 8/2 m = 4 Solve the equation. Check your solution. Question 4. 2x + 3x = 10 Answer: Given the equation 2x + 3x = 10 5x = 10 x = 10/5 x = 2 Question 5. x + $$\frac{1}{6}$$ = 4 – 2x Answer: Given the equation x + $$\frac{1}{6}$$ = 4 – 2x x + 2x = 4 – $$\frac{1}{6}$$ 3x = 4 – $$\frac{1}{6}$$ 3x = $$\frac{23}{6}$$ x = $$\frac{23}{18}$$ Question 6. 2(1 – x) = 11 Answer: 2(1 – x) = 11 2 – 2x = 11 2 – 11 = 2x 2x = -9 x = -9/2 Concepts, Skills, & Problem Solving USING EQUIVALENT RATIOS The graph shows amounts of water and flour that can be used to make dough. (See Exploration 1, p. 155.) Question 7. Use the graph to make a ratio table relating the quantities. Explain how the slope of the line is represented in the table. Answer: m = rise/run = (10 – 5)/(6 – 3) = 5/3 That means to every 5 cups of flour there is an increase of 3 cups of water. The slope m is 5/3. Question 8. Make a ratio table that represents a different ratio of flour to water. Use the table to describe the slope of the graph of the new relationship. Answer: From the table we find that for every increase of 7 cups of flour there is an increase of 4 cups of water. The slope is 7/4. Question 9. GRAPHING AN EQUATION The amount y(in dollars) that you raise by selling fundraiser tickets is represented by the equation y = 5x. Graph the equation and interpret the slope. Answer: The slope indicates that the unit cost is$5 per ticket.
IDENTIFYING PROPORTIONAL RELATIONSHIPS Tell whether and are in a proportional relationship. Explain your reasoning. If so, write an equation that represents the relationship.
Question 10.
Answer:
The graph doesn’t represent a proportional relationship because it doesn’t pass through the point (0, 0).
Question 11.
Answer:
The graph represents a proportional relationship because it is linear and passes through the point (0, 0)
(0, 0), (2, 8)
m = (8 – 0)/(2 – 0)
m = 8/2
m = 4
The equation is y = 4x
Question 12.
Answer:
(2 – 1)/(6 – 3) = 1/3
(3 – 2)/(9 – 6) = 1/3
(4 – 3)/(12 – 9) = 1/3
As the rate of change is constant, it means that the graph is a line.
(1 – y)/(3 – 0) = 1/3
(1 – y)/3 = 1/3
1 – y = 1
y = 1 – 1
y = 0
Therefore the point (0, 0) belomgs to the graph.
So the table represents a proportional relationship
y = 1/3 x
Question 13.
Answer:
(8 – 4)/(5 – 2) = 4/3
(13 – 8)/(8 – 5) = 5/3
(23 – 13)/10 – 8 = 10/2 = 5
Question 14.
MODELING REAL LIFE
The cost y (in dollars) to rent a kayak is proportional to the number x of hours that you rent the kayak. It costs $27 to rent the kayak for 3 hours. a. Write an equation that represents the situation. b. Interpret the slope of the graph of the equation. c. How much does it cost to rent the kayak for 5 hours? Justify your answer. Answer: y = kx 27 = k × 3 k = 27/3 k = 9 The equation is k = 9x b. The slope k = 3 shows that the cost of renting the kayak per hour is$9.
c. y = 9 × 5
y = 45
Question 15.
MODELING REAL LIFE
The distance y (in miles) that a truck travels on x gallons of gasoline is represented by the equation y = 18x. The graph shows the distance that a car travels.
a. Which vehicle gets better gas mileage? Explain how you found your answer.
Answer:
y = 18x
(0, 0), (2, 50)
m = (50 – 0)/(2 – 0)
m = 50/2
m = 25
25 > 18
Therefore the car has better mileage.
b. How much farther can the vehicle you chose in part(a) travel on 8 gallons of gasoline?
Answer:
y = 25 × 8 – 18 × 8
= 200 – 144
= 56 miles
Question 16.
PROBLEM SOLVING
Toenails grow about 13 millimeters per year. The table shows fingernail growth.
a. Do fingernails or toenails grow faster? Explain.
Answer:
y = 0.25x
m = (1.4 – 0.7)/(2 – 1)
m = 0.7
y = 0.7x
Because 0.7 > 0.25, the fingernails grow faster.
b. In the same coordinate plane, graph equations that represent the growth rates of toenails and fingernails. Compare and interpret the steepness of each graph.
Answer:
Question 17.
REASONING
The quantities and are in a proportional relationship. What do you know about the ratio of y to x for any point (x, y) on the graph of x and y?
Answer:
y = kx
where k is constant
y/x = k
This means the ratio of y to x is constant.
Question 18.
DIG DEEPER!
The graph relates the temperature change y (in degrees Fahrenheit) to the altitude change x (in thousands of feet).
a. Is the relationship proportional? Explain.
Answer: The relationship is proportional because the graph is linear and passes through the origin.
b. Write an equation of the line. Interpret the slope.
Answer:
(0,0), (10, -35)
m = (-35 – 0)/(10 – 0)
= -35/10
= -3.5
y = -3.5x
c. You are at the bottom of a mountain where the temperature is 74°F. The top of the mountain is 5500 feet above you. What is the temperature at the top of the mountain? Justify your answer.
Answer:
x = 5.5 – 0 = 5.5 thousand feet
y = -3.5x = -3.5(5.5) = -19.25
74 – 19.25 = 54.75°F
Question 19.
CRITICAL THINKING
Consider the distance equation d = rt, where d is the distance (in feet), r is the rate (in feet per second), and t is the time (in seconds). You run for 50 seconds. Are the distance you run and the rate you run at proportional? Use a graph to justify your answer.
Answer:
d = rt
d = 50r
Having the form y = kx the equation represents a proportional relationship.
### Lesson 4.4 Graphing Linear Equations in Slope-Intercept Form
EXPLORATION 1
Deriving an Equation
Work with a partner. In the previous section, you learned that the graph of a proportional relationship can be represented by the equation y = mx, where m is the constant of proportionality.
a. You translate the graph of a proportional relationship 3 units up as shown below. Let (x, y) represent any point on the graph. Make a conjecture about the equation of the line. Explain your reasoning.
b. Describe the relationship between the corresponding side lengths of the triangles. Explain your reasoning.
c. Use the relationship in part(b) to write an equation relating y, m, and x. Does your equation support your conjecture in part(a)? Explain.
d. You translate the graph of a proportional relationship b units up. Write an equation relating y, m, x, and b. Justify your answer.
Answer:
Try It
Find the slope and the y-intercept of the graph of the linear equation.
Question 1.
y = 3x – 7
Answer:
Given the equation
y = 3x – 7
Write the equation in slope – intercept form: y = mx + b
The slope of the line is m and the y – intercept of the line is b.
y = 3x – 7
Slope = 3 and y – intercept = -7
Question 2.
y – 1 = –$$\frac{2}{3}$$x
Answer:
Write the equation in slope – intercept form: y = mx + b
The slope of the line is m and the y – intercept of the line is b.
y – 1 = –$$\frac{2}{3}$$x
y = –$$\frac{2}{3}$$x + 1
Slope = –$$\frac{2}{3}$$ and y – intercept = 1
Graph the linear equation. Identify the x-intercept.
Question 3.
y = x – 4
Answer:
y = x – 4
Comparing the above equation with slope – intercept equation.
slope = 1, y-intercept = -4
Ploy y – intercept and slope
slope = rise/run = 1/1
Plot the point that is 1 unit right and 1 unit up from (0, -4) = (1, -3)
Thus the intercept is 4.
Question 4.
y = –$$\frac{1}{2}$$x + 1
Answer:
y = –$$\frac{1}{2}$$x + 1
Comparing the above equation with slope – intercept equation.
Slope = –$$\frac{1}{2}$$, y-intercept = 1
y-intercept = 1. So plot (0, 1)
Slope = rise/run = -1/2
Plot the point that is 2 units right and 1 unit down from (0, -4) = (2, 0)
So, the x-intercept is 2.
Self-Assessment for Concepts & Skills
Solve each exercise. Then rate your understanding of the success criteria in your journal.
Question 5.
IN YOUR OWN WORDS
Consider the graph of the equation y = mx + b.
a. How does changing the value of m affect the graph of the equation?
Answer:
The value of m is the slope of the graph. If the value of m changes it means the slope of the graph is changing, whether it will rise or fall from left or right is dependent on the value of m.
b. How does changing the value of b affect the graph of the equation?
Answer:
The value of b is the y-intercept of the graph. If the value of b changes it means it affects where the graph crosses the y – axis.
IDENTIFYING SLOPE AND y-INTERCEPT Find the slope and the y-intercept of the graph of the linear equation.
Question 6.
y = -x + 0.25
Answer:
y = mx + c
slope = -1 and y – intercept = 0.25
Question 7.
y – 2 = –$$\frac{3}{4}$$x
Answer:
Given the equation
y – 2 = –$$\frac{3}{4}$$x
y = –$$\frac{3}{4}$$x + 2
slope = –$$\frac{3}{4}$$ and y – intercept = 2
GRAPHING A LINEAR EQUATION Graph the linear equation. Identify the x-intercept.
Question 8.
y = x – 7
Answer:
The line crosses the x-axis at (7, 0)
So, the x – intercept is 7.
Question 9.
y = 2x + 8
Answer:
The line crosses the x – axis at (-4, 0)
So, the x – intercept is -4.
Self-Assessment for Problem Solving
Solve each exercise. Then rate your understanding of the success criteria in your journal.
Question 10.
The height y (in feet) of a movable bridge after rising for seconds is represented by the equation y = 3x + 6. Graph the equation. Interpret the y-intercept and slope. How many seconds does it take the bridge to reach a height of 76 feet? Justify your answer.
Answer:
Given,
y = 3x + 6.
slope = 3, y – intercept = 16
The y – intercept is 16. So, the initial height of the bridge is 16 feet.
The slope is 3. So, the bridge rises 3 feet per second.
The bridge will reach a height of 76 feet in 20 seconds.
Question 11.
The number of perfume bottles in storage after x months is represented by the equation y = -20x + 460. Graph the equation. Interpret the y-intercept and the slope. In how many months will there be no perfume bottles left in storage? Justify your answer.
Answer:
Given the equation
y = -20x + 460
Slope = -20, y-intercept = 460
The y-intercept is 460. So, the initial number of perfume in the storage is 460.
The slope is -20. So, the number of perfume bottle decrease with 20 bottles per months.
There will be no perfume bottle left in the storage in 23 months.
### Graphing Linear Equations in Slope-Intercept Form Homework & Practice 4.4
Review & Refresh
Tell whether x and y are in a proportional relationship. Explain your reasoning. If so, write an equation that represents the relationship.
Question 1.
Answer:
(8 – 6)/(2 – 1) = 2/1 = 2
(10 – 8)/(3 – 2) = 2/1 = 2
(12 – 10)/(4 – 3) = 2/1 = 2
The rate of change in the table is constant.
(6 – y)/(1 – 0) = 2
6 – y = 2
y = 6 – 2
y = 4
Therefore the graph does not pass through the origin.
So x and y are not proportional.
Question 2.
Answer:
(4 – 0)/(-8 – 0) = 4/-8 = -1/2 = -0.5
(2 – 4)/(-4 – (-8)) = -2/4 = -1/2 = -0.5
(-2 – 2)/(4 – (-4)) = -4/8 = -1/2 = -0.5
(-4 – (-2))/(8 – 4) = -2/4 = -1/2 = -0.5
As the rate of change is constant, x and y are in a proportional relationship.
y = -0.5x
Solve the equation for y.
Question 3.
x = 4y – 2
Answer:
Given the equation
x = 4y – 2
x – 2 = 4y
y = x/4 + 1/2
Question 4.
3y = -6x + 1
Answer:
Given the equation
3y = -6x + 1
y = -2x + 1/3
Question 5.
1 + y = –$$\frac{4}{5}$$x – 2
Answer:
Given the equation
1 + y = –$$\frac{4}{5}$$x – 2
y = –$$\frac{4}{5}$$x – 3
Question 6.
2.5y = 5x – 5
Answer:
Given the equation
2.5y = 5x – 5
y = 2x – 2
Question 7.
1.3y + 5.2 = -3.9x
Answer:
Given the equation
1.3y + 5.2 = -3.9x
1.3y = -3.9x – 5.2
y = -3x – 4
Question 8.
y – $$\frac{2}{3}$$x = -6
Answer:
Given the equation
y – $$\frac{2}{3}$$x = -6
y = $$\frac{2}{3}$$x -6
Concepts, Skills, &Problem Solving
GRAPHING A LINEAR EQUATION Graph the equation. (See Exploration 1, p. 161.)
Question 9.
The graph of y = 3.5x is translated up 2 units.
Answer:
Given the equation
y = 3.5x
The line obtained by translating the graph of the line y = 3.5x up 2 units has the same slope (3.5) and y – intercept 2 units greater, which means b = 0 + 2 = 2
Question 10.
The graph of y = -5x is translated down 3 units.
Answer:
y = -5x
The line obtained by translating the graph of the line y = -5x down 3 units has the same slope and the y – intercept 3 units smaller, which means b = 0 – 3 = -3
MATCHING EQUATIONS AND GRAPHS Match the equation with its graph. Identify the slope and the y-intercept.
Question 11.
y = 2x + 1
Answer:
Given the eqation
y = 2x + 1
slope = 2 and y – intercept = 1
Question 12.
y = $$\frac{1}{3}$$x – 2
Answer:
slope = 1/3 and y – intercept = -2
Question 13.
y = –$$\frac{2}{3}$$x + 1
Answer:
Answer:
Slope = -2/3 and y – intercept = 1
The graph which passes through the point (0, 1) and has a negative slope is the matching graph of the given equation.
IDENTIFYING SLOPES AND y-INTERCEPTS Find the slope and the y-intercept of the graph of the linear equation.
Question 14.
y = 4x – 5
Answer:
y = mx + b
slope = 4 and y — intercept = -5
Question 15.
y = -7x + 12
Answer:
y = -7x + 12
y = mx + b
slpoe = -7 and y – intercept = 12
Question 16.
y = –$$\frac{4}{5}$$x – 2
Answer:
y = mx + b
slope = -4/5
y – intercept = -2
Question 17.
y = 2.25x + 3
Answer:
y = mx + b
slope = 2.25 and y – intercept = 3
Question 18.
y + 1 = $$\frac{4}{3}$$x
Answer:
y = mx + b
y + 1 = $$\frac{4}{3}$$x
y = $$\frac{4}{3}$$x – 1
slope = $$\frac{4}{3}$$, y – intercept = -1
Question 19.
y – 6 = $$\frac{3}{5}$$x
Answer:
y = mx + b
y – 6 = $$\frac{3}{5}$$x
y = $$\frac{3}{5}$$x + 6
slope = 3/8 and y – intercept = 6
Question 20.
y – 3.5 = -2x
Answer:
y = mx + b
y – 3.5 = -2x
y = -2x + 3.5
slope = -2 and y – intercept = 3.5
Question 21.
y = -5 – $$\frac{1}{2}$$x
Answer:
y = mx + b
y = -5 – $$\frac{1}{2}$$x
y =- $$\frac{1}{2}$$x – 5
slope = – $$\frac{1}{2}$$ and y – intercept = -5
Question 22.
y = 11 + 1.5x
Answer:
y = mx + b
y = 1.5x + 11
slope = 1.5 and y – intercept = 11
Question 23.
YOU BE THE TEACHER
Your friend finds the slope and y-intercept of the graph of the equation y = 4x – 3. Is your friend correct? Explain your reasoning.
Answer:
y = 4x – 3
No my friend is not correct because the y – intercept is -3.
Question 24.
MODELING REAL LIFE
The number y of seasonal allergy shots available at a facility x days after receiving a shipment is represented by y = -15x + 375.
a. Graph the linear equation.
b. Interpret the slope and the y-intercept.
Answer:
y = -15x + 375
x = 0
y = -15(0) + 375 = 375
y = 0
0 = -15x + 375
15x = 375
x = 375/15
x = 25
The slope shows that the number of seasonal allergy shots decrease by 15 shots each day.
The y – intercept shows that the number of shots immediately after receiving a shipment is 375.
GRAPHING AN EQUATION Graph the linear equation. Identify the x-intercept.
Question 25.
y = x + 3
Answer:
Given the equation
y = x + 3
slope = 1 and y – intercept = 3
Slope = rise/run = 1/1
Plot the point that is 1 unit right and 1 unit up from (0, 3) = (1, 4)
So, the x – intercept is -3.
Question 26.
y = 4x – 8
Answer:
y = 4x – 8
Comparing the above equation with slope – intercept equation.
slope = 4 and y – intercept = -8
Slope = rise/run = 4/1 = 4
Plot the point that is 1 unit right and 4 unit up from (0, -8) = (1, -4)
Question 27.
y = -3x + 9
Answer:
y = -3x + 9
slope = -3 and y – intercept = 9
slope rise/run = -3/1 = -3
So, the intercept is 3.
Question 28.
y = -5x – 5
Answer:
y = -5x – 5
slope = -5 and y – intercept = -5
slope = rise/run = -5/1
Plot the point that is 1 unit right and 5 unit up from (0, -5) = (1, -10)
So, the x – intercept is -1.
Question 29.
y + 14 = -7x
Answer:
y + 14 = -7x
y = -7x – 14
slope = -7 and y – intercept = -14
Slope = rise/run = -7/1
Plot the point that is 1 unit right and 7 unit down from (0, -14) = (1, -21)
So, the x – intercept is -2.
Question 30.
y = 8 – 2x
Answer:
Given the equation
y = 8 – 2x
y = -2x + 8
slope = -2 and y – intercept = 8
slope = rise/run = -2/1
Plot the point 1 unit right and 2 units down from (0, 8) = (1, 6)
So, the x – intercept is 4.
Question 31.
PRECISION
You go to a harvest festival and pick apples.
a. Which equation represents the cost (in dollars) of going to the festival and picking x pounds of apples? Explain.
b. Graph the equation you chose in part(a).
Answer:
Picking a pound of apples costs $0.75, therefore x pounds cost 0.75 × x = 0.75x y = 0.75x + 5 Question 32. REASONING Without graphing, identify the equations of the lines that are parallel. Explain your reasoning. Answer: The lines which area parallel are those having the same slope. y = 2x + 4 y = 2x – 3 y = 2x + 1 y = 1/2x + 1 y = 1/2x + 2 Question 33. PROBLEM SOLVING A skydiver parachutes to the ground. The height y (in feet) of the skydiver after x seconds is y = -10x + 3000. a. Graph the linear equation. b. Interpret the slope, y-intercept, and x-intercept. Answer: y = -10x + 3000 x = 0 y = -10(0) + 3000 = 3000 y = 0 0 = -10 + 3000 10x = 3000 x = 3000/10 = 300 b. The slope shows that each second the skydiver descends 10 feet. The y – intercept shows that the skydiver begins its dive from 3000 feet. The x – intercept shows that he reaches the ground after 300 seconds. Question 34. DIG DEEPER! Six friends create a website. The website earns money by selling banner ads. It costs$120 a month to operate the website.
a. A banner ad earns $0.005 per click. Write a linear equation that represents the monthly profit after paying operating costs. b. Graph the equation in part(a). On the graph, label the number of clicks needed for the friends to start making a profit. Explain. Answer: y = 0.005x – 120 x = 0 y = 0.005(0) – 120 y = -120 y = 0 0 = 0.005x – 120 0.005x = 120 x = 24000 x > 24,000 ### Lesson 4.5 Graphing Linear Equations in Standard Form EXPLORATION 1 Using Intercepts Work with a partner. You spend$150 on fruit trays and vegetable trays for a party.
a. You buy x fruit trays and y vegetable trays. Complete the verbal model. Then use the verbal model to write an equation that relates x and y.
b. What is the greatest number of fruit trays that you can buy? vegetable trays? Can you use these numbers to graph your equation from part (a) in the coordinate plane? Explain.
c.Use a graph to determine the different combinations of fruit trays and vegetable trays that you can buy. Justify your answers algebraically.
d. You are given an extra $50 to spend. How does this affect the intercepts of your graph in part(c)? Explain your reasoning. Answer: Try It Graph the linear equation. Question 1. x + y = -2 Answer: Given the equation y = mx + b x + y = -2 y = -x – 2 Comparing the value of b and m from y = mx + b m = -1 and b = -2 Plot y – intercept = (0, b) = (0, -2) Slope = -1 run/rise = -1/1 Plot the point 1 unit down and 1 unit to the right = (1, -3) Now plot the points and draw the graph Question 2. –$$\frac{1}{2}$$x + 2y = 6 Answer: –$$\frac{1}{2}$$x + 2y = 6 2y = 6 + $$\frac{1}{2}$$x y = 0.25x + 3 Comparing the value of b and m from y = mx + b m = 0.25 and b = 3 Plot y – intercept = (0, b) = (0, 3) Slope = 0.25 run/rise = 0.25/1 Plot the point 0.25 unit up and 1 unit to the right = (1, 3.25) Now plot the points and draw the graph Question 3. –$$\frac{2}{3}$$x + y = 0 Answer: –$$\frac{2}{3}$$x + y = 0 y = $$\frac{2}{3}$$x Comparing the value of b and m from y = mx + b m = $$\frac{2}{3}$$ and b = 0 Plot y – intercept = (0, b) = (0, 0) Slope =$$\frac{2}{3}$$ run/rise = $$\frac{2}{3}$$ Plot the point 0.25 unit up and 1 unit to the right = (3, 2) Now plot the points and draw the graph Question 4. 2x + y = 5 Answer: 2x + y = 5 y = -2x + 5 Comparing the value of b and m from y = mx + b m = -2 and b = 5 Plot y – intercept = (0, b) = (0, 5) Slope = -2 run/rise = $$\frac{-2}{1}$$ Plot the point 0.25 unit up and 1 unit to the right = (1, 3) Now plot the points and draw the graph Graph the linear equation using intercepts. Question 5. 2x – y = 8 Answer: y = 0 2x – y = 8 2x – 0 = 8 2x = 8 x = 4 The x – intercept is (4, 0) Y – intercept : x = 0 2x – y = 8 2(0) – y = 8 y = -8 Question 6. x + 3y = 6 Answer: X-intercept: y = 0 x + 3y = 6 x + 3(0) = 6 x + 0 = 6 x = 6 The x – intercept is (6, 0) Y – intercept: x = 0 x + 3y = 6 0 + 3y = 6 y = 2 The y – intercept is (0, 2) Self-Assessment for Concepts & Skills Solve each exercise. Then rate your understanding of the success criteria in your journal. STRUCTURE Determine whether the equation is in standard form. If not, rewrite the equation in standard form. Question 7. y = x – 6 Answer: y = x – 6 The standard form of equation is: Ax + By = C The given equation is not in the standard form. y = x – 6 x – y = 6 Question 8. y – $$\frac{1}{6}$$x + 5 = 0 Answer: The standard form of equation is: Ax + By = C The given equation is not in the standard form. y – $$\frac{1}{6}$$x + 5 = 0 $$\frac{1}{6}$$x – y = 5 Question 9. 4x + y = 5 Answer: The standard form of equation is: Ax + By = C The given equation is in the form of the standard form. Question 10. WRITING Describe two ways to graph the equation 4x + 2y = 6. Answer: The two ways to graph the equation: 1. Graph the equation using standard form 2. Graph the equation using intercept. GRAPHING A LINEAR EQUATION Graph the linear equation. Question 11. 4x + y = 5 Answer: Given the equation 4x + y = 5 y = -4x + 5 Comparing the value of b and m from y = mx + b m = -4 and b = 5 Plot y – intercept = (0, b) = (0, 5) Slope = -4 run/rise = $$\frac{-4}{1}$$ Plot the point 4 unit down and 1 unit to the right = (1, 1) Now plot the points and draw the graph Question 12. $$\frac{1}{3}$$x + 2y = 8 Answer: X – intercept: y = 0 $$\frac{1}{3}$$x + 2y = 8 $$\frac{1}{3}$$x + 2(0) = 8 $$\frac{1}{3}$$x = 8 x = 24 The x – intercept is (24, 0) Y – intercept: x = 0 $$\frac{1}{3}$$x + 2y = 8 $$\frac{1}{3}$$(0) + 2y = 8 2y = 8 y = 4 The y – intercept is (0, 4) Question 13. 5x – y = 10 Answer: X – intercept: y = 0 5x – 0 = 10 5x = 10 x = 2 The x-intercept is (2, 0) Y – intercept: x = 0 5x – y = 10 5(0) – y = 10 -y = 10 y = -10 The y – intercept is (0, -10) Question 14. x – 3y = 9 Answer: X – intercept: y = 0 x – 3(0) = 9 x = 9 The x – intercept is (9, 0) Y – intercept: x = 0 0 – 3y = 9 -3y = 9 y = -3 The y – intercept is (0, -3) Self-Assessment for Problem Solving Solve each exercise. Then rate your understanding of the success criteria in your journal. Question 15. You have$30 to spend on paint and clay. The equation 2x + 6y = 30 represents this situation, where x is the number of paint bottles and y is the number of tubs of clay. Graph the equation. Interpret the intercepts. How many bottles of paint can you buy if you buy 3 tubs of clay? Justify your answer.
Answer:
Given,
You have $30 to spend on paint and clay. The equation 2x + 6y = 30 represents this situation, where x is the number of paint bottles and y is the number of tubs of clay. X – intercept: y = 0 2x + 6y = 30 2x + 6(0) = 30 2x = 30 x = 15 The x – intercept is (15, 0) Y – intercept: x = 0 2x + 6y = 30 2(0) + 6y = 30 6y = 30 y = 5 The y – intercept is (0, 5) From the graph, I can buy 6 bottles of point if I buy 3 tubs of clay. Question 16. You complete two projects for a class in 60 minutes. The equation x + y = 60 represents this situation, where x is the time (in minutes) you spend assembling a birdhouse and y is the time (in minutes) you spend writing a paper. a. Graph the equation. Interpret the intercepts. Answer: x + y = 60 y = -x + 60 b. You spend twice as much time assembling the birdhouse as you do writing the paper. How much time do you spend writing the paper? Justify your answer. Answer: We are given, y = 2x 2x = -x + 60 2x + x = 60 3x = 60 x = 20 y = 2 (20) y = 40 ### Graphing Linear Equations in Standard Form Homework & Practice 4.5 Review & Refresh Find the slope and the y-intercept of the graph of the linear equation. Question 1. y = x – 1 Answer: y = mx + b Slope = -1 and y – intercept = -1 Question 2. y = -2x + 1 Answer: y = -2x + 1 y = mx + b Slope = -2 and y – intercept = 1 Question 3. y = $$\frac{8}{9}$$x – 8 Answer: y = $$\frac{8}{9}$$x – 8 y = mx + b Slope = $$\frac{8}{9}$$ and y – intercept = -8 Tell whether the blue figure is a reflection of the red figure. Question 4. Answer: The blue figure is not a reflection of the red figure because, for example the reflection of the upper leg of the upper leg of the red triangle across the y-axis is the top vertex of the blue triangle, not a point. Question 5. Answer: The blue figure is a reflection of the red figure because to each point in the red figure corresponds a symmetrical point in the blue figure. Question 6. Answer: The blue figure is a reflection of the red figure because to each point in the red figure corresponds a symmetrical point in the blue figure. Concepts, Skills, &Problem Solving USING INTERCEPTS Define two variables for the verbal model. Write an equation in slope-intercept form that relates the variables. Graph the equation using intercepts. (See Exploration 1, p. 167.) Question 7. Answer: x = amount of peaches (in pounds) y = the amount of apples (in pounds) 2x + 1.5y = 15 y = 0 = 2x + 1.5(0) = 15 2x = 15 x = 7.5 x = 0 2(0) + 1.5y = 15 1.5y =15 y = 10 Question 8. Answer: x = the biked distance (in miles) y = the walked distance (in miles) y = 0 16x + 2(0) = 32 16x = 32 x = 2 x = 0 16(0) + 2y = 32 2y = 32 y = 16 REWRITING AN EQUATION Write the linear equation in slope-intercept form. Question 9. 2x + y = 17 Answer: Given the equation 2x + y = 17 y = 17 – 2x y = -2x + 17 Question 10. 5x – y = $$\frac{1}{4}$$ Answer: Given the equation 5x – y = $$\frac{1}{4}$$ -y = $$\frac{1}{4}$$ – 5x y = 5x – $$\frac{1}{4}$$ Question 11. –$$\frac{1}{2}$$x + y = 10 Answer: Given the equation –$$\frac{1}{2}$$x + y = 10 y = $$\frac{1}{2}$$x + 10 GRAPHING AN EQUATION Graph the linear equation. Question 12. -18x + 9y = 72 Answer: Given the equation -18x + 9y = 72 X – intercept: y = 0 -18x + 9(0) = 72 -18x = 72 x = -4 The x – intercept is (-4, 0) Y – intercept: x = 0 -18x + 9y = 72 -18(0) + 9y = 72 9y = 72 y = 8 Question 13. 16x – 4y = 2 Answer: Given the equation 16x – 4y = 2 X – intercept: y = 0 16x – 4y = 2 16x – 4(0) = 2 16x = 2 x = 0.125 The X – intercept is (0.125, 0) Y – intercept: x = 0 16(0) – 4y = 2 -4y = 2 y = -2 Question 14. $$\frac{1}{4}$$x + $$\frac{3}{4}$$y = 1 Answer: Given the equation $$\frac{1}{4}$$x + $$\frac{3}{4}$$y = 1 x + 3y = 4 y = 0 x + 3(0) = 4 x = 4 x = 0 0 + 3y = 4 3y = 4 y = 4/3 MATCHING Match the equation with its graph. Question 15. 15x – 12y = 60 Answer: y = 0 15x – 12(0) = 60 15x = 60 x = 60/15 x = 4 x = 0 15(0) – 12y = 60 -12y = 60 y = -5 The graph having the x – intercept 4 and y – intercept -5 Question 16. 5x + 4y = 20 Answer: Given the linear equation 5x + 4y = 20 y = 0 5x + 4(0) = 20 5x = 20 x = 4 x = 0 5(0) + 4y = 20 4y = 20 y = 5 Question 17. 10x + 8y = -40 Answer: 10x + 8y = -40 y = 0 10x + 8(0) = -40 10x = -40 x = -4 x = 0 10(0) + 8y = -40 8y = -40 y = -5 Question 18 YOU BE THE TEACHER Your friend finds the x-intercept of -2x + 3y = 12. Is your friend correct? Explain your reasoning. Answer: -2x + 3y = 12 y = 0 -2x + 3(0) = 12 -2x = 12 x = -6 Your friend is not correct because the x – intercept is the value of x corresponding to y = 0. Your friend computed the y – intercept. Question 19. MODELING REAL LIFE A charm bracelet costs$65, plus $25 for each charm. The equation -25x + y = 65 represents the cost y (in dollars) of the bracelet, where x is the number of charms. a. Graph the equation. b. How much does a bracelet with three charms cost? Answer: y = 25x + 65 Substitute the value of x in the equation y = 25(3) + 65 y = 75 + 65 y = 140 USING INTERCEPTS TO GRAPH Graph the linear equation using intercepts. Question 20. 3x – 4y = -12 Answer: Given the equation 3x – 4y = -12 3x – 4(0) = -12 3x = -12 x = -4 The x – intercept is (-4, 0) Y – intercept: x = 0 3(0) – 4y = -12 -4y = -12 y = 3 The y – intercept is (0, 3) Question 21. 2x + y = 8 Answer: X – intercept: y = 0 2x + y = 8 2x + 0 = 8 2x = 8 x = 4 The x – intercept is (4, 0) Y – intercept: x = 0 2x + y = 8 2(0) + y = 8 y = 8 The y – intercept is (0, 8) Question 22. $$\frac{1}{3}$$x – $$\frac{1}{6}$$y = –$$\frac{2}{3}$$ Answer: X – intercept: y = 0 $$\frac{1}{3}$$x – $$\frac{1}{6}$$(0) = –$$\frac{2}{3}$$ $$\frac{1}{3}$$x = –$$\frac{2}{3}$$ x = -2 The x – intercept is (-2, 0) Y – intercept: x = 0 $$\frac{1}{3}$$(0) – $$\frac{1}{6}$$y = –$$\frac{2}{3}$$ y = 4 The y – intercept is (0, 4) Question 23. MODELING REAL LIFE Your cousin has$90 to spend on video games and movies. The equation 30x + 15y = 90 represents this situation, where x is the number of video games purchased and y is the number of movies purchased. Graph the equation. Interpret the intercepts.
Answer:
30x + 15y = 90
x = 0
30(0) + 15y = 90
15y = 90
y = 6
y = 0
30x + 15(0) = 90
30x = 90
x = 3
The x – intercept shows that 3 video games are purchased when no movies are purchased.
The y – intercept shows that 6 movies are purchased when no video games are purchased.
Question 24.
PROBLEM SOLVING
A group of friends go scuba diving. They rent a boat for x days and scuba gear for y people, represented by the equation 250x + 50y = 1000.
a. Graph the equation and interpret the intercepts.
b. How many friends can go scuba diving if they rent the boat for 1 day? 2 days?
c. How much money is spent in total?
Answer:
250x + 50y = 1000
x = 0
250(0) + 50y = 1000
50y = 1000
y = 20
when y = 0
250x + 50(0) = 1000
250x = 1000
x = 4
b.
250(1) + 50y = 1000
250 + 50y = 1000
50y = 1000 – 250
50y = 750
y = 15
when x = 2
250(2) + 50y = 1000
500 + 50y = 1000
50y = 1000 – 500
50y = 500
y = 500/50
y = 10
Question 25.
DIG DEEPER!
You work at a restaurant as a host and a server. You earn $9.45 for each hour you work as a host and$3.78 for each hour you work as a server.
a. Write an equation in standard form that models your earnings.
b. Graph the equation.
Answer:
You earn $9.45 for each hour you work as a host and$3.78 for each hour you work as a server.
Number of hours worked as host + $3.78. Number of hours worked as server =$113.40
9.45x + 3.78y = 113.40
x = 0
9.45(0) + 3.78y = 113.40
3.78y = 113.40
y = 30
when y = 0
9.45x + 3.78(0) = 113.40
9.45x = 113.40
x = 12
Question 26.
LOGIC
Does the graph of every linear equation have an x-intercept? Justify your reasoning.
Answer:
y = mx + b
y = 0
0 = mx + b
mx = -b
x = -b/m for m ≠ 0
If m = 0 the equation has no solution. Therefore the equation y = b has no x – intercept.
Question 27.
CRITICAL THINKING
For a house call, a veterinarian charges $70, plus$40 per hour.
a. Write an equation that represents the total fee y (in dollars) the veterinarian charges for a visit lasting x hours.
b. Find the x-intercept. Does this value make sense in this context? Explain your reasoning.
c. Graph the equation.
Answer:
Total fee = fixed charge + number of hours . cost per hour
y = 70 + 40x
y = 0
0 = 70 + 40x
-70 = 40x
x = -1.75
x = 0
y = 70 + 40(0)
y = 70
### Lesson 4.6 Writing Equations in Slope-Intercept Form
EXPLORATION 1
Writing Equations of Lines
Work with a partner.For each part, answer the following questions.
• What are the slopes and the y-intercepts of the lines?
• What are equations that represent the lines?
• What do the lines have in common?
Answer:
EXPLORATION 2
Interpreting the Slope and the y-Intercept
Work with a partner. The graph represents the distance y (in miles) of a car from Phoenix after t hours of a trip.
a. Find the slope and the y-intercept of the line. What do they represent in this situation?
b. Write an equation that represents the graph.
c. How can you determine the distance of the car from Phoenix after 11 hours?
Answer:
Try It
Write an equation in slope-intercept form of the line that passes through the given points.
Question 1.
Answer:
m = (y2 – y1)/(x2 – x1)
= (4 – 2)/(1 – 0)
= 2/1
= 2
Because the line crosses the y – axis at (0, 2)
y = mx + b
y = 2x + 2
Question 2.
Answer:
m = (y2 – y1)/(x2 – x1)
= (-1 – 3)/(0 – (-3))
= -4/3
Because y = -1 when x = 0, the y – intercept is -1
y = mx + b
y = -4/3 x – 1
Write an equation of the line that passes through the given points.
Question 3.
Answer:
m = (y2 – y1)/(x2 – x1)
= (5 – 5)/(0 – (-4))
= 0/4
Because y = 5 when x = 0, the y – intercept is 5
y = mx + b
y = (0)x + 5
y = 5
Question 4.
Answer:
m = (y2 – y1)/(x2 – x1)
= (1 – 1)/(3 – 0)
= 0/3
= 0
Because the line crosses the y – axis at (0, 1) the y – intercept is 1
y = mx + b
y = (0)x + 1
y = 1
Self-Assessment for Concepts & Skills
Solve each exercise. Then rate your understanding of the success criteria in your journal.
WRITING EQUATIONS IN SLOPE-INTERCEPT FORM Write an equation in slope-intercept form of the line that passes through the given points.
Question 5.
Answer:
m = (y2 – y1)/(x2 – x1)
= (5 – 2)/(1 – 0)
= 3/1
= 3
Because y = 2 when x = 0, the y – intercept is 2
y = mx + b
y = (3)x + 2
y = 3x + 2
Question 6.
Answer:
m = (y2 – y1)/(x2 – x1)
= (-1 – 5)/(1 – (-1))
= -6/2
= -3
Because the line crosses the y – axis at (0, 2) the y – intercept is 2
y = mx + b
y = -3x + 2
Question 7.
WRITING AN EQUATION
Write an equation of the line that passes through (0, -5) and (2, -5).
Answer:
m = (y2 – y1)/(x2 – x1)
= (-5 – (-5))/(2 – 0)
= 0/2
= 0
Because y = -5 when x = 0, the y – intercept is -5
y = mx + b
y = (0)x + -5
y = -5
Self-Assessment for Problem Solving
Solve each exercise. Then rate your understanding of the success criteria in your journal.
Question 8.
You load boxes onto an empty truck at a constant rate. After 3 hours, there are 100 boxes on the truck. How much longer do you work if you load a total of 120 boxes? Justify your answer.
Answer:
Let x be the number of hours you work if you load a total of 120 boxes.
100/3 = 120/x
100x = 3 × 120
x = 360/100
x = 3.6 hours
3.6 – 3 = 0.6 hours
Question 9.
The table shows the amounts (in tons) of waste left in a landfill after x months of waste relocation. Interpret the slope and the y-intercept of the line that passes through the given points. How many months does it take to empty the landfill? Justify your answer.
Answer:
m = (12 – 15)/ (6 – 0)
m = -3/6
m = -0.5
b = 15
The y – intercept shows that there are 150 tons of waste in the beginning.
y = -0.5x + 15
y = 0
0 = -0.5x + 15
x = 30
So the ladfill will be emptied after 30 months.
Question 10.
DIG DEEPER!
A lifetime subscription to a website costs $250. A monthly subscription to the website costs$10 to join and $15 per month. Write equations to represent the costs of each plan. If you want to be a member for one year, which plan is less expensive? Explain. Answer: Given, A lifetime subscription to a website costs$250. A monthly subscription to the website costs $10 to join and$15 per month.
Total cost for plan 1 = the lifetime subscription
y = 250
Total cost for Plan 2 = Fixed tax + Number of months . monthly cost
y = 10 + 15x
Plan 1: y = 250
Plan 2: y = 10 + 15(12) = 190
As 190 < 250, plan 1 is less expensive.
### Writing Equations in Slope-Intercept Form Homework & Practice 4.6
Review & Refresh
Write the linear equation in slope-intercept form.
Question 1.
4x + y = 1
Answer:
Given the equation
4x + y = 1
y = -4x + 1
Question 2.
x – y = $$\frac{1}{5}$$
Answer:
Given the equation
x – y = $$\frac{1}{5}$$
x – $$\frac{1}{5}$$ = y
Question 3.
–$$\frac{2}{3}$$x + 2y = -7
Answer:
Given the equation
–$$\frac{2}{3}$$x + 2y = -7
2y = -7 + $$\frac{2}{3}$$x
y = $$\frac{1}{3}$$x – $$\frac{7}{2}$$
Plot the ordered pair in a coordinate plane.
Question 4.
(1, 4)
Answer:
Question 5.
(-1, -2)
Answer:
Question 6.
(0, 1)
Answer:
Question 7.
(2, 7)
Answer:
Concepts, Skills, & Problem Solving
INTERPRETING THE SLOPE AND THE y-INTERCEPT The graph y represents the cost (in dollars) to open an online gaming account and buy x games. (See Exploration 2, p. 173.)
Question 8.
Find the slope and the y-intercept of the line. What do they represent in this situation?
Answer:
(0, 15), (3, 45)
m = (45 – 15)/(3 – 0)
m = 30/3 10
Thus the slope of the line is m – 3.
b = 15
The slope represents the cost of one game, while the y – intercept is the cost of opening the gaming account.
Question 9.
Write an equation that represents the graph.
Answer:
m = 10
b = 15
y = mx + b
y = 10x + 15
Question 10.
How can you determine the total cost of opening an account and buying 6 games?
Answer:
y = 10x + 15
y = 10(6) + 15
y = 60 + 15
y = 75
WRITING EQUATIONS IN SLOPE-INTERCEPT FORM Write an equation in slope-intercept form of the line that passes through the given points.
Question 11.
Answer:
m = (y2 – y1)/(x2 – x1)
= (4 – 3)/(0 – (-1))
= 1/1
= 1
Because the line crosses the y – axis at (0, 4) the y – intercept is 4
y = mx + b
y = (1)x + 4
y = x + 4
Question 12.
Answer:
m = (y2 – y1)/(x2 – x1)
= (6 – 0)/(-3 – 0)
= 6/-3
= -2
Because the line crosses the y – axis at (0, 2) the y – intercept is 2
y = mx + b
y = -2x + 0
y = -2x
Question 13.
Answer:
m = (y2 – y1)/(x2 – x1)
= (2 – 1)/(4 – 0)
= 1/4
Because the line crosses the y – axis at (0, 1) the y – intercept is 1
y = mx + b
y = 1/4 x + 1
Question 14.
Answer:
m = (y2 – y1)/(x2 – x1)
= (1 – 2)/(0 – (-2))
= -1/2
Because y = 1 when x = 0, the y – intercept is 1
y = mx + b
y = -1/2 x + 2
Question 15.
Answer:
m = (y2 – y1)/(x2 – x1)
= (-3 – (-4))/(0 – (-3))
= 1/3
Because y = -3 when x = 0, the y – intercept is -3
y = mx + b
y = 1/3 x – 3
Question 16.
Answer:
m = (y2 – y1)/(x2 – x1)
= (-1 -4)/(0 – (-2))
= -5/2
Because y = -1 when x = 0, the y – intercept is -1
y = mx + b
y = -5/2 x – 1
WRITING EQUATIONS Write an equation of the line that passes through the given points.
Question 17.
(-1, 4), (0, 2)
Answer:
m = (y2 – y1)/(x2 – x1)
= (2 – 4)/(0 – (-1))
= -2/1
= -2
Because y = 2 when x = 0, the y – intercept is 2
y = mx + b
y = -2x + 2
Question 18.
(-1, 0), (0, 0)
Answer:
m = (y2 – y1)/(x2 – x1)
= (0 – 0)/(0 – (-1))
= 0/1
= 0
Because y = 0 when x = 0, the y – intercept is 0
y = mx + b
y = 0
Question 19.
(0, 4), (0, -3)
Answer:
Both points belong to the y-axis. Therefore the equation of the line passing through them is
x = 0
Question 20.
YOU BE THE TEACHER
Your friend writes an equation of the line shown. Is your friend correct? Explain your reasoning.
Answer:
Because in the given graph, y = -2 when x = 0, so the y – intercept is -2. The equation of the line should be: y = 1/2 x – 2
No my friend is NOT correct.
Question 21.
MODELING REAL LIFE
A boa constrictor is 18 inches long at birth and grows 8 inches per year. Write an equation in slope y-intercept form that represents the length (in feet) of a boa constrictor that is x years old.
Answer:
Given,
A boa constrictor is 18 inches long at birth and grows 8 inches per year.
Length after x years = birth length + number of years . Growth per year
y = 18 + 8x
y = 8x + 18
Convert it into feet
y = 2/3 x + 3/2
Question 22.
MODELING REAL LIFE
The table shows the speeds y (in miles per hour) of a car after x seconds of braking. Write an equation of the line that passes through the points in the table. Interpret the slope and the y-intercept of the line.
Answer:
m = (y2 – y1)/(x2 – x1)
= (60 – 70)/(1 – 0)
= -10/1
= -10
Because y = 70 when x = 0, the y – intercept is 70
y = mx + b
y = -10x + 70
Slope = -10 represents the decrease in the speed of the car each seconds after breaking.
The y – intercept of 70 represents the initial speed of the car.
Question 23.
MODELING REAL LIFE
A dentist charges a flat fee for an office visit, plus an additional fee for every tooth removed. The graph shows the total cost y (in dollars) for a patient when the dentist removes x teeth. Interpret the slope and the y-intercept.
Answer:
(2, 500), (4, 900)
m = (900 – 500)/(4 – 2)
m = 400/2
m = 200
y = mx + b
500 = 200(2) + b
500 = 400 + b
b = 500 – 400
b = 100
The slope shows that the amount charged for each removed tooth is $200. The y – intercept shows that the flat fee for an office visit is$100.
Question 24.
MODELING REAL LIFE
One of your friends gives you $10 for a charity walkathon. Another friend gives you an amount per mile. After 5 miles, you have raised$13.50 total. Write an equation that represents the amount y of money you have raised after x miles.
Answer:
Given,
One of your friends gives you $10 for a charity walkathon. Another friend gives you an amount per mile. After 5 miles, you have raised$13.50 total.
y = mx + b
b = 10
13.50 = 5m + 10
13.50 – 10 = 5m
3.50 = 5m
m = 3.50/5
m = 0.7
y = 0.7x + 10
Question 25.
PROBLEM SOLVING
You have 500 sheets of notebook paper. After 1 week, you have 72% of the sheets left. You use the same number of sheets each week. Write an equation that represents the number y of sheets remaining after x weeks.
Answer:
y = mx + b
500 – 0.72 × 500 = 500 – 360 = 140 sheets
m = -140
b = 500
y = -140x + 500
Question 26.
DIG DEEPER!
The palm tree on the left is 10 years old. The palm tree on the right is 8 years old. The trees grow at the same rate.
a. Estimate the height y (in feet) of each tree.
b. Plot the two points (x, y), where x is the age of each tree and y is the height of each tree.
c. What is the rate of growth of the trees?
d. Write an equation that represents the height of a palm tree in terms of its age.
Answer:
a. estimate
left: 18
right: 12
plot y = 1.8x
### Lesson 4.7 Writing Equations in Point-Slope Form
EXPLORATION 1
Deriving an Equation
Work with a partner. Let (x1, y1) represent a specific point on a line. Let (x, y) represent any other point on the line.
a. Write an equation that represents the slope m of the line. Explain your reasoning.
b. Multiply each side of your equation in part(a) by the expression in the denominator. What does the resulting equation represent? Explain your reasoning.
Answer:
EXPLORATION 2
Writing an Equation
Work with a partner.
For 4 months, you saved $25 a month. You now have$175 in your savings account.
a. Draw a graph that shows the balance in your account after t months.
b.Use your result from Exploration 1 to write an equation that represents the balance A after t months.
Answer:
Try It
Write an equation in point -slope form of the line that passes through the given point and has the given slope.
Question 1.
(1, 2); m = -4
Answer:
y – y1 = m(x – x1)
y – 2 = -4(x – (1))
y – 2 = -4(x – 1)
Question 2.
(7, 0); m = 1
Answer:
y – y1 = m(x – x1)
y – 0 = 1(x – (7))
y – 0 = 1(x – 7)
Question 3.
(-8, -5); m = –$$\frac{3}{4}$$
Answer:
y – y1 = m(x – x1)
y – (-5) = –$$\frac{3}{4}$$(x – (-8))
y + 5 = –$$\frac{3}{4}$$(x + 8)
Write an equation in slope-intercept form of the line that passes through the given points.
Question 4.
(-2, 1), (3, -4)
Answer:
Slope(m) = (-4 – 1)/(3 – (-2))
= -5/5
m = -1
y – y1 = m(x – x1)
y – 1 = -1(x – (-2))
y – 1 = -1(x + 2)
y – 1 = -x – 2
y = -x – 1
Question 5.
Answer:
Slope(m) = (3 – 5)/(-3 – (-5))
= -2/2
m = -1
y – y1 = m(x – x1)
y – 1 = -1(x – (-1))
y – 1 = -1(x + 1)
y – 1 = -x – 1
y = -x – 1 + 1
y = -x
Self-Assessment for Concepts & Skills
Solve each exercise. Then rate your understanding of the success criteria in your journal.
WRITING AN EQUATION Write an equation in point-slope form of the line that passes through the given point and has the given slope.
Question 6.
(2, 0); m = 1
Answer:
y – y1 = m(x – x1)
y – 0 = 1(x – (2))
y – 0 = 1(x – 2)
Question 7.
(-3, -1); m = –$$\frac{1}{3}$$
Answer:
y – y1 = m(x – x1)
y – (-1) = –$$\frac{1}{3}$$(x – (-3))
y + 1 = –$$\frac{1}{3}$$(x + 3)
Question 8.
(5, 4); m = 3
Answer:
y – y1 = m(x – x1)
y – 4 = 3(x – (5))
y – 4 = 3(x – 5)
Question 9.
WRITING AN EQUATION
Write an equation of the line that passes through the points given in the table.
Answer:
Slope(m) = (-2 – 1)/(5 – 3)
= -3/2
m = -1
y – y1 = m(x – x1)
y – (-5) = -3/2(x – 7)
y + 5 = -3/2(x – 7)
y + 5 = -3/2 x + 21/2
y = -3/2 x + 11/2
Question 10.
DIFFERENT WORDS, SAME QUESTION
Which is different? Sketch “both” graphs.
Answer:
y – 7 = 4x – 4
y = 4x + -4 + 7
y = 4x + 3
Graph line passes through the points (4, 5) and (5, 9)
Self-Assessment for Problem Solving
Solve each exercise. Then rate your understanding of the success criteria in your journal.
Question 11.
A writer finishes a project that a coworker started at a rate of 3 pages per hour. After 3 hours,25% of the project is complete.
a. The project is 200 pages long. Write and graph an equation for the total number y of pages that have been finished after the writer works for x hours.
b. The writer has a total of 45 hours to finish the project. Will the writer meet the deadline? Explain your reasoning.
Answer:
m = 3
y = 3x + b
b + 9 = 25%(200)
b + 9 = 0.25(200)
b + 9 = 50
b = 50 – 9
b = 41
y = 3x + 41
y = 3x + 41
y = 3(45) + 41 = 176 pages
As 176 < 200, the writer will not meet the deadline.
Question 12.
DIG DEEPER!
You and your friend begin to run along a path at different constant speeds.After 1 minute,your friend is 45 meters ahead of you. After 3 minutes, your friend is 105 meters ahead of you.
a. Write and graph an equation for the distance y (in meters) your friend is ahead of you after x minutes. Justify your answer.
Answer:
y = mx + b
45 = m + b
105 = 3m + b
105 – 45 = (3m + b) – (m + b)
60 = 2m
m = 30
45 = 30 + b
b = 45 – 30
b = 15
y = 30x + 15
b. Did you and your friend start running from the same spot? Explain your reasoning.
Answer:
The distance between you and your friend in the initial moment is b = 15 meters. So you are ahead your friend by 15 meters at the starting point.
### Writing Equations in Point-Slope Form Homework & Practice 4.7
Review & Refresh
Write an equation in slope-intercept form of the line that passes through the given points.
Question 1.
Answer:
Slope(m) = (5 – 4)/(0 – (-2))
= 1/2
m = 1/2
Because y = 5 when x = 0, the y – intercept is 5.
y = mx + b
y = 1/2 x + 5
Question 2.
Answer:
Slope(m) = (5 – (-1))/(2 – (-2))
= (5 + 1)/(2 + 2)
m = 6/4
m = 3/2
From the graph, the line crosses the y – axis at (0, 2)
y = mx + b
y = 3/2 x + 2
Solve the equation. Check your solution, if possible.
Question 3.
2x + 3 = 2x
Answer:
Given the equation
2x + 3 = 2x
3 = 2x – 2x
3 ≠ 0
Question 4.
6x – 7 = 1 – 3x
Answer:
Given the equation
6x – 7 = 1 – 3x
6x + 3x = 1 + 7
9x = 8
x = 8/3
Question 5.
0.1x – 1 = 1.2x – 5.4
Answer:
Given the equation
0.1x – 1 = 1.2x – 5.4
0.1x – 1.2x = 1 – 5.4
-1.1x = -4.4
x = 4
Concepts, Skills, &Problem Solving
WRITING AN EQUATION The value of a new car decreases $4000 each year. After 3 years, the car is worth$18,000. (See Exploration 2, p. 179.)
Question 6.
Draw a graph that shows the value of the car after t years.
Answer:
Question 7.
Write an equation that represents the value V of the car after t years.
Answer:
y = -4000t + b
where b is the original price
18,000 = -4000(3) + b
18,000 + 12,000 = b
b = 30,000
y = -4000t + 30,000
WRITING AN EQUATION Write an equation in point-slope form of the line that passes through the given point and has the given slope.
Question 8.
(3, 0); m = –$$\frac{2}{3}$$
Answer:
y – y1 = m(x – x1)
y – (0) = -2/3(x – 3)
y – 0 = -2/3(x – 3)
Question 9.
(4, 8); m = $$\frac{3}{4}$$
Answer:
y – y1 = m(x – x1)
y – (8) = 3/4(x – 4)
y – 8 = 3/4(x – 4)
Question 10.
(1, -3); m = 4
Answer:
y – y1 = m(x – x1)
y – (-3) = 4(x – 1)
y + 3 = 4(x – 1)
Question 11.
(7, -5); m = –$$\frac{1}{7}$$
Answer:
y – y1 = m(x – x1)
y – (-5) = –$$\frac{1}{7}$$(x – 7)
y + 5 = –$$\frac{1}{7}$$(x – 7)
Question 12.
(3, 3); m = $$\frac{5}{3}$$
Answer:
y – y1 = m(x – x1)
y – (3) = $$\frac{5}{3}$$(x – 3)
y – 3 = $$\frac{5}{3}$$(x – 3)
Question 13.
(-1, -4); m = -2
Answer:
y – y1 = m(x – x1)
y – (-4) = -2(x – (-1))
y + 4 = -2(x + 1)
WRITING AN EQUATION Write an equation in slope-intercept form of the line that passes through the given points.
Question 14.
(-1, -1), (1, 5)
Answer:
Slope(m) = (5 – (-1))/(2 – (-1))
= (5 + 1)/(1 + 1)
m = 6/2
m = 3
y – y1 = m(x – x1)
y – (5) = 3(x – (1))
y – 5 = 3x – 3
y = 3x + 2
Question 15.
(2, 4), (3, 6)
Answer:
Slope(m) = (6 – 4)/(3 – 2)
m = 2/1
m = 2
y – y1 = m(x – x1)
y – (4) = 2(x – (2))
y – 4 = 2x – 4
y = 2x
Question 16.
(-2, 3), (2, 7)
Answer:
Slope(m) = (7 – (3))/(2 – (-2))
= (7 – 3)/(2 + 2)
m = 4/4
m = 1
y – y1 = m(x – x1)
y – (3) = 1(x – (-2))
y – 3 = x + 2
y = x + 5
Question 17.
(4, 1), (8, 2)
Answer:
Slope(m) = (2 – (1))/(8 – (4))
= (2 – 1)/(8 – 4)
m = 1/4
y – y1 = m(x – x1)
y – (1) = 1/4(x – (4))
y – 1 = 1/4 x – 1
y = 1/4 x
Question 18.
(-9, 5), (-3, 3)
Answer:
Slope(m) = (3 – (5))/(-3 – (-9))
= (3 – 5)/(-3 + 9)
m = -2/6
m = -1/3
y – y1 = m(x – x1)
y – (3) = -1/3(x + 3)
y – 3 = -1/3 x – 1
y = -1/3 x + 2
Question 19.
(1, 2), (-2, -1)
Answer:
Slope(m) = (2 – (1))/(8 – (4))
= (-1 – 2)/(-2 – 1)
m = -3/-3
m = 1
y – y1 = m(x – x1)
y – (2) = 1(x – (1))
y – 2 = x – 1
y = x + 1
Question 20.
MODELING REAL LIFE
At 0° C, the volume of a gas is 22 liters. For each degree the temperature T (in degrees Celsius) increases, the volume V (in liters) of the gas increases by $$\frac{2}{25}$$. Write an equation that represents the volume of the gas in terms of the temperature.
Answer:
The equation modeling the situation has the form:
V = mT + b
m = 2/25
22 = 2/25(0) + b
b = 22
V = 2/25 T + 22
WRITING AN EQUATION Write an equation of the line that passes through the given points in any form. Explain your choice of form.
Question 21.
Answer:
m = (y2 – y1)/(x2 – x1)
= (2.5 – 1.5)/(0 – (-1))
= 1/1
= 1
Because the line crosses the y – axis at (0, 2.5), the y – intercept is 2.5
y = mx + b
y = (1)x + 2.5
y = x + 2.5
Question 22.
Answer:
m = (y2 – y1)/(x2 – x1)
= (3.5 – 1.5)/(2 – (1))
= 2/1
= 2
y – y1 = m(x – x1)
y – (1.5) = 2(x – (1))
y – 1.5 = 2x – 2
y = 2x – 0.5
Question 23.
Answer:
m = (y2 – y1)/(x2 – x1)
= (-1.5 – 4.5)/(1 – (-1))
= -6/2
= -3
y – y1 = m(x – x1)
y – (-1.5) = -3(x – (1))
y + 1.5 = -3x + 3
y = -3x + 1.5
Question 24.
Answer:
m = (y2 – y1)/(x2 – x1)
= (-0.5 – 3.5)/(1 – (-1))
= -4/2
= -2
y – y1 = m(x – x1)
y – (-0.5) = -2(x – (1))
y + 0.5 = -2x – 2
y = -2x – 2.5
Question 25.
Answer:
m = (y2 – y1)/(x2 – x1)
= (1 – (-1))/(0 – (-3))
= (1 + 1)/(0 + 3)
= 2/3
Because y = 1 when x = 0, the y – intercept is 1.
y = mx + b
y = 2/3 x + 1
Question 26.
Answer:
m = (y2 – y1)/(x2 – x1)
= (4 – 6)/(-3 – (-7))
= -2/4
= -1/2
y – y1 = m(x – x1)
y – (2) = -1/2(x – (1))
y – 2 = -1/2x + 1/2
y = -1/2 x + 5/2
Question 27.
REASONING
Write an equation of the line that passes through the point (8, 2) and is parallel to the graph of the equation y = 4x – 3.
Answer:
y = 4x – 3
Comparing the given equation with y = mx + b, we get
m = 4
y – y1 = m(x – x1)
y – 2 = 4(x – 8)
y – 2 = 4x – 32
y = 4x – 32 + 2
y = 4x – 30
Question 28.
MODELING REAL LIFE
The table shows the amount y (in fluid ounces) of carpet cleaner in a tank after x minutes of cleaning.
a. Write an equation that represents the amount of cleaner x in the tank after minutes.
b. How much cleaner is in the tank when the cleaning begins?
c. After how many minutes is the tank empty? Justify your answer.
Answer:
Question 29.
DIG DEEPER!
According to Dolbear’s law, you can predict the temperature T (in degrees Fahrenheit) by counting the number x of chirps made by a snowy tree cricket in 1 minute.When the temperature is 50°F, a cricket chirps 40 times in 1 minute. For each rise in temperature of 0.25°F, the cricket makes an additional chirp each minute.
a. You count 100 chirps in 1 minute. What is the temperature?
b. The temperature is 96°F.How many chirps do you expect the cricket to make? Justify your answer.
Answer:
Question 30.
PROBLEM SOLVING
The Leaning Tower of Pisa in Italy was built between 1173 and 1350.
a. Write an equation that represents the yellow line.
b. The tower is 56 meters tall. How far from the center is the top of the tower? Justify your answer.
Answer:
### Graphing and Writing Linear Equations Connecting Concepts
Using the Problem-Solving Plan
Question 1.
Every item in a retail store is on sale for 40% off. Write and graph an equation that represents the sale price of an item that has an original price of x dollars.
Understand the problem.
You know the percent discount of items in a retail store.You are asked to write and graph an equation that represents the sale price of an item that has an original price of x dollars.
Make a plan.
Selling an item for 40% off is the same as selling an item for 60% of its original price. Use this information to write and graph an equation that represents the situation.
Solve and check.
Use the plan to solve the problem. Then check your solution.
Answer:
40% = 0.40 and to find a percent of a number you multiply the number by the percent in decimal form.
So, the equation is d = 0.4p
Question 2.
Two supplementary angles have angle measures of x° and y°. Write and graph an equation that represents the relationship between the measures of the angles.
Answer:
Question 3.
A mechanic charges a diagnostic fee plus an hourly rate. The table shows the numbers of hours worked and the total costs for three customers.A fourth customer pays $285. Find the number of hours that the mechanic worked for the fourth customer. Answer: Performance Task Anatomy of a Hurricane At the beginning of this chapter, you watched a STEAM Video called “Hurricane!” You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task. ### Graphing and Writing Linear Equations Chapter Review Review Vocabulary Write the definition and give an example of each vocabulary term. Graphic Organizers You can use a Definition and Example Chart to organize information about a concept. Here is an example of a Definition and Example Chart for the vocabulary term linear equation. Choose and complete a graphic organizer to help you study the concept. 1. slope 2. slope of parallel lines 3. proportional relationship 4. slope-intercept form 5. standard form 6. point-slope form Chapter Self-Assessment As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal. 4.1 Graphing Linear Equations (pp. 141–146) Learning Target: Graph linear equations.Graph the linear equation. Question 1. y = $$\frac{3}{5}$$x Answer: Question 2. y = -2 Answer: Question 3. y = 9 – x Answer: Question 4. y = -0.25x + 4 Answer: Question 5. y = $$\frac{2}{3}$$x + 2 Answer: Question 6. x = -5 Answer: Question 7. The equation y = 0.53x + 3 represents the cost y (in dollars) of riding in a taxi x miles. a. Use a graph to estimate how much it costs to ride 5.25 miles in a taxi. b. Use the equation to find exactly how much it costs to ride 5.25 miles in a taxi. Answer: y = 0.5x + 3 y = 0.5(5.25) + 3 y ≈ 5.6 Question 8. The equation y = 9.5x represents the earnings y (in dollars) of an aquarium gift shop employee that works x hours. a. Graph the linear equation. b. How much does the employee earn for working 40 hours? Answer: Determine y for x = 40: y = 9.5x y = 9.5(40) = 380 Question 9. Is y = x2 a linear equation? Explain your reasoning. Answer: y = x2 The graph of the given equation passes through the origin, but is not linear, therefore it is not a linear equation. So, the answer is no. Question 10. The sum S of the exterior angle measures of a polygon with n sides is S = 360°. a. Plot four points (n, S) that satisfy the equation. Is the equation a linear equation? Explain your reasoning. b. Does the value n = 2 make sense in the context of the problem? Explain your reasoning. Answer: The value n = 2 does not make sense in the context of the problem because a polygon has at least 3 sides. 4.2 Slope of a Line (pp. 147–154) Learning Target: Find and interpret the slope of a line. Describe the slope of the line. Then find the slope of the line. Question 11. Answer: (x1, y1) = (3, 1) (x2, y2) = (-3, -3) m = (y2 – y1)/(x2 – x1) m = (-3 – 1)/(-3 – 3) m = -4/-6 m = 2/3 Question 12. Answer: (x1, y1) = (0, 4) (x2, y2) = (2, -2) m = (y2 – y1)/(x2 – x1) m = (-2 – 4)/(2 – 0) m = -6/2 m = -3 The slope is negative Find the slope of the line through the given points. Question 13. (-5, 4), (8, 4) Answer: (x1, y1) = (-5, 4) (x2, y2) = (8, 4) m = (y2 – y1)/(x2 – x1) m = (4 – 4)/(8 – (-5)) m = 0/13 m = 0 Question 14. (-3, 5), (-3, 1) Answer: (x1, y1) = (-3, 5) (x2, y2) = (-3, 1) m = (y2 – y1)/(x2 – x1) m = (1 – 5)/(-3 + 3) m = -4/0 m = undefined The points in the table lie on a line. Find the slope of the line. Question 15. Answer: (x1, y1) = (0, -1) (x2, y2) = (1, 0) m = (y2 – y1)/(x2 – x1) m = (0 – (-1))/(1 – 0) m = 1/1 m = 1 Question 16. Answer: (x1, y1) = (-2, 3) (x2, y2) = (0, 4) m = (y2 – y1)/(x2 – x1) m = (4 – 3)/(0 – (-2)) m = 1/2 Question 17. How do you know when two lines are parallel? Use an example to justify your answer. Answer: Two lines are parallel when their slopes are the same. In order for the two lines not to coincide, we must add the condition that their y – intercepts. Example 1: d1: y = 3x – 6 d2: 3x – y = 6 The lines d1 and d2 have the same slope and the same y – intercept, therefore they coincide. Question 18. Draw a line through the point (-1, 2) that is parallel to the graph of the line in Exercise 11. Answer: y = 2/3 x – 1 A (-1, 2) y = 2/3 x + b y = 2/3 (-1) + b b = 8/3 The equation of d1 is: y = 2/3 x + 8/3 Determine the x intercept of d1: 0 = 2/3 x + 8/3 0 = 2x + 8 2x = -8 x = -8/2 x = -4 4.3 Graphing Proportional Relationships (pp. 155–160) Learning Target: Graph proportional relationships. Tell whether x and y are in a proportional relationship. Explain your reasoning. If so, write an equation that represents the relationship. Question 19. Answer: x and y are not in a proportional relationship because the line does not pass through the origin. Question 20. Answer: x and y are in a proportional relationship because the line does passes through the origin. Determine the slope k using two points from the graph k = (10 – 0)/(2 – 0) k = 10/2 k = 5x Question 21. The cost y (in dollars) to provide food for guests at a dinner party is proportional to the number x of guests attending the party. It costs$30 to provide food for 4 guests.
a. Write an equation that represents the situation.
b. Interpret the slope of the graph of the equation.
c. How much does it cost to provide food for 10 guests? Justify your answer.
Answer:
y = kx
30 = 4k
k = 30/4
k = 7.5
y = 7.5x
b. The slope 7.5 represents the unit cost for a guest.
y = 7.5 × 10
y = 75
c. Determine y for x = 10
So it costs $75 to provide food for 10 guests. Question 22. The distance y (in miles) you run after weeks is represented by the equation y =8x. Graph the equation and interpret the slope. Answer: y = 8x Question 23. You research that hair grows 15 centimeters per year on average. The table shows your friend’s hair growth. a. Does your friend’s hair grow faster than average? Explain. Answer: The rate of growth on average is 15/12 = 1.25 cm/month The slope/rate of growth for your friend is (6 – 3)/(4 – 2) = 3/2 = 1.5 cm/month As 1.5 > 1.25, your friends hair grows faster than average. b. In the same coordinate plane, graph the average hair growth and the hair growth of your friend. Compare and interpret the steepness of each of the graphs. Answer: The equation for the average growth is y = 1.25x The equation for the friends growth is y = 1.5 x 4.4 Graphing Linear Equations in Slope-Intercept Form (pp. 161–166) Learning Target: Graph linear equations in slope-intercept form. Find the slope and the -intercept of the graph of the linear equation. Question 24. y = -4x + 1 Answer: y = mx + b slope = -4 and y – intercept = 1 Question 25. y = $$\frac{2}{3}$$x – 12 Answer: y = mx + b slope = $$\frac{2}{3}$$ and y – intercept = -12 Question 26. y – 7 = 0.5x Answer: Given the equation y – 7 = 0.5x y = 0.5x + 7 slope = 0.5 and y – intercept = 7 Graph the linear equation. Identify the -intercept. Question 27. y = 2x – 6 Answer: Given the equation y = 2x – 6 Comparing the above equation with slope – intercept equation slope = 2, y – intercept = -6 Slope = rise/run = 2/1 Plot the point that is 1 unit right and 2 units up from (0, -6) = (1, -4) The line crosses the x – axis at (3, 0) So, the x – intercept is 3. Question 28. y = -4x + 8 Answer: y = -4x + 8 slope = -4 and y – intercept = 8 So plot (0, 8) Slope = rise/run = -4/1 plot the point that is 1 unit right and 4 units down from (0, 8) = (1, 4) The line crosses the x- axis at (2, 0) So the x – intercept is 2. Question 29. y = -x – 8 Answer: Given the equation y = -x – 8 comparing the above equation with sloope – intercept equation. Slope = -1 and y – intercept = -8 Slope = rise/run = -1/1 Plot the point that is 1 unit right and 1 unit down from (0, -8) = (1, -9) The line crosses the x-axis at (-8, 0) So, the intercept is -8. Question 30. The cost y (in dollars) of one person buying admission to a fair and going on x rides is y = x + 12. a. Graph the equation. b. Interpret the y-intercept and the slope. Answer: y = x + 12 Comparing the above equation with slope – intercept equation. Slope = 1 and y – intercept = 12 So plot (0, 20) Slope = rise/run = 1/1 Plot the point that is 1 unit right and 1 unit up from (0, 12) = (1, 13) The y – intercept is 12 so the initial cost of admission is$12.
The slope is 1 so for each ride the cost of the person increases $1 per ride. Question 31. Graph the linear equation with slope -5 and y-intercept 0. Answer: y – intercept = 0. So plot (0, 0) Plot the point that is 1 unit right and 5 unit down from (0, 0) = (1, -5) 4.5 Graphing Linear Equations in Standard Form (pp. 167–172) Learning Target: Graph linear equations in standard form. Write the linear equation in slope-intercept form. Question 32. 4x + 2y = -12 Answer: 4x + 2y = -12 2y = -12 – 4x y = -6 – 2x y = -2x – 6 Question 33. x – y = $$\frac{1}{4}$$ Answer: Given the equation x – y = $$\frac{1}{4}$$ y = x – $$\frac{1}{4}$$ Graph the linear equation. Question 34. $$\frac{1}{4}$$x + y = 3 Answer: $$\frac{1}{4}$$x + y = 3 y = 3 – $$\frac{1}{4}$$x y = –$$\frac{1}{4}$$x + 3 Slope = –$$\frac{1}{4}$$ and y – intercept = 3 So plot (0, 3) Slope = rise/run = –$$\frac{1}{4}$$ Plot the point that is 4 units right and 1 unit down from (0, 3) = (4, 2) Question 35. -4x + 2y = 8 Answer: -4x + 2y = 8 2y = 8 + 4x y = 2x + 4 Slope = 2 and y – intercept = 4 So plot (0, 4) Slope = rise/run = 2/1 Plot the point that is 1 unit right and 2 units up from (0, 4) = (1, 6) Question 36. x + 5y = 10 Answer: x + 5y = 10 5y = -x + 10 y = -1/5 x + 2 Slope = -1/5 and y – intercept = 2 So, plot (0, 2) Slope = rise/run = -1/5 Plot the point that is 5 unit right and 1 unit down from (0, 2) = (5, 1) Question 37. –$$\frac{1}{2}$$x + $$\frac{1}{8}$$y = $$\frac{3}{4}$$ Answer: –$$\frac{1}{2}$$x + $$\frac{1}{8}$$y = $$\frac{3}{4}$$ $$\frac{1}{8}$$y = $$\frac{3}{4}$$ + $$\frac{1}{2}$$x y = 4x + 6 Slope = 4 and y – intercept = 6 So plot (0, 6) Slope = rise/run = 4/1 Plot the point that is 1 unit right and 4 units up from (0, 6) = (1, 10) Question 38. A dog kennel charges$30 per night to board your dog and $6 for each hour of playtime. The amount of money you spend is given by 30x + 6y = 180, where x is the number of nights and y is the number of hours of playtime. Graph the equation and interpret the intercepts. Answer: Given, A dog kennel charges$30 per night to board your dog and $6 for each hour of playtime. The amount of money you spend is given by 30x + 6y = 180, where x is the number of nights and y is the number of hours of playtime. 30x + 6y = 180 6y = -30x + 180 y = -5x + 30 The x – intercept is 6, which means that the dog can stay for 6 nights when there is no playtime. The y – intercept is 30, which means the dog can play for 30 hours when he does not spend any night at the kennel. 4.6 Writing Equations in Slope-Intercept Form (pp. 173–178) Learning Target: Write equations of lines in slope-intercept form. Write an equation in slope-intercept form of the line that passes through the given points. Question 39. Answer: m = (y2 – y1)/(x2 – x1) m = (1 – (-2))/(3 – 0) m = (1 + 2)/(3 – 0) m = 3/3 m = 1 We have to find the y – intercept because the line crosses the y – axis at (0, -2) y = mx + b y = x – 2 Question 40. Answer: m = (y2 – y1)/(x2 – x1) m = (4 – 2)/(0 – 4) m = 2/-4 m = -1/2 We have to find the y – intercept because the line crosses the y – axis at (0, 4) y = mx + b y =-1/2 x + 4 Question 41. Answer: m = (y2 – y1)/(x2 – x1) m = (-2 – 1)/(2 – 0) m = -3/2 We have to find the y – intercept because y = 1 when x = 0, the y – intercept is 1. y = mx + b y = -3/2 x + 1 Question 42. Answer: m = (y2 – y1)/(x2 – x1) m = (-1 – (-3))/(1 – 0) m = 2/1 m = 2 We have to find the y – intercept because y = -3 when x = 0, the y – intercept is -3. y = mx + b y = 2x + (-3) y = 2x – 3 Question 43. Write an equation of the line that passes through (0, 8) and (6, 8). Answer: m = (y2 – y1)/(x2 – x1) m = (8 – 8)/(6 – 0) m = 0/6 m = 0 We have to find the y – intercept because y = 8 when x = 0, the y – intercept is 8. y = mx + b y = (0) x + 8 y = 8 Question 44. Write an equation of the line that passes through (0, -5) and (-5, -5). Answer: m = (y2 – y1)/(x2 – x1) m = (-5 – (-5))/(-5 – 0) m = 0/-5 m = 0 We have to find the y – intercept because y = -5 when x = 0, the y – intercept is -5 y = mx + b y = (0) x + (-5) y = -5 Question 45. A construction crew is extending a highway sound barrier that is 13 miles long. The crew builds $$\frac{1}{2}$$ of a mile per week. Write an equation in slope -intercept form that represents the length y (in miles) of the barrier after x weeks. Answer: Given, A construction crew is extending a highway sound barrier that is 13 miles long. The crew builds $$\frac{1}{2}$$ of a mile per week. y = mx + b m = $$\frac{1}{2}$$ b = 13 y = $$\frac{1}{2}$$x + 13 4.7 Writing Equations in Point-Slope Form (pp. 179–184) Learning Target: Write equations of lines in point-slope form. Write an equation in point-slope form of the line that passes through the given point and has the given slope. Question 46. (4, 4); m = 3 Answer: y – y1 = m(x – x1) Substitute m value, x and y value in the equation y – (4) = 3(x – 4) y – 4 = 3(x – 4) Question 47. (2, -8); m = –$$\frac{2}{3}$$ Answer: y – y1 = m(x – x1) Substitute m value, x and y value in the equation y – (-8) = –$$\frac{2}{3}$$(x – 2) y + 8 = –$$\frac{2}{3}$$(x – 2) Write an equation in slope-intercept form of the line that passes through the given points. Question 48. (-4, 2), (6, -3) Answer: m = (y2 – y1)/(x2 – x1) m = (-3 – 2)/(6 – (-4)) m = -5/10 m = -1/2 y – y1 = m(x – x1) Substitute m value, x and y value in the equation y – 2 = –$$\frac{1}{2}$$(x – (-4)) y – 2 = –$$\frac{1}{2}$$(x + 4) y = –$$\frac{1}{2}$$x Question 49. Answer: m = (y2 – y1)/(x2 – x1) m = (5 – 1)/(3 – 2) m = 4/1 m = 4 y – y1 = m(x – x1) Substitute m value, x and y value in the equation y – (-3) = 4(x – 1) y + 3 = 4x – 4 y = 4x – 7 Question 50. The table shows your elevation y (in feet) on a ski slope after x minutes. a. Write an equation that represents your elevation after x minutes. Answer: m = (600 – 800)/(2 – 1) m = -200 800 = -200(1) + b 800 = -200 + b 800 + 200 = b b = 1000 feet b. What is your starting elevation? Answer: The starting elevation is the y – intercept b = 1000 feet c. After how many minutes do you reach the bottom of the ski slope? Justify your answer. Answer: 0 = -200x + 1000 0 – 1000 = -200x -1000 = -200x 200x = 1000 x = 5 minutes Question 51. A company offers cable television at$29.95 per month plus a one-time installation fee. The total cost for the first six months of service is $214.70. a. Write an equation in point-slope form that represents the total cost you pay for cable television after x months. b. How much is the installation fee? Justify your answer. Answer: y – y1 = m(x – x1) m = 29.95 y – 214.70 = 29.95(x – 6) y – 214.70 + 214.70 = 29.95x – 179.97 + 2147.70 y = 29.95x + 35 b = 35 Question 52. When might it be better to represent an equation in point-slope form rather than slope-intercept form? Use an example to justify your answer. Answer: When we are given the slope and a point that is the y – intercept, then the easiest way is to use the slope – intercept form y = mx + b Example: m = 2 (0, 5) y = 2x + 5 m = 2 (1, 3) y – 3 = 2(x – 1) Easier when given the slope and a point that is not the y – intercept. ### Graphing and Writing Linear Equations Practice Test Find the slope and the -intercept of the graph of the linear equation. Question 1. y = 6x – 5 Answer: y = 6x – 5 Slope = 6 and y – intercept = -5 Question 2. y – 1 = 3x + 8.4 Answer: Given the equation y – 1 = 3x + 8.4 y = 3x + 8.4 + 1 y = 3x + 9.4 Slope = 3 and y – intercept = 9.4 Question 3. –$$\frac{1}{2}$$x + 2y = 7 Answer: Given the equation –$$\frac{1}{2}$$x + 2y = 7 y = $$\frac{1}{4}$$x + $$\frac{7}{2}$$ Slope = $$\frac{1}{4}$$ and y – intercept = $$\frac{7}{2}$$ Graph the linear equation. Question 4. y = –$$\frac{1}{2}$$x – 5 Answer: Given the equation y = –$$\frac{1}{2}$$x – 5 Slope = –$$\frac{1}{2}$$ and y – intercept = -5 So plot (0, -5) Plot the point that is 2 units right and 1 unit down from (0, -5) = (2, -6) Draw a line through the two points. Question 5. -3x + 6y = 12 Answer: Given the equation -3x + 6y = 12 6y = 3x + 12 y = $$\frac{1}{2}$$x + 2 Slope = $$\frac{1}{2}$$, y – intercept = 2 Slope = rise/run = $$\frac{1}{2}$$ Plot the point that is 2 units right and 1 unit up from (0, 2) = (2, 3) Question 6. y = $$\frac{2}{3}$$x Answer: Given the equation y = $$\frac{2}{3}$$x Slope = $$\frac{2}{3}$$, y – intercept = 0 Slope = rise/run = $$\frac{2}{3}$$ Plot the point that is 3 units right and 2 unit up from (0, 0) = (3, 2) Question 7. Which lines are parallel? Explain. Answer: Red line: (x1, y1) = (-4, 1) (x2, y2) = (2, 4) m = (y2 – y1)/(x2 – x1) m = (4 – 1)/(2 – (-4)) m = 3/6 m = 1/2 Blue line: (x1, y1) = (-4, -1) (x2, y2) = (2, 0.5) m = (y2 – y1)/(x2 – x1) m = (0.5 – (-1))/(2 – (-4)) m = 1.5/6 m = 1/4 Green Line: (x1, y1) = (-2, -4) (x2, y2) = (2, -2) m = (y2 – y1)/(x2 – x1) m = (-2 – (-4))/(2 – (-2)) m = 2/4 m = 1/2 Red lines and Green lines are parallel because both have same slope = 1/2 Question 8. The points in the table lie on a line. Find the slope of the line. Answer: (x1, y1) = (-1, -4) (x2, y2) = (0, -1) m = (y2 – y1)/(x2 – x1) m = (-1 – (-4))/(0 – (-1)) m = 3/1 m = 3 Write an equation in slope-intercept form of the line that passes through the given points. Question 9. Answer: (x1, y1) = (-4, 1) (x2, y2) = (2, 4) m = (y2 – y1)/(x2 – x1) m = (-5 – (-1))/(3 – 0) m = -4/3 Because the line crosses the y – axis at (0, -1), the y – intercept is -1. y = mx + b y = -4/3x – 1 Question 10. Answer: m = (y2 – y1)/(x2 – x1) m = (2 – 2)/(0 – (-2)) m = 0/2 m = 0 Because y = 2 when x =0, the y – intercept is 2. y = mx + b y = 2 Question 11. Write an equation in point-slope form of the line that passes through (-4, 1) and (4, 3). Answer: m = (y2 – y1)/(x2 – x1) m = (3 – 1)/(4 – (-4)) m = 2/8 m = 1/4 y – y1 = m(x – x1) y – 1 = 1/4(x – (-4)) y – 1 = 1/4(x + 4) Question 12. The number y of new vocabulary words that you learn after x weeks is represented by the equation y = 15x. a. Graph the equation and interpret the slope. b. How many new vocabulary words do you learn after 5 weeks? c. How many more vocabulary words do you learn after 6 weeks than after 4 weeks? Answer: a. b. y = 15 . 5 y = 75 words c. 15 . 6 – 15 . 4 = 90 – 60 = 30 words Question 13. You used$90 worth of paint for a school float. The amount of money you spend is given by 18x + 15y = 90, where x is the number of gallons of blue paint and y is the number of gallons of white paint. Graph the equation and interpret the intercepts.
Answer:
Given,
18x + 15y = 90
15y = -18x + 90
y = -6/5 x + 6
The x – intercept is 5 and shows that 5 gallons of blue paint might be bought when no gallon of the white pants is bought.
The y – intercept is 6 and shows that 6 gallons of white paint might be bought when no gallon of blue is bought.
### Graphing and Writing Linear Equations Cumulative Practice
Question 1.
Which equation matches the line shown in the graph?
A. y =2x – 2
B. y = 2x + 1
C. y = x – 2
D. y = x + 1
Answer:
m = (-2 – 0)/(0 – 1)
m = 2
y = 2x – 2
Thus the correct answer is option A.
Question 2.
Which point lies on the graph of 6x – 5y = 14?
F. (-4, -1)
G. (-2, 4)
H. (-1, -4)
I. (4, -2)
Answer:
6x – 5y = 14
F. 6(-4) – 5(-1) = 14
-24 + 5 = 14
-19 ≠ 14
G. 6(-2) – 5(4) = 14
-12 – 20 = 14
-32 ≠ 14
H. 6(-1) – 5(-4) = 14
-6 + 20 = 14
14 = 14
Thus the correct answer is option H.
Question 3.
You reflect the triangle in the x-axis. What are the coordinates of the image?
A. X'(4, 1), Y'(2, 3), Z'(-2, 1)
B. X'(4, -1), Y'(2, -3), Z'(-2, -1)
C. X'(-4, -1), Y(-2, -3), Z'(2, -1)
D. X'(1, 4), Y'(3, 2), Z'(1, -2)
Answer:
Thus the correct answer is option C.
Question 4.
Which of the following is the equation of a line parallel to the line shown in the graph?
Answer:
m = (-4 – 2)/(6 – 4)
m = -6/2
m = -3
Two lines parallel if they have the same slope.
From the given equations, the one having the slope -3 is y = -3x + 5
Thus the correct answer is option H.
Question 5.
What is the value of x?
Answer:
122 = 47 + x
47 + x = 122
x = 122 – 47
x = 75
Question 6.
An emergency plumber charges $49.00 plus$70.00 per hour of the repair. A bill to repair your sink is $241.50. This can be modeled by 70.00 h + 49.00 = 241.50, where h represents the number of hours for the repair. How many hours did it take to repair your sink? A. 2.75 hours B. 3.45 hours C. 4.15 hours D. 13,475 hours Answer: 70.00 h + 49.00 = 241.50 70h = 241.50 – 49 70h = 192.5 h = 2.75 hours Thus the correct answer is option A. Question 7. It costs$40 to rent a car for one day. In addition, the rental agency charges you for each mile driven, as shown in the graph.
Part A Determine the slope of the line joining the points on the graph.
Part B Explain what the slope represents.
Answer:
m = (50 – 40)/(100 – 0)
m = 10/100
m = 0.1
Question 8.
What value of makes the equation true?
7 + 2x = 4x – 5
Answer:
7 + 2x = 4x – 5
2x – 4x = -5 – 7
-2x = -12
x = 6
Question 9.
Trapezoid KLMN is graphed in the coordinate plane shown.
Rotate Trapezoid KLMN 90° clockwise about the origin. What are the coordinates of point M’, the image of point M after the rotation?
F. (-3, -2)
G. (-2, -3)
H. (-2, 3)
I. (3, 2)
Answer: M'(-3, -2)
Thus the correct answer is option F.
Question 10.
Solve the formula K = 3M – 7.
A. M = K + 7
B. M = $$\frac{K+7}{3}$$
C. M = $$\frac{K}{3}$$ + 7
D. M = $$\frac{K-7}{3}$$
Answer:
K = 3M – 7
K + 7 = 3M
M = $$\frac{K+7}{3}$$
Thus the correct answer is option B.
Question 11.
What is the distance across the canyon?
F. 3.6 ft
G. 12 ft
H. 40 ft
I. 250 ft
Answer:
100/30 = d/12
3d = 12 × 10
3d = 120
d = 40 feet
Thus the correct answer is option H.
Conclusion:
All the solutions in the above article are beneficial for all the students of middle school students. All the solutions are prepared by the math professionals. The solutions are given clearly with step by step explanations. If you have any doubts regarding the chapter we are always ready to clarify your doubts. All you have to do is to post the comments in the below comment box.
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http://www.ck12.org/geometry/Classifying-Polygons-by-Sides/exerciseint/Word-Problem-Solve-for-the-Side-of-a-Regular-Polygon./ | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Classifying Polygons by Sides
## Determining the measure of a side of regular polygons.
%
Progress
MEMORY METER
This indicates how strong in your memory this concept is
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Word Problem--Solve for the Side of a Regular Polygon.
Teacher Contributed
The lengths of two sides of a regular pentagon are represented by the expressions $\left(9x+18\right)$$(9x + 18)$ and $\left(13x-6\right)$$(13x -6)$. What is the length of one side of the pentagon?
qid: 100104
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http://export.arxiv.org/abs/1908.08304 | ### Current browse context:
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# Title: High-Pressure Synthesis of Magnetic Neodymium Polyhydrides
Abstract: Search for room-temperature superconductivity is inspired by the unique properties of the electron-phonon interaction in metal superhydrides.Encouraged by the recently found highest-$T_C$ superconductor $fcc$-$LaH_{10}$, here we discover several polyhydrides of another lanthanide - neodymium. We identified three novel metallic Nd-H phases at pressures of 90 to 130 GPa: $I4/mmm$-$NdH_4$, $C2/m$-$NdH_7$ and $P6_3/mmc$-$NdH_{9+x}$ (x=0-0.5), synthesized by laser-heating metal samples in $NH_3BH_3$ media for in situ generation of hydrogen. A lower trihydride $Fm\bar{3}m$-$NdH_3$ was found at pressures from 2 to 52 GPa. $I4/mmm$-$NdH_4$ and $C2/m$-$NdH_7$ were stable from 130 down to 85 GPa, and $P6_3/mmc$-$NdH_{9+x}$ at 110 to 130 GPa. Theoretical calculations predict that all the neodymium hydrides have a strong magnetism at pressures below 150 GPa (> 2.2 $\mu_B$ per Nd atom): $C2/m$-$NdH_7$ and $hcp$-$NdH_{9}$ possess collinear anti-ferromagnetic [110] and [100]_2 orders respectively, while $NdH_4$ is a ferromagnetic with the (110) easy-axis. The critical Curie or Neel temperatures for new neodymium hydrides were estimated using the mean-field approximation as 100 K ($NdH_7$), 95 K ($NdH_9$) and 167 K ($NdH_4$).
Comments: 12 pages, 5 figures, 1 table, Supporting Information Subjects: Superconductivity (cond-mat.supr-con); Materials Science (cond-mat.mtrl-sci) Cite as: arXiv:1908.08304 [cond-mat.supr-con] (or arXiv:1908.08304v1 [cond-mat.supr-con] for this version)
## Submission history
From: Alexander Kvashnin [view email]
[v1] Thu, 22 Aug 2019 10:51:39 GMT (5825kb)
Link back to: arXiv, form interface, contact. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3094549775123596, "perplexity": 9489.21068004943}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574501.78/warc/CC-MAIN-20190921125334-20190921151334-00508.warc.gz"} |
https://one-generation.info/ethics-the-fundamentals-juli-99/ | However, the magnitudes of most fundamental e. Perceptual grouping of speech components differing in fundamental frequency and onset-time. Neuropsychologia 42 , — In a recent note, Graff promotes the use of the log-ratio distance function, arguing that relative differences between physical quantities are often more informative than absolute differences. An influence of the carrier can also be inferred from the study of van Heuven and van den Broecke , who obtained somewhat smaller Weber fractions for stimuli with tone than with broadband noise carriers of the same sound level 60 dB , though the data are noisy. Abstract Onsets of acoustic stimuli are salient transients and are relevant in humans for the perception of music and speech. We propose novel measures based on geometric descriptive statistics and the log-ratio distance function, the Euclidean distance function on the positive-real numbers.
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After both onset durations had been drawn once, the next total duration was selected, and so on, until all six combinations of onset and total durations had been presented four times. The [email protected] relative constant errors are independent of Stbut increase with increasing geometric variance. Our results have broad implications for psychophysical studies that use arithmetic measures to quantify performance when geometric measures should instead be used.
In addition, the experimental data do not follow perfect multiplicative normal distributions. She proposes that ethics can be independent of religion, ethicw that while her liberationist ethic can be either Christian or universal, finally the poor and oppressed are the paradigm source of the disclosure of God and of final salvation.
For all listeners but one, the multiplicative normal distribution is increasingly favored as additional matches are included. The ethica were presented at sensation levels of 10, 22, and 34 dB SL.
## Fundamentals of Ethics
Listen to Domenico Modugno in full in the Spotify app. An influence of the carrier can dthics be inferred from the study of van Heuven and van den Broeckewho obtained somewhat smaller Weber fractions for stimuli with tone than with broadband noise carriers of the same sound level fundamenatls dBthough the data are noisy.
It may be criticized that the Gedanken experiment rests on the assumption that matches follow a multiplicative normal distribution and that the outcome may differ if the matches followed other distributions. However, Weber fractions are approximately constant over only a limited range of onset durations. In contrast, and as shown in Figure 5Bthe arithmetic mean of CE G is mostly negative, except at the two shortest onset durations of ethisc standard.
The conventional measures of accuracy and precision are defined by arithmetic descriptive statistics and the Euclidean distance function on the real numbers.
It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. The listeners in the study of van Heuven and van den Broecke made only two matches per condition, and difference limens and Weber fractions were calculated from matches pooled across all listeners. He knows he has an ethics blind spot the moment he develops it. A similar reduction of the standard deviations will occur for matches to standards with the shortest onset durations.
Discriminability of differences in the rise time of a tone. Fitting these two distributions therefore suffices to distinguish between additive and multiplicative models as long as no other constraints are imposed.
To test this idea, we employed standards with total durations of ms as in Experiment 1ms, and ms.
Size of the Mueller-Lyer illusion as a function of its dimensions: A,B,D,E Dependence of accuracy top row and precision bottom row of onset-duration matching on the onset duration of the standard, when using the conventional left column and our proposed middle column psychophysical measures. Perceptual scaling of synthesized musical timbres: The rate of rise increases by a factor of four for a dB increment in sound level. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.827817440032959, "perplexity": 2766.495712280405}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141672314.55/warc/CC-MAIN-20201201074047-20201201104047-00706.warc.gz"} |
http://mathoverflow.net/questions/160896/what-is-the-multiplicative-unitary-for-su-q2-or-other-quantum-groups | # What is the multiplicative unitary for SU_q(2) (or other quantum groups)?
Consider a (von Neumann algebraic) locally compact quantum group $(M, \Delta, \phi, \psi)$ where the von Neumann algebra $M$ is realized as operators on the Hilbert space $H$. There is a multiplicative unitary $W$ in $B(H\otimes H)$that generates the comultiplication $\Delta$ via $$\Delta(x)=W^*(1\otimes x)W.$$
For a group, the multiplicative unitary for $L^\infty(G)$ acts on $L^2(G\times G)$ via $$Wf(g, h) = f(g, g^{-1}h).$$ Relatedly, for $VN(G)$ the multiplicative unitary acts on $L^2(G\times G)$ via $$\hat{W}f(g, h) = f(hg, h).$$
Beyond these two examples, are there nice descriptions of any multiplicative unitaries? (I'd like to know about $SU_q(2)$, but any example would be nice.)
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https://www.physicsforums.com/threads/physical-vs-unphysical.1004315/ | # Physical vs. UnPhysical
• #1
Gold Member
4,471
275
I was and am reading quite a lot of books on GR and QFT and there's the distinction between a physical state and an unphysical state.
What is the difference?
What makes a state physical?
I know this is a bit philosophical .
Doesn't this distinction change with time and experiments?
## Answers and Replies
• #2
Staff Emeritus
27,244
11,236
I think this will fall into the Potter Stewart "I know it when I see it" definition.
As an example, I might solve for the electric field from a configuration of charges and have two solutions - one that gets small when I am far from the ensemble of charges and one that gets larger the farther away I get. I would dismiss the second solution as unphysical.
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• #3
Mister T
Gold Member
2,690
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I was and am reading quite a lot of books on GR and QFT and there's the distinction between a physical state and an unphysical state.
Can you tell us more about which books you're reading and the context in which they're making this distinction?
When I think of a state it implies the existence of a system. That is, a system is in some particular state. If the state is physical then there are experiments that can be performed, at least in principle, to verify the state. On the other hand if there is no experiment that can be performed, even in principle, to verify the state of a system then the state is not physical.
• #4
hutchphd
Homework Helper
3,247
2,422
What makes a state physical?
I think the designation as unphysical is merely one of convenience, and not, in a narrow sense, at all worrisome. Subsystems (this contrivance or that field) are written down without initially worrying about interactions with all the myriad other degrees of freedom. To solve a real world system boundaries in time and space must be specified. It turns out that some subset of boundary conditions are never encountered for the subsystem and these are simply declared inutile. There is no particular reason to expect otherwise.
• #5
Gold Member
4,471
275
Can you tell us more about which books you're reading and the context in which they're making this distinction?
When I think of a state it implies the existence of a system. That is, a system is in some particular state. If the state is physical then there are experiments that can be performed, at least in principle, to verify the state. On the other hand if there is no experiment that can be performed, even in principle, to verify the state of a system then the state is not physical.
Specifically, now I am reading on and off the book Perutrbative QCD by Muller.
Oldie but Goldie.
• #6
Paul Colby
Gold Member
1,369
381
one that gets small when I am far from the ensemble of charges and one that gets larger the farther away I get. I would dismiss the second solution as unphysical.
Just to expand on an already excellent answer, the solution which gets larger with increased distance is physical, it's just not the physics you were looking for. The solution which increases with distance describes sources residing at infinity. One needs both the field equations and the correct boundary conditions to describe a given physical problem.
• #7
Gold Member
4,471
275
It seems to me that what is unphysical may someday in the future turn to be physical, of course not including logical contradictions, which are discarded anyway.
• #8
7
2
I was and am reading quite a lot of books on GR and QFT and there's the distinction between a physical state and an unphysical state.
What is the difference?
What makes a state physical?
I know this is a bit philosophical .
Doesn't this distinction change with time and experiments?
There are many examples of unphysical or immaterial entities. Mathematics is an immaterial entity. So are the laws of logic. While certain types of thought cause the brain to “fire” differently on a scan, no neurologist on the planet can tell you what you are thinking - they must ask you for that information leading many to conclude that the soul is immaterial. Likewise, many religions teach that “God” is immaterial. You’re right that this question touches both physics and philosophy - nothing wrong with that.
• #9
vanhees71
Gold Member
18,036
8,987
I don't know what your book means by "unphysical states". If it's in the context of quantum gauge-field theories, it may refer to various "ghost states", i.e., contributions from unphysical components of the gauge fields which have to be cancelled by the either unphysical Faddeev Popov ghosts.
• #10
Gold Member
4,471
275
I don't know what your book means by "unphysical states". If it's in the context of quantum gauge-field theories, it may refer to various "ghost states", i.e., contributions from unphysical components of the gauge fields which have to be cancelled by the either unphysical Faddeev Popov ghosts.
Why those are unphysical? do we argue that such ghosts cannot exist in reality? why not?
• #11
vanhees71
Gold Member
18,036
8,987
The ghosts have been introduced in the formalism of calculating proper vertex functions to cancel the contribution from unphysical pieces of the gauge fields.
Take, as the most simple example, QED, i.e., the (un-Higgsed) U(1) gauge theory describing a Dirac field ("electrons and positrons") interacting through a minimally coupled U(1) gauge field ("photons"). First you start with four gauge fields.
The physical meaning is in the asymptotic free states, and as you well know, what's described with them are free photons being composed in terms of momentum-helicity single-photon Fock states. Of these only the 2 helicity states are physical, i.e., two field degrees of freedom are unphysical already in the sense of asymptic free states.
Now when calculating higher-order corrections (loops in Feynman diagrams) you formally sum also over the unphysical states, and this is on the first glance fatal, because it means you sum over states which have a negative norm, and the so calculated naive S-matrix wouldn't be unitary and also the microcausality condition may does not hold.
The path-integral formalism then shows that the correct way is to integrate over one physical field configuration only once and not over the infinitely many possibilities describe one and the same state expressed in different "gauges". So you choose a gauge-fixing condition and make sure by an appropriate functional ##\delta## distribution that you only pick out the one gauge configuration subject to this constraint. However, this is not so easily implemented in terms of a perturbative treatment, and that's why you use the trick to integrate over the gauge group and then expressing the arising functional determinant in the pertinent path-integral measure in terms of also unphysical Faddeev Popov ghost fields (which are formally scalar fields but implemented in the path integral as Grassmann fields, because the corresponding functional Jacobi determinant is in the numerator rather than the denominator), and these exactly cancel the contributions from the unphysical states of the gauge field.
In QED the Faddeev-Popov ghosts in the usual linear gauges are non-interacting and thus can be omitted, but that's not so for the non-Abelian case.
For details, see my QFT notes:
https://itp.uni-frankfurt.de/~hees/publ/lect.pdf
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7K | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8462228178977966, "perplexity": 756.6706250315209}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154796.71/warc/CC-MAIN-20210804045226-20210804075226-00207.warc.gz"} |
http://ngraph.nervanasys.com/index.html/ops/cos.html | # Cos¶
Cos // Elementwise cosine operation
## Description¶
Produces a tensor of the same element type and shape as arg, where the value at each coordinate of output is the cosine of the value at the corresponding coordinate of arg.
### Inputs¶
Name Element Type Shape
arg Any Any
### Outputs¶
Name Element Type Shape
output Same as arg Same as arg
## Mathematical Definition¶
$\mathtt{output}_{i_0, \ldots, i_{n-1}} = \cos(\mathtt{arg}_{i_0, \ldots, i_{n-1}})$
## Backprop¶
$\overline{\mathtt{arg}} \leftarrow -\Delta\ \sin(\mathtt{arg})$
## C++ Interface¶
class Cos : public ngraph::op::util::UnaryElementwiseArithmetic
Elementwise cosine operation.
Public Functions
const NodeTypeInfo &get_type_info() const
Returns the NodeTypeInfo for the node’s class. During transition to type_info, returns a dummy type_info for Node if the class has not been updated yet.
Cos()
Constructs a cosine operation.
Cos(const Output<Node> &arg)
Constructs a cosine operation.
Parameters
• arg: Node that produces the input tensor. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8874380588531494, "perplexity": 17646.30592397848}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514575844.94/warc/CC-MAIN-20190923002147-20190923024147-00156.warc.gz"} |
https://www.bartleby.com/solution-answer/chapter-85-problem-9ty-discrete-mathematics-with-applications-5th-edition/9781337694193/given-a-set-a-that-is-partially-ordered-with-respect-to-a-relation-_-the-relation-_-is-a/c276ed2a-e176-44c4-a74e-f99e43fce25b | Chapter 8.5, Problem 9TY
Discrete Mathematics With Applicat...
5th Edition
EPP + 1 other
ISBN: 9781337694193
Chapter
Section
Discrete Mathematics With Applicat...
5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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Given a set A that is partially ordered with respect to a relation ≺ _ , the relation ≺ _ is a topological sorting for ≺ _ , if , and only if, ≺ _ is a ______and for all a and b in A if a ≺ _ b then______.
To determine
To fill in the blanks provided.
Explanation
Calculation:
Given a set A that is partially ordered with respect to a given relation , the relation ' is topological sorting for , if and only if,
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Get Started | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.944542646408081, "perplexity": 4015.1094099233915}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541307813.73/warc/CC-MAIN-20191215094447-20191215122447-00114.warc.gz"} |
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## keeponbleeding 2 years ago Find f(x) and g(x) so that the function can be described as y = f(g(x)). y=2/(x^2) +9 Delete Cancel Submit
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1. dumbcow
• 2 years ago
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g(x) = x^2 f(x) = 2/(x+9)
2. surdawi
• 2 years ago
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@keeponbleeding what are the choices?
3. keeponbleeding
• 2 years ago
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wait how did that happen?
4. keeponbleeding
• 2 years ago
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no multiple choices
5. surdawi
• 2 years ago
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is that y? $y = \frac{ 2 }{ x^2 }+9$
6. keeponbleeding
• 2 years ago
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yes
7. dumbcow
• 2 years ago
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y = f(g(x)) means that g(x) is input for variable of f(x) say f(x) = 2/? + 9 , this is general form so ? must be x^2 thus g(x) = x^2
8. keeponbleeding
• 2 years ago
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thanks! got it
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9998266100883484, "perplexity": 15571.884510991733}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645241661.64/warc/CC-MAIN-20150827031401-00008-ip-10-171-96-226.ec2.internal.warc.gz"} |
http://www.imaios.com/en/e-Courses/e-MRI/Improving-MRI-contrast-Imaging-water-and-fat/fat-saturation | # MRI Fat Saturation (Fat Sat, CHESS, SPIR, SPECIAL)
by Denis Hoa
In the triglyceride molecules of fat, the electronic environment (shield) of the protons is not the same as that of water molecules.
The 2 kinds of molecules have different proton resonance frequencies, measured by chemical shift (3.5 ppm).
This difference in proton resonance frequency in lipid molecules can be used to suppress their signal. To do so, a selective RF excitation wave is applied with a narrow bandwidth.
The selective 90° RF wave will flip the magnetization of the fat protons without affecting the proton magnetization of other tissues. Gradients then destroy the magnetization in the transverse plane and the imaging sequence begins just after that, to avoid leaving the fat magnetization time to regrow.
The fat signal will thus be weaker in relation to the other tissues.
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This method requires good magnetic field homogeneity (figure 7.4) namely in the case of a large field of view (so the lipid protons resonate at the same frequency throughout the explored volume) and a selective pulse frequency bandwidth that is well adapted (to saturate the signal of all the lipid protons without affecting the soft tissue signal).
It can be used before virtually all types of sequence.
This technique can be combined with inversion-recovery: SPIR (Philips) / SPECIAL (GE) combine a fat-selective 100-120° RF inversion pulse, followed by dephasing gradients and an adapted TI. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8482815623283386, "perplexity": 2797.7849827926525}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997888216.78/warc/CC-MAIN-20140722025808-00175-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/385343/how-to-show-this-matrix-has-eigenvalues-lambda-j-4-sin2-fracj-pi2n1 | How to show this matrix has eigenvalues $\lambda_{j}=4\sin^2{\frac{j\pi}{2(n+1)}}$?
Show that the $n\times n$ tridiagonal matrix $$A=\begin{bmatrix} 2&-1&0&0&0\\ -1&2&-1&0&0\\ \vdots&\ddots&\ddots&\ddots&\vdots\\ 0&0&-1&2&-1\\ 0&0&0&-1&2 \end{bmatrix}$$
has the eigenvalues $$\lambda_{j}=4\sin^2{\dfrac{j\pi}{2(n+1)}},j=1,2,\cdots,n$$
• joriki has written down the eigenvectors. If you don't understand his answer, you may ping him first to see if he has time to give you more details. – user1551 May 8 '13 at 9:36
• yes, I have some questions, and don't have solve it,Thank you – math110 May 8 '13 at 10:20
So we need to solve the following problem: $Ax =\lambda x$.
Or $$cx_{j−1} + ax_j + bx_{j+1} = \lambda x_j , \ j = 1,\ldots ,m$$ $$x_0 = x_{m+1} = 0$$ where $a=2, \ b=c=-1$ which is equivalent to $$cx_{j−1} +(a-\lambda)x_j + bx_{j+1} = 0 , j = 1,\ldots ,m$$ $$x_0 = x_{m+1} = 0$$ Its solution is represented in the form: $$x_j = \alpha r_1^j+\beta r_2^j$$ where $r_1^j, \ r_2^j$ are solutions of the characteristic polymonial $f(r)=b r^2+(a-\lambda)r+c$: $$r_1=\frac{-(a-\lambda)+\sqrt{(a-\lambda)^2-4b c}}{2b}$$ $$r_2=\frac{-(a-\lambda)-\sqrt{(a-\lambda)^2-4b c}}{2b}$$ We can find the unknown coefficients by using the initial condition: $$x_0 = \alpha+\beta = 0 \Rightarrow \alpha=-\beta$$ $$x_j = \alpha (r_1^j-r_2^j)$$ $$x_{m+1} = \alpha(r_1^{m+1}-r_2^{m+1})=0 \Rightarrow \left(\frac{r_1}{r_2}\right)^{m+1}=1$$ $$r_1 r_2=\frac{c}{b}$$ $$\left(\frac{r_1}{r_2}\right)^{m+1}=\left(\frac{b r_1^2}{c}\right)^{m+1}=1$$ Plugging in $b=c=-1$ leads us to $r^{m+1}=1$, so $$r_{1,j}=e^{\pi i \left(\frac{j}{n+1}\right)}$$ $$r_{2,j}=e^{-\pi i \left(\frac{j}{n+1}\right)}$$ But one can see that $r_{1,j}+r_{2,j}=\frac{\lambda_{j}-a}{b}=2-\lambda_{j}$. Using the Euler's formula one can obtain: $$\lambda_{j}=2\left(1-\cos\left(\frac{j\pi}{n+1} \right)\right)=4\sin^2\left(\frac{j\pi}{2(n+1)} \right)$$
Hint: Find $\det (A-\lambda I)$ by induction on size of $A$ (you will get a recurrent equation of order 2). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9340552687644958, "perplexity": 186.0298384197942}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251694071.63/warc/CC-MAIN-20200126230255-20200127020255-00348.warc.gz"} |
https://boopathi.blog/modeling-errors-in-graphql | Published on
# Modeling errors in GraphQL
Authors
Tags
## Tags
Cross posted -
Zalando Engineering Blog - Modeling Errors in GraphQL
GraphQL is a great language for writing data requirements in a declartive fashion. It gives us a clear and a well-defined concept of nullability constraints and error propagation. In this post, let's discuss how GraphQL lacks in certain places with regards to errors and how we can model those errors to fit some of our use-cases.
Before we dive into the topic, let's understand how GraphQL currently treats and handles errors. The response of a GraphQL query is of the following structure —
{
"data": {
"foo": null
},
"errors": [
{
"message": "Something happened",
"path": ["foo", "bar"]
}
]
}
## Error extensions
The schema we define for GraphQL is used only in the data field of the response. The errors field is a well defined structure — Array<{ message: string, path: string[] }> in its simplest form. The schema we define does not affect this error.
Let's say the client queries a field using an ID. How can the client know from the above error object whether the error is due to an Internal Server Error or the ID is Not Found. Parsing the message is a no-go beacuse it is not reliable.
Luckily, in GraphQL, there is a way to provide extensions to the error structure - using extensions. The error.extensions can be used to convey other information related to the error - properties, metadata, or other clues that the client can benefit from. As for the above example, we can model the response to be —
const err = {
data: {},
errors: [
{
extensions: {
code: 'NOT_FOUND',
},
},
],
}
## Errors for Customers
When we have a GraphQL API that is used to deliver content to the end-user — the customers, i.e. we have two levels of users —
1. The consumer or user of the API — UI/UX/front-end developer.
2. The end-user or customer — The one who does not see any of the technical layers, but gets the product's experience in its most presentable format. The Front-end developer builds this experience using data from the GraphQL API.
Since using the word user might be confusing, from now on, Consumer will refer to the front-end developer and Customer will refer to the end-user.
When we have an API whose data is directly consumed by two levels of these users - Consumer and Customer, there might be different error data requirements. For example, let's take mutations — when the customer enters an invalid email address,
1. The Consumer of the API needs to know that the Customer has entered an Invalid Email address via a parseable format — a boolean or enum or whatever data structure you choose will work except parsing the error message.
2. The Customer needs cares about the error message in a nicely styled format close to the text box. Oh!, one more thing, for different languages or locales, the error message needs to be in the corresponding translated text.
Let's try to model this using the error extensions discussed above —
{
"data": {},
"errors": [
{
"message": "Die e-mail Adresse ist ungültig",
"extensions": {
"code": "INVALID_EMAIL"
}
}
]
}
While this would work, we soon end up in a case where multiple input fields in a mutation can be invalid. What can we do here? Do we model them as different errors or fit everything into the same error.
The Customer errors still need to be usable by the Consumers so as to propagate it — the front-end developers are the ones ultimately transforming our data structures to UI elements. So they need to understand the error to highlight that input text-box with a red border. So, to make it easy, let's try modeling these as a single error with multiple validation messages —
{
"data": {},
"errors": [
{
"message": "Multiple inputs are invalid",
"extensions": {
"invalidInputs": [
{
"code": "INVALID_EMAIL",
"message": "Die e-mail Adresse ist ungültig"
},
{
"message": "Das Passwort nicht erfüllen Sicherheitsstandards"
}
]
}
}
]
}
The codes INVALID_EMAIL, and INVALID_PASSWORD will help the front-end dev or consumer to highlight the field in the UI, and the message will be displayed to the user right under that textbox.
This becomes a complicated structure very soon and is not as friendly as data modeled with a GraphQL schema.
## Why you no Schema?
The biggest problem we face in modeling all of requirements inside the extensions object is that it's not discoverable. We use such a powerful language like GraphQL to define each field in our big data structure using Schemas, but when designing the errors, we went back to a loose mode of not using any of the ideas GraphQL brought us.
Maybe, in future extensions of the language, we are able to write schemas for Errors like we write for Queries and Mutations. The developers using the schema get all the benefit of GraphQL even when handling errors. For now, let's concentrate on modeling this using the existing language specification.
## Errors in Schema
We want to enjoy the power of GraphQL - the discoverability of fields of data, the tooling, and other aspects for errors. So, why not simply put some of these errors in the Schema instead of capturing them separately in the error extensions.
For example, the mutation discussed previously can be modeled like this —
1. mutation returns a Result type
2. Result type is a union of Success, Error.
3. Error schema contains necessary error info — like translated messages, etc...
type Mutation {
}
union RegisterResult = RegisterSuccess | RegiterError
type RegisterSuccess {
id: ID!
email: String!
}
type RegisterError {
invalidInputs: [RegisterInvalidInput]
}
type InvalidInput {
field: RegisterInvalidInputField!
message: String!
}
enum RegisterInvalidInputField {
EMAIL
}
This structure looks exactly like the one we designed above inside error extensions. The advantage of modeling it like this would be that we are using the benefits of GraphQL for errors.
## When you have a hammer,
Now, we are left with a couple of questions more than answers, and this is good.
1. Should I model all errors as GraphQL types?
2. How should I decide when to use error extensions and when to use GraphQL types for modeling errors?
3. etc...
When working in big teams, many people contribute and think about modeling different parts of the schema. There should be clear definitions for many aspects of the existing data structures, and the idea behind how we reached such solutions. The design and schema is changed or modified far fewer times than it is read / used.
GraphQL gave us the mindset of "Thinking in Graphs". If we are suggesting a new way of modeling errors, we need to talk about this mindset and ideas behind them. Not all errors fit into this modeling (error types in schema) and it will make the GraphQL API less usable if we approach it by looking at all the errors as nails.
## Classification
In order to model errors, let's try to find some analogies. I'd like to think about modeling these errors in terms of programming languages errors. For example,
1. Go: error vs panic
2. Java: Error vs Exception
3. Rust: error vs runtime exception
The programming languages also model errors as 2 variants. In one model, for example, an error type in go, it informs the consumer of the function and the consumer decides either to handle it or to pass it through. In the other variant, for example, panic in go, it skips everything and brings the program to a halt to inform the end-user of the program that something has happened. This small variation captured as two different things help us understand the intention of data in errors.
### Part 1. Action-ables
What is an error? It tells us that something is wrong and gives us some information of what action can be taken. We can think of errors as containers of action-ables. When modeling them, we classify them into different groups depending on who can take that action.
In GraphQL context, for some errors, the front-end takes care of it — either by a fallback or a retry. In case of some other errors like the invalid inputs, the front-end cannot take an action, only the customer who entered the invalid input can take the action — fixing the input.
Instead of modeling the errors loosely, we now have a solid use-case — model it for the whoever can take the action.
### Part 2. Bugs in the system
Errors convey information — either to Consumer or Customer. If the error is conveying some bug in the system, then it should not be modeled as schema error types. Here, system means all the services and software involved in our entire Product and not just the GraphQL service. This is important because it separates the view of the end-user / customer vs consumer of the API. The end-user looks at our product as one thing not many individual services.
In the 404 Not Found case, if we had modeled the errors as schema types, it would make the schema less usable. Let's take a product look-up use-case —
{
product(id: "foo") {
... on ProductSuccess { }
... on ProductError { }
}
collection(id: "bar") {
... on CollectionSuccess {
products {
... on ProductSuccess {}
}
}
... on CollectionError {}
}
}
This way of handling errors at every level is not friendly for front-end developers. It's too much to type in a query and too many branches to handle in the code.
### Part 3. Error propagation
We also have to remember to not disrupt GraphQL semantics of error propagation. If an error occurs in one place in the query, it propagates upwards in the tree till the first non-null field occurs. This does not happen with error types in schema. It is important to model these schema error types for only specific use-cases. This goes back to Part 1: Action-ables — we design these types for actions that the end-user or customer can take.
## The Problem type
Naming is half the battle in GraphQL. Since the name error is already taken by the GraphQL language (response.errors), it would be confusing to name our error types in schema as Error. As we did before to look for inspirations, there is a well-defined concept in IEFT — RFC 7807 — Problem details for HTTP API. So, we are going to call all our errors in schema as Problems and as it has always been, all other errors as errors.
The above register schema with the problem type would look like this —
type Mutation {
}
union RegisterResult = RegisterSuccess | RegiterProblem
type RegisterSuccess {
id: ID!
email: String!
}
type RegisterProblem {
"translated message encompassing all invalid inputs"
title: String!
invalidInputs: [RegisterInvalidInput]
}
type InvalidInput {
field: RegisterInvalidInputField!
"translated message"
message: String!
}
enum RegisterInvalidInputField {
EMAIL
}
## Problem or Error
Problem refers to the error as a schema type. Error refers to the error that appears in the reponse.errors array with an error code at error.extensions.code.
This is a bug in the system in case of navigation. If the user navigates from the home page to a product page, and they end up in a 404 page, it means that some service provided an id that is already not found. It's not something because the user entered some input. Also, these errors need to be propagated. So, this becomes an Error with an error code as NOT_FOUND and not a Problem.
### Case 2: Authorization
Authorization errors are of the Error type and do not fit a problem type. Here, the action taker looks like it's the customer who needs to login. But, the UI can take an action here and show a login dialog box to the customer. In apps, the app decides to take the customer to the login view. The action really belongs to the Front-end and only then the customer. So, we model it for the consumer / front-end as an Error with error code NOT_AUTHORIZED and not a Problem.
### Case 3: Mutation Inputs
This is the only case where it is important to construct Problem types. This contains inputs directly from the customer, and only the customer can take an action for this. So, we model these errors as Problems and not Errors.
### Case 4: All other bugs / errors
Any runtime exception in the code or Internal Server Errors from any backends that the GraphQL layer connects to should be modeled as Error and need not contain an error code. This way it is easy for front-end to treat all non error code responses as Internal Server Errors and take an action accordingly — to retry or show the customer a 500 page.
## Conclusion
We have discussed Problem type as a possible solution where the error object in GraphQL response does not suffice the use-cases. But we have to be careful about not overusing this for lot of use-cases where the error extensions already provide enough value.
We have to understand that the Problem type in unnecessary places does make the query and front-end code complicated. Our GraphQL schema should try to simplify and provide a friendly interface.
This blog post got longer than I expected. Thanks for reading it through.
As always, if you have any doubts or comments or questions or fixes for this post, please feel free to tweet to me at @heisenbugger. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.237201526761055, "perplexity": 1987.0719652753519}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300805.79/warc/CC-MAIN-20220118062411-20220118092411-00320.warc.gz"} |
https://proofwiki.org/wiki/Upper_Closure_of_Element_without_Element_is_Filter_implies_Element_is_Meet_Irreducible | # Upper Closure of Element without Element is Filter implies Element is Meet Irreducible
## Theorem
Let $L = \left({S, \vee, \wedge, \preceq}\right)$ be a lattice.
Let $x \in S$.
Let
$x^\succeq \setminus \left\{ {x}\right\}$ be a filter in $L$.
Then $x$ is meet irreducible.
## Proof
Let $a, b \in S$.
Aiming for a contradiction suppose that
$x = a \wedge b$ and $x \ne a$ and $x \ne b$
$x \preceq b$ and $x \preceq a$
By definition of upper closure of element:
$b, a \in x^\succeq$
By definitions of singleton and difference:
$b, a \in x^\succeq \setminus \left\{ {x}\right\}$
By definition of filtered:
$\exists z \in x^\succeq \setminus \left\{ {x}\right\}: z \preceq a \land z \preceq b$
By definition of infimum:
$z \preceq x$
By definition of upper set:
$x \in x^\succeq \setminus \left\{ {x}\right\}$
Thus this contradicts $x \in \left\{ {x}\right\}$ by definition of singleton.
$\blacksquare$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9894768595695496, "perplexity": 1232.8830801214892}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541308149.76/warc/CC-MAIN-20191215122056-20191215150056-00350.warc.gz"} |
https://mathematica.stackexchange.com/questions/156715/replacing-for-loop-with-multiple-iterator-with-table | # Replacing For loop with multiple iterator with Table
I have written code for calculating cristofell symbol using for loop with 3 iterators for each coordinate
A = {
{1, 0, 0},
{0, r^2, 0},
{0, 0, 1}
} ;
Kor[n_] := \[Piecewise] {
{(r), n == 1},
{(\[Theta]), n == 2},
{(z), n == 3}
}
ChristoffelSymbol1[i_, j_, k_] :=
1/2 (-D[A[[i, j]], Korr[k]] + D[A[[j, k]], Korr[i]] +
D[A[[k, i]], Korr[j]])
For[i = 1, i < 4, i++,
For[j = 1, j < 4, j++,
For[k = 1, k < 4, k++,
Print[Subscript[\[CapitalGamma], i, j, k], " = ",
ChristoffelSymbol1[i, j, k]]
]
]
]
I was wandering if I could use Map/Table to do the same without changing the functions too much. As far as I could tell I need to make the Piecewise function return symbols for i, j, k when they are entered instead of number so I dont get an error when I do ChristoffelSymbol1[1,j,k] and (this I don't know how) somehow define what happens when I try to access the matrix A with A[[1,j]] for example , so it doesn't give me "expression j cannot be used as a part specification" and leave it in symbolic notation so it can be used when j iterators start.
• if you actually want to Print like that you would use Do. I dont see why you would have the part issue you are imagining -- try it. I wouldn't bother with that Piecewise by the way , just do Kor[1]=r;Kor[2]=theta;Kor[3]=z or do Kor={r,theta,z} and reference it as a list. Sep 28, 2017 at 18:22
• You can use for example Tuples and then Map function over the obtained list. However, it is unclear from your question what exactly you want to do? Sep 28, 2017 at 18:58
• I want a table of {Symbol,value} pairs outputted in 1 cell,but for the symbol to keep the formatting from print. Sep 28, 2017 at 19:26
\[CapitalGamma]ddd[i_, j_, k_] :=
1/2 (-D[A[[i, j]], Kor[[k]]] + D[A[[j, k]], Kor[[i]]] +
D[A[[k, i]], Kor[[j]]])
A = DiagonalMatrix[{1, r^2, 1}]
Kor = {r, \[Theta], z}
Table[{Subscript[\[CapitalGamma], i, j, k], \[CapitalGamma]ddd[i, j,
k]}, {i, 1, 3}, {j, 1, 3}, {k, 1, 3}] // TableForm
Got it
A = {
{1, 0, 0},
{0, r^2, 0},
{0, 0, 1}
} ; B = {
{1, 0, 0},
{0, 1/r^2, 0},
{0, 0, 1}
};
Kor[n_] := \[Piecewise] {
{(r), n == 1},
{(\[Theta]), n == 2},
{(z), n == 3}
}
ChristoffelSymbol1[i_, j_, k_] :=
1/2 (-D[A[[i, j]], Kor[k]] + D[A[[j, k]], Kor[i]] +
D[A[[k, i]], Kor[j]])
ChristoffelSymbol2[i_, j_, m_] :=
Sum[B[[k, m]] ChristoffelSymbol1[i, j, k], {k, 1, 3}]
TableForm[
Table[{Subscript[\[CapitalGamma], i, j, k],
ChristoffelSymbol1[i, j, k]}, {i, 1, 3}, {j, 1, 3}, {k, 1, 3}]]
TableForm[
Table[{Subscript[Superscript[\[CapitalGamma], m], i, j],
ChristoffelSymbol2[i, j, m]}, {i, 1, 3}, {j, 1, 3}, {m, 1, 3}]]
When i tried to replace For with Table i just copied the iterators,they were going from 1-4 in the loop and the marix is 3x3 so it bugged out :p | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40399056673049927, "perplexity": 3984.2383876570793}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662627464.60/warc/CC-MAIN-20220526224902-20220527014902-00064.warc.gz"} |
https://mattermodeling.stackexchange.com/questions/1240/is-the-original-structure-invalid-if-its-found-later-that-the-material-crystall/1242 | Is the original structure invalid if it's found later that the material crystallises with a slightly different space group symmetry?
I am studying a material which was first discovered in the early 1960s. It was reported then that it crystallized in the hexagonal $$P6_3/mmc$$ space group. Recently the material was synthesized again and found that it posses $$P6_3mc$$ symmetry. My own DFT calculations and another published work find that the latter structure is more stable. Hence during the review of my work, the reviewer mentioned the original $$P6_3/mmc$$ structure as hypothetical.
How can the structure be called hypothetical if it was reported from experiments and corroborated by others?
Also in general, if an earlier experiment identifies a material with a crystal type and later its found (experiment and theory) that the material crystallizes with a different structure, is the original structure invalid?
2 Answers
Let's imagine we have two different structures for the same compound, and that structure 1 has the lower energy and structure 2 has the higher energy. If you consider the potential energy surface of all potential atomic configurations, then each of these structures sits at a local minimum, and the minimum associated with structure 1 is lower in energy than the minimum associated with structure 2. I am also going to assume, for simplicity, that structure 1 is the global minimum, so it is the ground state structure.
What does this mean regarding the experimental synthesis of these structures? Structure 1, which is the global minimum, is the most stable structure. What this means is that it will typically be easier to synthesize, and if you wait long enough, any structure of that compound will eventually turn into structure 1. However, it may still possible to synthesize structure 2 experimentally. Depending on your synthesis route, you can create structure 2, which is then "stuck" in that minimum and, even though the minimum of structure 1 is lower in energy, there is an energy barrier to get there. A very famous example of this is carbon structures. The ground state structure of carbon is graphite (my structure 1), but you can also find diamond (my structure 2). In this case, diamond is synthesized at high pressures (where it is actually the lowest energy structure), and then releasing pressure leaves it stuck at its local minimum of energy. Even though diamond is not the lowest energy structure at ambient pressure, it is a structure that carbon can adopt.
What does all this mean for your question? I guess there could be two things going on here:
1. Both structures can be synthesized. The old experiment happened to synthesize a higher energy but locally stable structure (think diamond), and the new experiment has synthesized the true ground state (think graphite). In this case, I would not call any of the two structures hypothetical, as they have both been confirmed experimentally.
2. Another option that always needs to be considered is that one of the experiments is wrong.
• To say it differently: If the thermodynamics allow the reaction/transformation to happen that does not mean it will happen. The kinetics of that reaction/transformation should also be fast enough. If a particular experiment/analysis technique is not sufficiently advance then the future studies/analyses can add to those earlier findings. – Sufyan Jun 11 '20 at 16:38
Sometime the experiments can also be interpreted incorrectly. Namely, not all kinds of experiments are unambiguous; some require computational modeling to extract the structure.
That is, even if the experiment were done correctly, the assignment can still be wrong if the interpretation is not correct.
(I'm not sure this applies to crystal structure modeling; if you have e.g. x-ray diffraction spectra the interpretation is quite straightforward. However, if your material contains hydrogens, x-ray diffraction spectroscopy can't usually locate the hydrogens and so your interpretations may again be limited. A full characterization tends to require both x-ray and neutron diffraction spectra.)
• Crystal structure determination is not modeling. Also, if the structure was determined by single crystal x-ray diffraction, it's almost (99.9%?) that it's structure is correctly determined. I think that what we have here is just a polymorphism case. – Camps Jun 11 '20 at 3:11
• Molecular crystals aren't that easy, and it wasn't specified whether there is hydrogen in the system or not. Looks like crystal structure determination has advanced recently; a 2016 paper [1] claims that hydrogens can be located precisely but I get the feeling that the method is limited to small molecules. [1] advances.sciencemag.org/content/2/5/e1600192.full – Susi Lehtola Jun 11 '20 at 7:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 3, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9220503568649292, "perplexity": 640.4484688945797}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487611445.13/warc/CC-MAIN-20210614043833-20210614073833-00091.warc.gz"} |
https://www.techwhiff.com/issue/what-are-the-solutions-to-this-quadric-equation-x-2--469950 | # What are the solutions to this quadric equation? X^2 + 13 = 8x + 37
###### Question:
What are the solutions to this quadric equation? X^2 + 13 = 8x + 37
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Explain how water, glucose and mineral salts are transported through a plant... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.27585676312446594, "perplexity": 3132.662220228073}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104692018.96/warc/CC-MAIN-20220707124050-20220707154050-00024.warc.gz"} |
http://mathoverflow.net/questions/99076/symplectic-structures-from-lagrangians | # Symplectic structures from Lagrangians?
In Witten's paper 'Quantization of Chern-Simons Gauge Theory with Complex Gauge Group,' he makes the statement (p. 35) that the symplectic form on the moduli space of flat $G_\mathbb{C}$ connections on a surface can be derived from the Chern-Simons Lagrangian and depends upon the coupling chosen.
Now I am familiar with the bracket on the moduli space of connections obtained via Goldman's construction, but what is this method for getting a symplectic form from a Lagrangian and where could I learn more about it? It sounds like this is a general construction, too, that could apply any time a phase space is derived from a configuration space, not just something that applies to this particular case?
-
A related question with some details: mathoverflow.net/questions/81800 – Igor Khavkine Jun 8 '12 at 10:07
The reference is Deligne-Freed, Classical Field Theory, chapter 2. I will follow their notation.
Let $M$ be a spacetime manifold (for simplicity assume oriented) and $\mathcal{F}$ the space of fields. $d$ is the de Rham differential along $M$ and $\delta$ the differential along $\mathcal{F}$.
If the action $S$ is local, in the sense that $S=\int_M L$ for $L\in\Omega^{0,n}(\mathcal{F}\times M)$, then the procedure is the following. Find a form (variational one-form) $\gamma\in\Omega^{1,n-1}(\mathcal{F}\times M)$, such that $\alpha=\delta L+d\gamma\in\Omega^{1,n}(\mathcal{F}\times M)$ is linear over functions. What this means is that $\alpha(f\xi)=f\alpha(\xi)$ for every vector field $\xi\in T\mathcal{F}$ and a function $f\in\mathcal{O}(M)$. Then the symplectic form is defined to be $\omega=\int_H\delta\gamma\in\Omega^2(\mathcal{F})$ for $H$ a hypersurface in $M$. It is closed on the space of classical solutions, but may be degenerate.
In the case of Chern-Simons, this is literally true if $\mathcal{F}$ is the affine space of connections before modding out by the gauge transformations. I will consider the compact group Chern-Simons, the complex group version is similar. Let $M=\Sigma\times\mathbf{R}$ and $H=\Sigma\times\{0\}$. $$S=\int_M Tr(A\wedge dA+\frac{2}{3}A\wedge A\wedge A).$$ Then $$\delta L=Tr(\delta A\wedge dA-A\wedge \delta dA+2\delta A\wedge A\wedge A).$$ In this formula only the second term is not linear over functions. It can be killed off if one takes $$\gamma=Tr(A\wedge \delta A).$$ Its derivative is $$d\gamma = Tr(dA\wedge \delta A-A\wedge d\delta A),$$ so the nonlinear term in $\delta L+d\gamma$ disappears, since $d\delta +\delta d=0$.
Here the choice of $\gamma$ is unique if one assumes it itself is linear over functions. In the end one gets the standard symplectic form on the space of flat connections $$\omega=\int_\Sigma Tr(\delta A\wedge \delta A).$$
One should note that the action is not local in the naive sense on the space of connections mod gauge: the Lagrangian changes by a closed form under gauge transformations. However, the symplectic form does descend to the space of classical solutions mod gauge.
-
I will give a much simpler answer than the others. Given a Lagrangian, there is a corresponding Hamiltonian obtained via Legendre transformation. The symplectic structure comes along with this.
-
Chern-Simons is a first-order theory, so the momentum is independent of the velocity $dA/dt$. This gives constraints on the phase space and one has to take a symplectic reduction with respect to the flows generated by these constraints. – Pavel Safronov Jun 8 '12 at 15:58
Additional information at the nlab: covariant phase space
- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9790723323822021, "perplexity": 180.6760274257654}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645171365.48/warc/CC-MAIN-20150827031251-00299-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://par.nsf.gov/biblio/10340073-transient-radio-source-consistent-merger-triggered-core-collapse-supernova | A transient radio source consistent with a merger-triggered core collapse supernova
A core collapse supernova occurs when exothermic fusion ceases in the core of a massive star, which is typically caused by exhaustion of nuclear fuel. Theory predicts that fusion could be interrupted earlier by merging of the star with a compact binary companion. We report a luminous radio transient, VT J121001+495647, found in the Very Large Array Sky Survey. The radio emission is consistent with supernova ejecta colliding with a dense shell of material, potentially ejected by binary interaction in the centuries before explosion. We associate the supernova with an archival x-ray transient, which implies that a relativistic jet was launched during the explosion. The combination of an early relativistic jet and late-time dense interaction is consistent with expectations for a merger-driven explosion.
Authors:
; ; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10340073
Journal Name:
Science
Volume:
373
Issue:
6559
Page Range or eLocation-ID:
1125 to 1129
ISSN:
0036-8075
5. ABSTRACT We present X-ray and radio observations of what may be the closest Type Iax supernova (SN) to date, SN 2014dt (d = 12.3–19.3 Mpc), and provide tight constraints on the radio and X-ray emission. We infer a specific radio luminosity $L_R\lt (1.0\!-\!2.4)\times 10^{25}\, \rm {erg\, s^{-1}\, Hz^{-1}}$ at a frequency of 7.5 GHz and a X-ray luminosity $L_X\lt 1.4\times 10^{38}\, \rm {erg\, s^{-1}}$ (0.3–10 keV) at ∼38–48 d post-explosion. We interpret these limits in the context of Inverse Compton (IC) emission and synchrotron emission from a population of electrons accelerated at the forward shock of the explosion in a power-law distribution $N_e(\gamma _e)\propto \gamma _e^{-p}$ with p = 3. Our analysis constrains the progenitor system mass-loss rate to be $\dot{M}\lt 5.0 \times 10^{-6} \rm {M_{\odot }\, yr^{-1}}$ at distances $r\lesssim 10^{16}\, \rm {cm}$ for an assumed wind velocity $v_w=100\, \rm {km\, s^{-1}}$, and a fraction of post-shock energy into magnetic fields and relativistic electrons of ϵB = 0.01 and ϵe = 0.1, respectively. This result rules out some of the parameter space of symbiotic giant star companions, and it is consistent with the low mass-loss rates expected from He-star companions. Our calculations also show that the improved sensitivity of the next-generation Very Largemore » | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9524335265159607, "perplexity": 2016.3391643815864}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710870.69/warc/CC-MAIN-20221201221914-20221202011914-00606.warc.gz"} |
https://worldwidescience.org/topicpages/i/igneous+rocks+western.html | #### Sample records for igneous rocks western
1. Multistage amphiboles from the Galinge iron skarn deposit in Qiman Tagh, western China: evidence of igneous rocks replacement
Science.gov (United States)
Yu, M.; Feng, C.-Y.; Zhu, Y.-F.; Mao, J.-W.; Zhao, Y.-M.; Li, D.-X.
2017-02-01
Amphiboles from the Galinge skarn deposit, the largest iron (Fe) polymetallic skarn deposit in the Qiman Tagh metallogenic belt (western China), were formed by multistage fluid-rock interactions. Mineral analysis of the various amphiboles suggest that they were formed by the replacement of mafic to intermediate igneous rocks. The two alteration phases have formed three generations of compositionally distinct amphiboles: Amp-I: Ferro-edenitic hornblende (FE); Amp-II: Deep bluish-green magnesian-hastingsite (MH); Amp-III: Light greenish-beige ferro-actinolite (FA). The Amp-I preserves the primary igneous amphibole composition, and was subsequently replaced by Amp-II. The amphibole Cl content markedly increases from the FE (0.176 - 0.582 wt.%) to the MH (0.894 - 3.161 wt.%), and abruptly drops in the FA (0.017 - 0.039 wt.%). The Cl-rich MH contains the lowest concentration of Si [5.64 - 6.28 atoms per formula unit (apfu)], and the highest (K + Na) values (0.72 - 1.06 apfu) in the amphibole A-site with a high K/(K + Na) of 0.491 to 0.429. Both Mg and Fe contents of the MH and FA vary widely, possibly due to the interactions of magma-derived hydrothermal fluids with the basaltic / andesitic host rocks.
2. Multistage amphiboles from the Galinge iron skarn deposit in Qiman Tagh, western China: evidence of igneous rocks replacement
Science.gov (United States)
Yu, M.; Feng, C.-Y.; Zhu, Y.-F.; Mao, J.-W.; Zhao, Y.-M.; Li, D.-X.
2016-08-01
Amphiboles from the Galinge skarn deposit, the largest iron (Fe) polymetallic skarn deposit in the Qiman Tagh metallogenic belt (western China), were formed by multistage fluid-rock interactions. Mineral analysis of the various amphiboles suggest that they were formed by the replacement of mafic to intermediate igneous rocks. The two alteration phases have formed three generations of compositionally distinct amphiboles: Amp-I: Ferro-edenitic hornblende (FE); Amp-II: Deep bluish-green magnesian-hastingsite (MH); Amp-III: Light greenish-beige ferro-actinolite (FA). The Amp-I preserves the primary igneous amphibole composition, and was subsequently replaced by Amp-II. The amphibole Cl content markedly increases from the FE (0.176 - 0.582 wt.%) to the MH (0.894 - 3.161 wt.%), and abruptly drops in the FA (0.017 - 0.039 wt.%). The Cl-rich MH contains the lowest concentration of Si [5.64 - 6.28 atoms per formula unit (apfu)], and the highest (K + Na) values (0.72 - 1.06 apfu) in the amphibole A-site with a high K/(K + Na) of 0.491 to 0.429. Both Mg and Fe contents of the MH and FA vary widely, possibly due to the interactions of magma-derived hydrothermal fluids with the basaltic / andesitic host rocks. Formation of the Cl-rich MH may have been associated with the early high-temperature and high-saline hydrothermal fluids, meanwhile the Cl-poor FA may have formed from later low-temperature and low-saline hydrothermal fluids. The MH plays an important role for consuming Cl carried by hydrothermal fluids. The Cl-rich fluids may have mobilized some elements, such as Fe, Al, Mg, Ca and Ti from the host rocks. Considerable amounts of Ti, Al, Mg and Fe were incorporated into the sphene and Fe-Ti oxides that coexist with the MH.
3. Geochemistry and petrogenesis of anorogenic basic volcanic-plutonic rocks of the Kundal area, Malani Igneous Suite, western Rajasthan, India
A Krishnakanta Singh; G Vallinayagam
2004-12-01
The Kundal area of Malani Igneous Suite consists of volcano-plutonic rocks. Basalt flows and gabbro intrusives are associated with rhyolite. Both the basic rocks consist of similar mineralogy of plagioclase, clinopyroxene as essential and Fe-Ti oxides as accessories. Basalt displays sub-ophitic and glomeroporphyritic textures whereas gabbro exhibits sub-ophitic, porphyritic and intergrannu- lar textures. They show comparable chemistry and are enriched in Fe, Ti and incompatible ele- ments as compared to MORB/CFB. Samples are enriched in LREE and slightly depleted HREE patterns with least significant positive Eu anomalies. Petrographical study and petrogenetic mod- eling of [Mg]-[Fe], trace and REE suggest cogenetic origin of these basic rocks and they probably derived from Fe-enriched source with higher Fe/Mg ratio than primitive mantle source. Thus, it is concluded that the basic volcano-plutonic rocks of Kundal area are the result of a low to moderate degree (> 30%) partial melting of source similar to picrite/komatiitic composition. Within plate, anorogenic setting for the basic rocks of Kundal area is suggested, which is in conformity with the similar setting for Malani Igneous Suite.
4. Geochemistry and petrogenesis of anorogenic basic volcanic-plutonic rocks of the Kundal area, Malani Igneous Suite, western Rajasthan, India
Science.gov (United States)
Krishnakanta Singh, A.; Vallinayagam, G.
2004-12-01
The Kundal area of Malani Igneous Suite consists of volcano-plutonic rocks. Basalt flows and gabbro intrusives are associated with rhyolite. Both the basic rocks consist of similar mineralogy of plagioclase, clinopyroxene as essential and Fe-Ti oxides as accessories. Basalt displays sub-ophitic and glomeroporphyritic textures whereas gabbro exhibits sub-ophitic, porphyritic and intergrannular textures. They show comparable chemistry and are enriched in Fe, Ti and incompatible elements as compared to MORB/CFB. Samples are enriched in LREE and slightly depleted HREE patterns with least significant positive Eu anomalies. Petrographical study and petrogenetic modeling of [Mg]-[Fe], trace and REE suggest cogenetic origin of these basic rocks and they probably derived from Fe-enriched source with higher Fe/Mg ratio than primitive mantle source. Thus, it is concluded that the basic volcano-plutonic rocks of Kundal area are the result of a low to moderate degree (conformity with the similar setting for Malani Igneous Suite.
5. Quantitative Chemical Indices of Weathered Igneous Rocks
Institute of Scientific and Technical Information of China (English)
2001-01-01
A study was conducted to compare the effectiveness of different weathering indices for characterising weathered igneous rocks of Hong Kong. Among eight chemical indices evaluated in this study, the Parker index has been found most suitable for a quantitative description of state of weathering. Based on geochemical results of 174 samples, the index decreases almost linearly with an increasing extent of weathering. The results enable a better understanding of the modification of geotechnical properties of igneous rocks associated with weathering processes.
6. Orogeny processes of the western Jiangnan Orogen, South China：Insights from Neoproterozoic igneous rocks and a deep seismic profile
Science.gov (United States)
Su, Jinbao; Dong, Shuwen; Zhang, Yueqiao; Li, Yong; Chen, Xuanhua; Ma, Licheng; Chen, Jiansheng
2017-01-01
The Jiangnan Orogen is a collisional suture belt between the Yangtze and Cathaysia Blocks in South China, with many unanswered questions regarding its tectonic evolution. Using the basement structure of the Jiangnan Orogen, we investigate the granite and dacite exposed along the western Jiangnan Orogen and present new LA-ICP-MS zircon U-Pb ages, Hf isotopes, and whole rock geochemistry data. The results suggest that the granite plutons belong to the calc-alkaline series and are typical S-type granites. It yields a mean U-Pb age of 854 ± 2 Ma, which is determined from the core of zircon and possibly inherited from its source or wall rocks. The initial emplacement age of granite may be 826-805 Ma, whereas the dacites yield an age of 805 ± 1.6 Ma and belong to the shoshonite series. The initial Hf-isotope ratios (176Hf/177Hf) in the granite sample are mostly negative εHf(t), with a few of positive value with 1.38-1.6 Ga TDM and 1.67-2.06 Ga TDM2, whereas the dacite samples have mostly positive εHf(t), with a 0.78-1.6 Ga TDM and 0.83-2.2 Ga TDM2t. A comparison of the εHf(t) and TDM2t with the corresponding intruded strata, helps illustrate the origin of the magma and the finals stages ofcollision. Based on our results, we conclude that the western Jiangnan Orogen was a back-arc foreland basin that developed on the margin of the Yangtze continent and collided with the Cathaysia Block, forming a continent-arc-continent accretionary orogeny between 860 and 800 Ma.
7. Selected references on alkalic igneous rocks of the United States
Energy Technology Data Exchange (ETDEWEB)
Hall, C.R. (comp.)
1976-01-01
A compilation of references is presented providing background information on rock and mineral associations, geochemistry, geophysics, structural relationships, and geochronology of sialic, feldspathoidal, and some mafic alkalic igneous rock exposures in the US. Their locations and major characteristics are cited. No implication regarding U potential in these areas is intended. The first part of the bibliography provides general references to overall features of alkaline igneous rocks by region. The second part is a compilation of references on alkalic igneous rocks by state or groups of states. The third part provides information on rock type, age, and location for most of the references cited in part two. (JSR)
8. Geochemistry of Carboniferous low metamorphic grade sedimentary and tholeiitic igneous rocks in the western Acatlán complex, southern Mexico: deposition along the active western margin of Pangea
National Research Council Canada - National Science Library
Ortega Obregón, Carlos; Duncan Keppie, J; Brendan Murphy, J
2010-01-01
Low grade metasedimentary rocks in the western Acatlán complex (Olinalá area) of southern Mexico occur in two units termed here the Progreso and Zumpango units of Lower and middle Carboniferous ages, respectively...
9. Magnetostriction and palæomagnetism of igneous rocks
Science.gov (United States)
Graham, John W.; Buddington, A.F.; Balsley, J.R.
1959-01-01
IN a recent communication, Stott and Stacey1 report on a “crucial experiment” from which they conclude: “This excellent agreement between the dip and the directions of artificial thermoremanent magnetization of the stressed and unstressed rocks indicates that large systematic errors due to magnetostriction are most improbable in igneous rocks of types normally used for palæomagnetic work”. This experiment was intended to test the proposals2 and measurements3 bearing on the role of magnetostriction in rock magnetism. We present here our reasons for believing that the experiment was not crucial and that the conclusion is not justified.
10. Application of seismic facies and attributes analysis on the identification of Permian igneous rock
Institute of Scientific and Technical Information of China (English)
Xu Yongzhong; Yang Haijun; Liu Yongfu; Wang Shuangshuang; Yang Peng; Zhao Jixiang
2012-01-01
Seismic facies and attributes analysis techniques are introduced.The geological characteristics of some oil fields in western China are used in conjunction with drilling results and logging data to identify the lithology,intrusion periods,and distribution range of the Permian igneous rocks in this area.The lithologic classification,the vertical and horizontal distribution,and the intrusion periods of igneous rock were deduced through this study.Combining seismic facies and attributes analysis based on optimization can describe the igneous rock in detail.This is an efficient way to identify lithology and intrusion periods.Using geological data and GR-DT logging cross-plots the Permian igneous rock from TP to TT was divided into three periods.The lithology of the first period is tuff and clasolite with a thickness ranging from 18 to 80 ms.The second is basalt with a thickness ranging from 0 to 20 ms.The third is tuff and clasolite and dacite whose thickness ranges from 60 to 80 ms.These results can help understand the clasolite trap with low amplitude and the lithologic trap of the Carboniferous and Silurian.They can also guide further oil and/or gas exploration.
11. Igneous rocks of the Indian ocean floor
Science.gov (United States)
Engel, C.G.; Fischer, R.L.; Engel, A.E.J.
1965-01-01
Four dredge hauls from near the crest and from the eastern flank of the seismically active Mid-Indian Ocean Ridge at 23?? to 24??S, at depths of 3700 to 4300 meters, produced only low-potassium tholeiitic basalt similar in chemical and mineralogic composition to basalts characteristic of ridges and rises in the Atlantic and Pacific oceansA fifth haul, from a depth of 4000 meters on the lower flank of a seamount on the ocean side of the Indonesian Trench, recovered tholeiitic basalt with higher concentrations of K and Ti and slightly lower amounts of Si and Ca than the typical oceanic tholeiite of the ridgeThe last sample is vesicular, suggesting depression of the area since the basalt was emplacedMany of the rocks dredged are variously decomposed and hydrated, but there is no evidence of important chemical modification toward conversion of the lava flows to spilite during extrusion or solidification.
Energy Technology Data Exchange (ETDEWEB)
Moura, C.L.; Artur, A.C. [Departamento de Petrologia e Metalogenia, Instituto de Geociencias e Ciencias Exatas, Universidade Estadual Paulista (UNESP), Av. 24-A No. 1515, C.P. 178, CEP 13506-900, Rio Claro, Sao Paulo (Brazil); Bonotto, D.M., E-mail: danielbonotto@yahoo.com.b [Departamento de Petrologia e Metalogenia, Instituto de Geociencias e Ciencias Exatas, Universidade Estadual Paulista (UNESP), Av. 24-A No. 1515, C.P. 178, CEP 13506-900, Rio Claro, Sao Paulo (Brazil); Guedes, S. [Departamento de Cronologia e Raios Cosmicos, Instituto de Fisica Gleb Wataghin, Universidade Estadual de Campinas (UNICAMP), Rua Sergio Buarque de Holanda No. 777, CEP 13083-859, Campinas, Sao Paulo (Brazil); Martinelli, C.D. [Departamento de Petrologia e Metalogenia, Instituto de Geociencias e Ciencias Exatas, Universidade Estadual Paulista (UNESP), Av. 24-A No. 1515, C.P. 178, CEP 13506-900, Rio Claro, Sao Paulo (Brazil)
2011-07-15
This paper reports the natural radioactivity of Brazilian igneous rocks that are used as dimension stones, following the trend of other studies on the evaluation of the risks to the human health caused by the rocks radioactivity as a consequence of their use as cover indoors. Gamma-ray spectrometry has been utilized to determine the {sup 40}K, {sup 226}Ra and {sup 232}Th activity concentrations in 14 rock types collected at different quarries. The following activity concentration range was found: 12.18-251.90 Bq/kg for {sup 226}Ra, 9.55-347.47 Bq/kg for {sup 232}Th and 407.5-1615.0 Bq/kg for {sup 40}K. Such data were used to estimate Ra{sub eq}, H{sub ex} and I{sub {gamma}}, which were compared with the threshold limit values recommended in literature. They have been exceeded for Ra{sub eq} and H{sub ex} in five samples, where the highest indices corresponded to a rock that suffered a process of ductile-brittle deformation that caused it a microbrecciated shape. The exhalation rate of Rn and daughters has also been determined in slabs consisting of rock pieces {approx}10 cm-long, 5 cm-wide and 3 cm-thick. It ranged from 0.24 to 3.93 Bq/m{sup 2}/h and exhibited significant correlation with eU (={sup 226}Ra), as expected. The results indicated that most of the studied rocks did not present risk to human health and may be used indoors, even with low ventilation. On the other hand, igneous rocks that yielded indices above the threshold limit values recommended in literature may be used outdoors without any restriction or indoors with ample ventilation.
13. Comparison between several multi-parameter seismic inversion methods in identifying plutonic igneous rocks
Institute of Scientific and Technical Information of China (English)
Yang Haijun; Xu Yongzhong; Huang Zhibin; Chen Shizhong; Yang Zhilin; Wu Gang; Xiao Zhongyao
2011-01-01
With the objective of establishing the necessary conditions for 3-D seismic data from a Permian plutonic oilfield in western China,we compared the technology of several multi-parameter seismic inversion methods in identifying igneous rocks.The most often used inversion methods are Constrained Sparse Spike Inversion (CSSI).Artificial Neural Network Inversion (ANN) and GR Pseudo-impedance Inversion.Through the application of a variety of inversion methods with log curves correction,we obtained relatively high-resolution impedance and velocity sections,effectively identifying the lithology of Permian igneous rocks and inferred lateral variation in the lithology of tgneous rocks.By means of a comprehensive comparative study,we arrived at the following conclusions:the CSSI inversion has good waveform continuity,and the ANN inversion has lower resolution than the CSSI inversion.The inversion results show that multi-parameter seismic inversion methods are an effective solution to the identification of igneous rocks.
14. Igneous Petrogenesis of Tequila Volcano, Western Mexico
Science.gov (United States)
Vázquez-Duarte, A.; Gómez-Tuena, A.; Díaz-Bravo, B.
2011-12-01
Tequila volcano belongs to a Quaternary volcanic chain that runs in parallel to the Middle American Trench, but that have been constructed within the so-called Tepic-Zacoalco rift: an extensional tectonic structure that has been active for the past 3.5 Ma. This unusual tectonic setting, and the existence of a high-resolution stratigraphy for the Tequila Volcanic Field (Lewis-Kenedi, 2005, Bull Volcanol), provide an excellent opportunity to study andesite petrogenesis. New comprehensive geochemical data allow the recognition of at least four different magmatic series around Tequila: 1) The Santa Rosa intraplate basalts (1.0 - 0.2 Ma), a volcanic plateau constructed along the Santiago River Fault north of Tequila volcano. These Na-alkaline basalts are olivine-phyric, have negligible subduction signatures (Ba/Nb= 11.75 - 49.36), and display Sr-Nd-Pb isotopic compositions that correlate with fractionation indexes, probably indicating melt-crust interactions. 2) A group of vitreous domes and flows of dacitic to rhyolitic compositions, mostly contemporaneous to the Santa Rosa basalts, that were emplaced on the periphery of Tequila volcano. These rocks can have very low Sr and Eu contents but their isotopic compositions are remarkably constant and similar to the Santa Rosa basalts, probably indicating a genetic link through low pressure fractionation in the stability field of plagioclase. 3) The main edifice of Tequila volcano (~0.2 Ma) is made of two pyroxene andesites and dacites with strong subduction signatures (Ba/Nb= 53-112), that inversely correlate with MgO contents, but that follow a diverging evolutionary trend as the rest of the sequences. The isotopic compositions of Tequila main edifice can extend to slightly more enriched values, but do not correlate with fractionation indexes, thus indicating provenance from a different source. 4) The youngest activity on Tequila volcano (~0.09 Ma) is represented by amphibole bearing andesites that erupted through the
15. Petrology of Igneous Rocks in Northern Golpayegan, Iran
Institute of Scientific and Technical Information of China (English)
1998-01-01
A preliminary study on petrological features of igneous rocks was carried out in northern Golpayegan, Iran, in an area of about 60 km2. According to the limited available data the sequence of the magma activity could be considered as follows: (1) Precambrian (?) granite connected with a continental-continental collision event, (2) Precambrian (?) syenite emplaced at a post continental-continental collision environment, (3) Cretaceous volcanic rocks generated by a local extensional system at an active continental margin and (4) Cenozoic doleritic veins generated in a post collision event. Geochemical characteristics of the granitic intrusion show that it originated from crust and belongs to S-type one. Syenitic body consists of syenitic affinities ranging from alkali-syenite to syenodiorite. These rocks were cut by Cenozoic doleritic veins, which consist of dolerite and olivine dolerite. Both syenite and dolerite are thought to originate from upper mantle but their ages are different. Cretaceous volcanic rocks include basalt, andesite, trachyandesite, trachyte and tuff. They are compositionally alkaline and erupted in a shallow graben basin. Their eruption has been in connection with deep-seated faults, which brought out the magma from the source.
16. Integrating isotopic fingerprinting with petrology: how do igneous rocks evolve?
Science.gov (United States)
Davidson, J. P.
2002-12-01
In the title of his seminal work, N.L. Bowen recognized the fundamental importance of magmatic evolution in producing the spectrum of igneous rocks. Indeed it is difficult to imagine a hot highly reactive fluid passing through c. 100 km of a chemically distinct medium (lithosphere) without evolving through cooling, crystallization and interaction with the wall rocks. The fact that magmas evolve - almost invariably through open system processes - has been largely marginalized in the past 30 years by the desire to use them as probes of mantle source regions. This perspective has been driven principally by advances offered by isotope geochemistry, through which components and sources can be effectively fingerprinted. Two fundamental observations urge caution in ignoring differentiation effects; 1) the scarcity of truly primary magmas according to geochemical criteria (recognized long ago by petrologists), and 2) the common occurrence of petrographic criteria attesting to open system evolution. Recent advances in multicollector mass spectrometry permit integration of the powerful diagnostic tools of isotope geochemistry with petrographic observations through accurate and precise analysis of small samples. Laser ablation and microdrilling enable sampling within and between mineral phases. The results of our microsampling investigations give widespread support for open system evolution of magmas, and provide insights into the mechanisms and timescales over which this occurs. For example; 1) core-rim decreases in 87Sr/86Sr in zoned plagioclase crystals from 1982 lavas of El Chichon volcano, Mexico, argue that the zoning and isotopic changes are in response to magma recharge mixing with an originally contaminated resident magma; 2) Single grain and intra-grain isotopic analyses of mineral phases from Ngauruhoe andesites (New Zealand) are highly variable, arguing that bulk rock data reflect mechanical aggregations of components which have evolved in discrete domains of the
17. Geochemical characteristics of igneous rocks associated with epithermal mineral deposits—A review
Science.gov (United States)
du Bray, Edward A.
2017-01-01
Newly synthesized data indicate that the geochemistry of igneous rocks associated with epithermal mineral deposits varies extensively and continuously from subalkaline basaltic to rhyolitic compositions. Trace element and isotopic data for these rocks are consistent with subduction-related magmatism and suggest that the primary source magmas were generated by partial melting of the mantle-wedge above subducting oceanic slabs. Broad geochemical and petrographic diversity of individual igneous rock units associated with epithermal deposits indicate that the associated magmas evolved by open-system processes. Following migration to shallow crustal reservoirs, these magmas evolved by assimilation, recharge, and partial homogenization; these processes contribute to arc magmatism worldwide.Although epithermal deposits with the largest Au and Ag production are associated with felsic to intermediate composition igneous rocks, demonstrable relationships between magmas having any particular composition and epithermal deposit genesis are completely absent because the composition of igneous rock units associated with epithermal deposits ranges from basalt to rhyolite. Consequently, igneous rock compositions do not constitute effective exploration criteria with respect to identification of terranes prospective for epithermal deposit formation. However, the close spatial and temporal association of igneous rocks and epithermal deposits does suggest a mutual genetic relationship. Igneous systems likely contribute heat and some of the fluids and metals involved in epithermal deposit formation. Accordingly, deposit formation requires optimization of source metal contents, appropriate fluid compositions and characteristics, structural features conducive to hydrothermal fluid flow and confinement, and receptive host rocks, but not magmas with special compositional characteristics.
18. Crystal Size Distributions in Igneous rocks: Where are we now?
Science.gov (United States)
Higgins, M.
2003-12-01
in either slope of intercept is significant and can be related to other parameters. Concave down CSDs, with no small crystals, are commonly encountered in porphyritic, oikocrystic and plutonic rocks. This texture may be produced by textural coarsening (Ostwald ripening, annealing): this occurs when the magma is maintained close to the mineral liquidus. In this situation the nucleation rate is zero, but growth rates are significant. The classic LSW model is not the only solution possible: more modern solutions, such as Communicating Neighbours may be more appropriate. Variable degrees of textural coarsening will produce CSDs that appear to rotate about a single point. This again reflects closure. Concave up CSDs with no lower size limit are very common. They do not generally have a lognormal or fractal size distribution. They can be produced by mixing of two or more magmas, or crystallisation under several different conditions of undercooling. They can also result from alternations of nucleation and growth followed by textural coarsening. Crystal accumulation and fraction should modify existing CSDs in a predictable manner. An exact solution to this problem has not yet been developed, but simplistic models suggest that CSDs should rotate upwards about the size origin for accumulation and downwards for fractionation. However, clear evidence for such effects has not yet been observed, even in well-layered rocks. There are many igneous systems still to be explored using CSDs. An exiting new domain may be the application of CSDs in experimental petrology.
19. PETROS - Worldwide Databank of Major Element Chemical Analyses of Igneous Rocks
Data.gov (United States)
National Oceanic and Atmospheric Administration, Department of Commerce — PETROS is a worldwide data bank of major element chemical analyses of igneous rocks compiled for research and teaching purposes by Dr. Felix Mutschler and Staff at...
20. Classification scheme for sedimentary and igneous rocks in Gale crater, Mars
Science.gov (United States)
Mangold, N.; Schmidt, M. E.; Fisk, M. R.; Forni, O.; McLennan, S. M.; Ming, D. W.; Sautter, V.; Sumner, D.; Williams, A. J.; Clegg, S. M.; Cousin, A.; Gasnault, O.; Gellert, R.; Grotzinger, J. P.; Wiens, R. C.
2017-03-01
Rocks analyzed by the Curiosity rover in Gale crater include a variety of clastic sedimentary rocks and igneous float rocks transported by fluvial and impact processes. To facilitate the discussion of the range of lithologies, we present in this article a petrological classification framework adapting terrestrial classification schemes to Mars compositions (such as Fe abundances typically higher than for comparable lithologies on Earth), to specific Curiosity observations (such as common alkali-rich rocks), and to the capabilities of the rover instruments. Mineralogy was acquired only locally for a few drilled rocks, and so it does not suffice as a systematic classification tool, in contrast to classical terrestrial rock classification. The core of this classification involves (1) the characterization of rock texture as sedimentary, igneous or undefined according to grain/crystal sizes and shapes using imaging from the ChemCam Remote Micro-Imager (RMI), Mars Hand Lens Imager (MAHLI) and Mastcam instruments, and (2) the assignment of geochemical modifiers based on the abundances of Fe, Si, alkali, and S determined by the Alpha Particle X-ray Spectrometer (APXS) and ChemCam instruments. The aims are to help understand Gale crater geology by highlighting the various categories of rocks analyzed by the rover. Several implications are proposed from the cross-comparisons of rocks of various texture and composition, for instance between in place outcrops and float rocks. All outcrops analyzed by the rover are sedimentary; no igneous outcrops have been observed. However, some igneous rocks are clasts in conglomerates, suggesting that part of them are derived from the crater rim. The compositions of in-place sedimentary rocks contrast significantly with the compositions of igneous float rocks. While some of the differences between sedimentary rocks and igneous floats may be related to physical sorting and diagenesis of the sediments, some of the sedimentary rocks (e
1. Igneous rock from Severnyi Kolchim (H3) chondrite: Nebular origin
Science.gov (United States)
Nazarov, M. A.; Brandstaetter, F.; Kurat, G.
1993-01-01
The discovery of lithic fragments with compositions and textures similar to igneous differentiates in unequilibrated ordinary chondrites (UOC's) and carbonaceous chondrites (CC's) has been interpreted as to suggest that planetary bodies existed before chondrites were formed. As a consequence, chondrites (except, perhaps CI chondrites) cannot be considered primitive assemblages of unprocessed nebular matter. We report about our study of an igneous clast from the Severnyi Kolchim (H3) chondrite. The results of the study are incompatible with an igneous origin of the clast but are in favor of a nebular origin similar to that of chondrules.
2. Electrical resistivity measurement to predict uniaxial compressive and tensile strength of igneous rocks
Sair Kahraman; Tekin Yeken
2010-12-01
Electrical resistivity values of 12 different igneous rocks were measured on core samples using a resistivity meter in the laboratory. The resistivity tests were conducted on the samples fully saturated with brine (NaCl solution) and the uniaxial compressive strength (UCS), Brazilian tensile strength, density and porosity values of the samples were determined in the laboratory. The test results were evaluated using simple and multiple regression analysis. It was seen that the UCS and tensile strength values were linearly correlated with the electrical resistivity. The correlation coefficients are generally higher for the multiple regression models than that of the simple regression models. It was concluded that the UCS and tensile strength of igneous rocks can be estimated from electrical resistivity. However, the derived relations are purely empirical and they should be checked for other igneous rocks. The effect of rock types such as sedimentary and metamorphic rocks on the derived equations also needs to be investigated.
3. [High Precision Identification of Igneous Rock Lithology by Laser Induced Breakdown Spectroscopy].
Science.gov (United States)
Wang, Chao; Zhang, Wei-gang; Yan, Zhi-quan
2015-09-01
In the field of petroleum exploration, lithology identification of finely cuttings sample, especially high precision identification of igneous rock with similar property, has become one of the geological problems. In order to solve this problem, a new method is proposed based on element analysis of Laser-Induced Breakdown Spectroscopy (LIBS) and Total Alkali versus Silica (TAS) diagram. Using independent LIBS system, factors influencing spectral signal, such as pulse energy, acquisition time delay, spectrum acquisition method and pre-ablation are researched through contrast experiments systematically. The best analysis conditions of igneous rock are determined: pulse energy is 50 mJ, acquisition time delay is 2 μs, the analysis result is integral average of 20 different points of sample's surface, and pre-ablation has been proved not suitable for igneous rock sample by experiment. The repeatability of spectral data is improved effectively. Characteristic lines of 7 elements (Na, Mg, Al, Si, K, Ca, Fe) commonly used for lithology identification of igneous rock are determined, and igneous rock samples of different lithology are analyzed and compared. Calibration curves of Na, K, Si are generated by using national standard series of rock samples, and all the linearly dependent coefficients are greater than 0.9. The accuracy of quantitative analysis is investigated by national standard samples. Element content of igneous rock is analyzed quantitatively by calibration curve, and its lithology is identified accurately by the method of TAS diagram, whose accuracy rate is 90.7%. The study indicates that LIBS can effectively achieve the high precision identification of the lithology of igneous rock.
4. Petrographic analysis of igneous and metamorphic rocks from the Fishguard 1:50000 sheet, south Wales
OpenAIRE
McKervey, J.A.
2005-01-01
This report presents the results of petrographic analysis of samples of igneous and metamorphic rocks collected as part of a mapping survey of the Fishguard 1:50000 sheet, south Wales. The objective of the report is to provide petrographic descriptions of the rocks and to discuss the origin of the fabrics present.
5. The Law of Element Abundance Relationships in Igneous Rocks Petrogenetically Associated with Fractional Crystallization
Institute of Scientific and Technical Information of China (English)
汪云亮; 王旺章
1991-01-01
Reported in this paper are:1)the law of element abundance relationships:element abun-dances are of power function with each other in an igneous rock petrogenetically associated with fractional crystallization,2)deduction of the law and relevant parameters:abundance relationship constant(a°) and phase constant? from Henry's law and the law of mass conservation,3)the data basis and evidence of the law of element abundance relationships,4)establishment of the equa-bions for element abundance relationships in igneous rocks formed from the same parental magma during the same fractional crystallization stage ,and all measurable parameters involved in the equations.
6. Petrological and Geochemical Studies of the Igneous Rocks at Cerro EL Borrego, Chihuahua, Mexico
Science.gov (United States)
Estrada, V. M.; Espejel-Garcia, V. V.; Villalobos-Aragon, A.
2013-05-01
Cerro El Borrego, which is a hill composed of igneous rocks, is located 13.7 km to the SW of Chihuahua city, in northern Mexico. The coordinates of the hill are 28° 11' 07'' N latitude and 105° 33' 23'' W longitude. The study area is within the Basin and Range Physiographic Province, characterized by a complex tectonic-structural pattern, such as elongated ranges with folds and igneous rock formations of Paleogene age. A lava flow of Oligocene age is part of the large volcanic and plutonic activity at the early times of the Cenozoic, which occurred to the NW portion of Mexico. In Cerro El Borrego, the rocks that outcrop are middle Oligocene's rhyolitic tuff to the NW of the hill, while to its SE there is a Pleistocene polymictic conglomerate. Previous work shows different interpretations about the origin and composition of the igneous rocks at Cerro El Borrego. This project includes whole rock and textural analyses, which helped to discern the petrogenesis of these rocks. Preliminary petrographic analyses indicate that the Cerro El Borrego, is a structural dome, and its feldspar-rich rocks contain large crystals that can be appreciated without a microscope. The presence of a porphyritic texture, suggest a sallow intrusion origin. A preliminary conclusion is that Cerro El Borrego is a shallow depth intrusive body with a syenitic composition derived from the Oligocene plutonic activity.
7. Spores and Pollen in Oil From Igneous Rock Petroleum Pool and Petroleum Origin of Junggar Basin
Institute of Scientific and Technical Information of China (English)
江德昕; 杨惠秋
1994-01-01
Ninety-six species of fossil spores and pollen referred to 55 genera found in crude oil fromthe Beisantai igneous rock petroleum pool of the southeastern part of the Junggar Basin in Xinjiang have beenstudied.Based on the investigation of the spores and pollen in crude oil,the petroleum source rocks of thepetroliferous province are identified,the petroleum origin theory is discussed and the organic petroleum ori-gin theory is confirmed.
8. Comparison between the chemistry of igneous and hydrothermal biotite in the igneous rocks of Sakhtehesar mountain
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Farima Ayati
2015-12-01
Full Text Available Sakhtehesar mountain is located in Urumieh-Dokhtar magmatic belt and is composed of volcanic and subvolcanic rocks (Pliocene andesite to dacite which intruded the volcanics and pyroclastics of Paleocene age. Three alteration zones including potassic, phyllic and propylitic are recognized in the area. In this paper, the mineral chemistry of magmatic and primary biotite and the mineral chemistry of biotite in potassic and phyllic alteration zones have been studied. Investigations show that primary and secondary biotites are different from each other and hydrothermal fluids associated with the potassic alteration are distinctively different from the fluids associated with the phyllic alteration zone in the area.
9. Continental igneous rock composition: A major control of past global chemical weathering.
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Bataille, Clément P; Willis, Amy; Yang, Xiao; Liu, Xiao-Ming
2017-03-01
The composition of igneous rocks in the continental crust has changed throughout Earth's history. However, the impact of these compositional variations on chemical weathering, and by extension on seawater and atmosphere evolution, is largely unknown. We use the strontium isotope ratio in seawater [((87)Sr/(86)Sr)seawater] as a proxy for chemical weathering, and we test the sensitivity of ((87)Sr/(86)Sr)seawater variations to the strontium isotopic composition ((87)Sr/(86)Sr) in igneous rocks generated through time. We demonstrate that the (87)Sr/(86)Sr ratio in igneous rocks is correlated to the epsilon hafnium (εHf) of their hosted zircon grains, and we use the detrital zircon record to reconstruct the evolution of the (87)Sr/(86)Sr ratio in zircon-bearing igneous rocks. The reconstructed (87)Sr/(86)Sr variations in igneous rocks are strongly correlated with the ((87)Sr/(86)Sr)seawater variations over the last 1000 million years, suggesting a direct control of the isotopic composition of silicic magmatism on ((87)Sr/(86)Sr)seawater variations. The correlation decreases during several time periods, likely reflecting changes in the chemical weathering rate associated with paleogeographic, climatic, or tectonic events. We argue that for most of the last 1000 million years, the ((87)Sr/(86)Sr)seawater variations are responding to changes in the isotopic composition of silicic magmatism rather than to changes in the global chemical weathering rate. We conclude that the ((87)Sr/(86)Sr)seawater variations are of limited utility to reconstruct changes in the global chemical weathering rate in deep times.
10. Classification and Geochemical Characterization of Igneous Rocks: Southern Part of Chihuahua City, Mexico
Science.gov (United States)
Fontes, I. D.; Espejel-Garcia, V. V.; Villalobos-Aragon, A.
2013-05-01
Chihuahua City is the capital of the state with the same name, located in northern Mexico. The city was established near the Chuviscar River, but in the last decades it has been extended to the nearby areas (mountains), with volcanic (rhyolitic tuffs), and sedimentary rocks (limestone). The study area includes areas in the south part of Chihuahua City, where we can still find unbuilt lands and it is possible to appreciate outcrops of igneous rocks. This project includes 5 study spots, which are located about 9 km. far from the south extreme of the city. This research is developed in order to complement the geological information in this area, as there is no is detailed record of it. In the geological map H13-10 (SGM, 1997), it is said that the urban area is covered by Quaternary conglomerates, while exploring the region we have located several igneous rocks outcrops. In three of the sampling points, dark colored intrusive igneous rocks with large crystals appear in blocks without noticeable fractures. While in the other two sampling points, highly fractured blocks of pink aphanitic igneous rocks, showing traces of pyrolusite were observed. The petrographic study shows the two different textures that classify these rocks as extrusive (aphanitic) or intrusive (phaneritic), both with quartz and feldspars being the dominant minerals. Geochemical analyses confirm the felsic composition of the rocks, varying form trachytes to rhyolites. The trace element results show high contents of Sr, Ba, V, Rb, and Zr in trachytic compositions, while there are high concentrations of Mn, W, Rb and Co for rhyolitic compositions.
11. Igneous rocks of Arctic Ocean deep sea ridges: new data on petrology, geochemistry and geochronology
Science.gov (United States)
Petrov, Oleg; Morozov, Andrey; Shokalsky, Sergey; Sobolev, Nikolay; Kashubin, Sergey; Shevchenko, Sergey; Sergeev, Sergey; Belyatsky, Boris; Shatov, Vitaly; Petrov, Eugeny
2015-04-01
The aggregate results of studies of igneous rocks, collected from the central part of the Arctic Ocean during scientific marine expeditions «Arctic-2000, 2005, 2007 and 2012» are presented and discussed in the frame of modern understanding of High Polar Arctic tectonic constraint. Petrological, geochemical and isotope-geochronological studies of more than 500 samples have shown that the sedimentary rocks are of dominated population among the rock fragments dredged from deep-sea bottom, and represented by metamorphosed dolomite and quartz sandstone, limestone, sometimes with the Devonian - Permian fauna. Igneous rocks are 10-15% only (Archean and Paleoproterozoic gneissouse granites and gabbro, Neoproterozoic dolerite) and metamorphic rocks (green shales, metabasites, gneisses). Apparently, these rocks are part of the acoustic basement underlying the Late Mesozoic - Cenozoic layered loose sediments. In addition to the dredged fragments of the ancient mafic rocks, some samples were taken as a core during deep-water drilling in the northern and southern slopes of the Mendeleev Ridge and represented by trachybasalts, marking the border of Late-Cenozoic deposit cover and acoustic basement and quite similar in composition to those of Early-Late Cretaceous basalts form northward of the Chukchi Plateau seamounts, Alpha Ridge, Franz Josef Land, De Long islands and other parts of the large igneous province of the High Arctic (HALIP). Video-filming of Mendeleev Ridge escarps proofs the existing of rock outcrops and supports local origin of most of the rock fragments found in the sampling areas. Thus the continental type of the earth's crust of the Central Arctic Ridges basement is based on all obtained results of our study of sea-bottom excavated rock material.
12. Pristine Igneous Rocks and the Early Differentiation of Planetary Materials
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Warren, Paul H.
2005-01-01
Our studies are highly interdisciplinary, but are focused on the processes and products of early planetary and asteroidal differentiation, especially the genesis of the ancient lunar crust. The compositional diversity that we explore is the residue of process diversity, which has strong relevance for comparative planetology. Most of the accessible lunar crust consists of materials hybridized by impact-mixing. Our lunar research concentrates on the rare pristine (unmixed) samples that reflect the original genetic diversity of the early crust. Among HED basalts (eucrites and clasts in howardites), we distinguish as pristine the small minority that escaped the pervasive thermal metamorphism of the parent asteroid's crust. We have found a correlation between metamorphically pristine HED basalts and the similarly small minority of compositionally evolved "Stannern trend" samples, which are enriched in incompatible elements and titanium compared to main group eucrites, and yet have relatively high mg ratios. Other topics under investigation included: lunar and SNC (martian?) meteorites; igneous meteorites in general; impact breccias, especially metal-rich Apollo samples and polymict eucrites; siderophile compositions of the lunar and martian mantles; and planetary bulk compositions and origins.
13. Complex Dielectric Properties of Several Igneous and Metamorphic Rocks
Science.gov (United States)
1980-10-01
Padovani et al. (1980). 2383 New York (eastern Garnet granulite Adirondacks) 2390 New York (eastern Garnet granulite Adirondacks) 2422 Central Maine...File Report 79-993, 1979. Padovani, E.R., S.B. Shirey, and G. Simons, Microcracks in amphibolite and granulite facies grade rocks from southeastern...hypersthene (pyroxene)-plagioclase granulite with lesser amounts of clinopyroxene, K-feldspar, and pyrite. Garnet, hornblende, and clinopyroxene occur as
14. Lead isotope systematics of some igneous rocks from the Egyptian Shield
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Gillespie, J. G.; Dixon, T. H.
1983-01-01
Lead isotope data on whole-rock samples and two feldspar separates for a variety of Pan-African (late Precambrian) igneous rocks for the Egyptian Shield are presented. It is pointed out that the eastern desert of Egypt is a Late Precambrian shield characterized by the widespread occurrence of granitic plutons. The lead isotope ratios may be used to delineate boundaries between Late Precambrian oceanic and continental environments in northeastern Africa. The samples belong to three groups. These groups are related to a younger plutonic sequence of granites and adamellites, a plutonic group consisting of older tonalites to granodiorites, and the Dokhan volcanic suite.
15. Distinct Igneous APXS Rock Compositions on Mars from Pathfinder, MER and MSL
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Gellert, Ralf; Arvidson, Raymond; Clark, Benton, III; Ming, Douglas W.; Morris, Richard V.; Squyres, Steven W.; Yen, Albert S.
2015-01-01
The alpha particle x-ray spectrometer (APXS) on all four Mars Rovers returned geochemical data from about 1000 rocks and soils along the combined traverses of over 50 kilometers. Here we discuss rocks likely of igneous origin, which might represent source materials for the soils and sediments identified along the traverses. Adirondack-type basalts, abundant in the plains of Gusev Crater, are primitive, olivine bearing basalts. They resemble in composition the basaltic soils encountered at all landing sites, except the ubiquitous elevated S, Cl and Zn in soils. They have been postulated to represent closely the average Martian crust composition. The recently identified new Martian meteorite Black Beauty has similar overall geochemical composition, very distinct from the earlier established SNC meteorites. The rim of the Noachian crater Endeavour, predating the sulfate-bearing Burns formation at Meridiani Planum, also resembles closely the composition of Adirondack basalts. At Gale Crater, the MSL Curiosity rover identified a felsic rock type exemplified by the mugearitic float rock JakeM, which is widespread along the traverse at Gale. While a surprise at that time, possibly related more evolved, alkaline rocks had been previously identified on Mars. Spirit encountered the Wishstone rocks in the Columbia Hills with approx. 6% Na2O+K2O, 15 % Al2O3 and low 12% FeO. Pathfinder rocks with elevated K and Na and >50% SiO2 were postulated to be andesitic. Recently Opportunity encountered the rock JeanBaptisteCharbonneau with >15% Al2O3, >50% SiO2 and approx. 10% FeO. A common characteristic all these rocks is the very low abundance of Cr, Ni and Zn, and an Fe/Mn ratio of about 50, indicating an unaltered Fe mineralogy. Beside these likely igneous rock types, which occurred always in several rocks, a few unique rocks were encountered, e.g. Bounce Rock, a pyroxene-bearing ejecta rock fragment resembling the Shergottite EETA 79001B meteorite. The APXS data can be used to
16. Igneous rocks of alpine age associated with Keuper material in the Iberian Mountains, near Teruel (Spain
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Sánchez Cela, V.
1984-04-01
Full Text Available In the present work, some rocks of igneous facies associated to Keuper materials, are studied. These rocks, previously referred to as ophites, consist in fact of plutonic rocks, compositionally ranging from syenites to monzogabbros. Field, petrographic and geochemical data appear to indicate that these igneous rocks facies were a consequence of metasomatic transformation processes that took place between allocthonous silica-alkaline elements and suitable wall-rocks, constituted, in this case, of evaporitic marls of Keuper facies.
Se describen algunos caracteres geológicos, petrográficos y geoquímicos de unas rocas ígneas, que en pequeños afloramientos aparecen asociadas a materiales del Keuper. Estas rocas, que estaban citadas como ofitas, corresponden principalmente a facies granudas entre sienitas y monzogabros. El ambiente de los afloramientos, relaciones de contacto, caracteres petrográficos y químicos, parecen indicar que las rocas ígneas fueron el resultado de procesos de metasomatismo originados por fluidos sílico-alcalinos que transformaron los materiales encajantes margoevaporíticos del Keuper.
17. Igneous rocks identification on well-log data; Classificacao de rochas igneas em perfis eletricos
Energy Technology Data Exchange (ETDEWEB)
Souza-Lima, Wagner [PETROBRAS S.A., Salvador, BA (Brazil). Unidade de Negocio de Exploracao e Producao de Sergipe e Alagoas. Ativo de Exploracao], E-mail: wagnersl@petrobras.com.br; Pinho, Gustavo de Carvalho; Silva, Patricia Martins; Paraizo, Paulo Lopes Brandao
2005-11-15
An attempt to discriminate and characterise igneous rocks on well-log data is made in a well drilled on the Cabo Sub-basin (JG-1 well, Sergipe- Alagoas Basin), situated on the northeastern coast of Brazil. Log data from the twelve drilled igneous intervals were analysed on RHOBxPHIN and DTxGRxResistivity cross plots. Similar diagrams were constructed for igneous data from the 1-CPE-1-PE well, drilled on the same basin, and with igneous data from other Brazilian basins. At the RHOBxPHIN cross plot, twelve lithologic fields were discriminated, and their characteristics verified against petrographic data. Two trends are perceptible: the basic rocks set (olivine-basalt, andesite, basaltic pumice and basaltic andesite) distributed along the dolomite line, and the acid rocks set (trachyandesite/quartz-latite, trachyandesite, trachyte, olivine-trachyandesite and acid pumice) coincident with the calcite line. At the DTxGRxResistivity cross plot, the basic set occurs around low-GR field, and the acid set is distributed around high-GR field. The JG-1 well's log data were submitted to discriminant analysis, and the results were checked against the CPE-1 well's curves, for validation. For the first well, the hits ranged from 82 and 100%. For the second well, a perfect lithologic identification was obtained, except for those cases where the lithotypes does not exist in the JG-1 well. One of the main applications for this technique is the stratigraphic correlation for the volcanic successions from sedimentary basins, mainly in the absence of good biostratigraphic markers. (author)
18. A physical basis for remote rock mapping of igneous rocks using spectral variations in thermal infrared emittance
Science.gov (United States)
Walter, L. S.; Labovitz, M. L.
1980-01-01
Results of a theoretical investigation of the relation between spectral features in the 8-12 micrometer region and rock type are presented. Data on compositions of a suite of rocks and measurements of their spectral intensities in 8.2-10.9 and 9.4-12.1 micrometer bands published by Vincent (1973) were subjected to various quantitative procedures. There was no consistent direct relationship between rock group names and the relative spectral intensities. However, there is such a relationship between the Thornton-Tuttle (1960) Differentiation Index and the relative spectral intensities. This relationship is explicable on the basis of the change in average Si-O bond length which is a function of the degree of polymerization of the SiO4 tetrahedra of the silicate minerals in the igneous rocks.
19. Determination and distribution of diesel components in igneous rock surrounding underground diesel storage facilities in Sweden.
Science.gov (United States)
Loren, A; Hallbeck, L; Pedersen, K; Abrahamsson, K
2001-01-15
In Sweden, a preliminary investigation of the contamination situation of igneous rock surrounding underground storage facilities of diesel showed that the situation was severe. The diesel was believed to have penetrated into the rock as far as 50 m from the walls of the vaults. Consequently, the risk for contamination of groundwater and recipients could not be neglected. To be able to assess the fate of diesel components in rock, both a suitable drilling method and a method for the determination of a wide range of diesel components were needed. The analytical method presented made it possible to quantify a number of hydrocarbons in rock samples collected with triple-tube core drilling. The samples were dissolved in hydrofluoric acid (HF) with hexane in Teflon centrifuge tubes. After digestion of the rock, extraction of the analytes with hexane was performed. Determination of the individual hydrocarbons present was done with gas chromatography-mass spectrometry (GC-MS). The method was used to study the environmental impact of the underground storage of diesel. The drilling method enabled sampling without contamination risks. Our data show that the major transport of diesel components in rock occurs through fracture systems and that diffusion of diesel through the rock is of minor importance. The results have drastically changed the view of the contamination situation of diesel in the vicinity of storage facilities in hard rock in Sweden.
20. Sulfur isotope evidence for penetration of MVT fluids into igneous basement rocks, southeast Missouri, USA
Science.gov (United States)
Shelton, K. L.; Burstein, I. B.; Hagni, R. D.; Vierrether, C. B.; Grant, S. K.; Hennigh, Q. T.; Bradley, M. F.; Brandom, R. T.
1995-08-01
Previous studies of galena and sphalerite from Paleozoic MVT deposits in the Viburnum Trend, southeast Missouri documented large variations in δ34S values throughout the ore-forming event. The present study of Cu-Fe-sulfides reveals a similar δ34S variation that reflects two end-member sulfur reservoirs whose relative importance varied both temporally and spatially. More 34S-enriched sulfides (δ34S approaching 25‰) indicate introduction of sulfur from basinal sedimentary sources, whereas more 32S-enriched sulfides (δ34S Precambrian, igneous-hosted FeCu mineralization in southeast Missouri (West and Central Domes of Boss-Bixby) were investigated to elucidate their relationship to Cu-rich MVT orebodies hosted nearby within the overlying Cambrian Bonneterre Dolomite. Mineralization at Boss-Bixby is composed of an early phase of iron oxide deposition followed by Cu-Fe-sulfides. The Central Dome is faulted and its mineralization is more fracture-controlled than the typically podiform ores of the West Dome. The δ34S values of West Dome sulfides are 0.9 to 6.5‰ and pyrite-chalcopyrite indicate a temperature of 525° ± 50 °C. These data indicate an igneous source of sulfur during Precambrian ore deposition. In contrast, δ34S values of Central Dome sulfides are 9.4 to 20.0‰ and pyrite-chalcopyrite indicate temperatures of 275° ± 50 °C. Similar δ34S values are obtained for chalcopyrite from the overlying MVT deposits. We speculate that deeply circulating, basin-derived MVT fluids mobilized sulfur and copper from the underlying igneous basement and redeposited them in overlying Curich MVT orebodies, as well as overprinting earlier Precambrian sulfides of the Central Dome with a later, Paleozoic MVT sulfur isotope signature. Many models for MVT fluid circulation in the Midcontinent region of North America assume that igneous basement rocks are an impermeable boundary, but in southeast Missouri, evidence exists for structurally controlled MVT fluid movement
1. Stable Isotope Constraints on the Ocean from Hydrothermally-altered Igneous Rocks
Science.gov (United States)
Gregory, R. T.
2007-12-01
The 18O/16O ratio of the ocean provides an important constraint on the global geochemical cycles in the Precambrian Earth. The oxygen isotope ratio of the ocean is most likely buffered near its present day value as long as plate tectonics is operative. A quasi-steady state value for oxygen isotopes is reached on a 100 Myr timescale after the onset of plate tectonics. Hydrothermally-altered igneous rocks constrain the oxygen and hydrogen isotope value of the hydrosphere back through time. Whereas, the oxygen isotope composition of seawater owes its value to the competition between low temperature chemical weathering and mid-ocean ridge hydrothermal exchange, there is no such process for hydrogen isotopes. Changes in the oxygen isotope ratio of seawater should be reflected in hydrothermally altered rocks by the presence of low or high 18O exchanged igneous rocks with normal δD values. The distribution of D and 18O in hydrothermally rocks is used to infer the position of the meteoric water line back through time. Results from the Phanerozoic, the Proterozoic, and the Archean fail to confirm the hypothesis that the global oceans were ever strongly 18O-depleted. The meteoric water line is anchored to the isotopic composition of seawater, the isotope standard for both oxygen and hydrogen isotopes. The ability to use sedimentary rocks or other proxies for climate depend upon the variation in the stable isotopic composition of seawater. Thus far, the hydrothermal record does not support the existence of low 18O oceans. This suggests that low 18O values observed in carbonates and cherts result from either precipitation from oceans with higher temperature or from bodies of water isolated from the open ocean.
2. Sepctral Reflectance of Recently Fallen Chondrites and Some Igneous Rocks in China
Institute of Scientific and Technical Information of China (English)
林文祝; 高来之
1991-01-01
Polarization and radiation measurements and microwave studies show that the planets and the great majority of asteroids in the solar system are covered by soils similar to regolith on the moon surface.The soils repesent the composition of the asteroids and the geological elements of the planets. The spectral reflectance shows a tendency of decreasing from near ultraviolet,visible to near-infrared in order of LL→L→H→H with increasing Fe0/Fet rato and toward to absorption for Jilin,Xinyang and Zanoyang ordinary chondrites and Qinzhen enstatite chondrite recently fallen in China,The same chemical group of meteorites feature deeper absorption valleys with increasing metamorphic grade.The spectal reflectance of igneous rocks varies from strong to what is like that of H-group chondrites in order of acid→basic→ultrabasic rocks.
3. Magnetic petrofabric of igneous rocks: Lessons from pyroclastic density current deposits and obsidians
Science.gov (United States)
Cañón-Tapia, E.; Mendoza-Borunda, R.
2014-12-01
Measurement of the anisotropy of magnetic susceptibility (AMS) of igneous rocks can provide clues concerning their mechanism of formation and in particular are very helpful as flow direction indicators. Unlike other igneous rocks, however, pyroclastic density current deposits (PDCDs) present a challenge in the interpretation of AMS measurements due to the complexity of their mechanism of emplacement. In this paper we review the most common assumptions made in the interpretation of the AMS of PDCD, taking advantage of key lessons obtained from obsidians. Despite the complexities on the mechanism of formation of PDCDs, it is shown that a key element for the fruitful interpretation of AMS is to give proper attention to the various components likely to be involved in controlling their general petrofabric. The anisotropies of ferromagnetic crystals (whether as free phases or embedded within clasts or shards), and those of paramagnetic minerals (mainly ferrosilicates) need to be taken into consideration when interpreting the AMS measurements of PDCDs. Variations of the deposition regime both as a function of position and of time also need to be considered on the interpretations. Nevertheless, if a suitable sampling strategy is adopted, the potential of the AMS method as a petrofabric indicator is maximized.
4. Distribution of chemical elements in calc-alkaline igneous rocks, soils, sediments and tailings deposits in northern central Chile
Science.gov (United States)
Oyarzún, Jorge; Oyarzun, Roberto; Lillo, Javier; Higueras, Pablo; Maturana, Hugo; Oyarzún, Ricardo
2016-08-01
This study follows the paths of 32 chemical elements in the arid to semi-arid realm of the western Andes, between 27° and 33° S, a region hosting important ore deposits and mining operations. The study encompasses igneous rocks, soils, river and stream sediments, and tailings deposits. The chemical elements have been grouped according to the Goldschmidt classification, and their concentrations in each compartment are confronted with their expected contents for different rock types based on geochemical affinities and the geologic and metallogenic setting. Also, the element behavior during rock weathering and fluvial transport is here interpreted in terms of the ionic potentials and solubility products. The results highlight the similarity between the chemical composition of the andesites and that of the average Continental Crust, except for the higher V and Mn contents of the former, and their depletion in Mg, Ni, and Cr. The geochemical behavior of the elements in the different compartments (rocks, soils, sediments and tailings) is highly consistent with the mobility expected from their ionic potentials, their sulfates and carbonates solubility products, and their affinities for Fe and Mn hydroxides. From an environmental perspective, the low solubility of Cu, Zn, and Pb due to climatic, chemical, and mineralogical factors reduces the pollution risks related to their high to extremely high contents in source materials (e.g., rocks, altered zones, tailings). Besides, the complex oxyanions of arsenic get bound by colloidal particles of Fe-hydroxides and oxyhydroxides (e.g., goethite), thus becoming incorporated to the fine sediment fraction in the stream sediments.
5. Book Review: Potassic igneous rocks and associated gold-copper mineralization, Fourth edition (D. Muller and D.I. Groves)
Science.gov (United States)
Kelley, Karen D.
2016-01-01
The fourth edition of this comprehensive textbook, which succeeds those published in 1995, 1997, and 2000, very nicely summarizes the geochemical and petrological characteristics of potassic igneous rock complexes and the different tectonic settings in which they occur. The authors provide an overview and a classification of these rocks and they outline the geochemical differences between barren and mineralized potassic igneous complexes. Owing to the common association of potassic igneous rocks with many gold- and copper-rich ore deposits, this book will be of interest not only to research scientists but also to those exploring for major deposits in young and ancient terranes. In fact, there was a clear attempt by the authors to provide a good mix of theoretical discussions based on experimental work, with case studies that illustrate field and applied research.
6. Geochemical characteristics of Cenozoic high-K igneous rocks from Liuhe-Xiangduo area, eastern Tibet
Institute of Scientific and Technical Information of China (English)
WEI Qirong; WANG Jianghai
2005-01-01
The major elements, trace elements and Nd-Sr isotopic composition of Cenozoic high-K igneous rocks and mafic deep-derived enclaves from the Liuhe-Xiangduo area, eastern Tibet, indicate the high-K igneous rocks are characterized as being enriched in Ca (CaO= 1.20% - 8.80% ), alkali (Na2O+K2O= 3.47% - 10.65% ), especially K (K2O up to 5.96% ) and depleted in Ti (TiO2= 0.27% - 1.50% ). Their REE contents are very high (REE= 91.29 - 231.11 μg/g). Their REE distribution patterns are of the right-inclined type, characterized by intense LREE enrichment [(La/Yb)N= 7.44 - 15.73 ]. The rocks are distinctly enriched in Rb, Sr and Ba ( 46.3 -316 μg/g, 349-1220 μg/g and 386-2394 μg/g, respectively), high in U and Th ( 1.17 - 8.10 μg/g and 2.58 - 27.0 μg/g, respectively), moderate in Zr and Hf ( 87.5 -241 μg/g and 2.83 - 7.52 μg/g, respectively), and depleted in Nb and Ta ( 4.81 - 16.8 μg/g and 0.332 - 1.04 μg/g, respectively). In the primitive mantle-normalized incompatible element spidergram, U, K, Sr and Hf show positive anomalies, whereas Th, Nb, Ta, P, and Ti show negative anomalies. The rocks are strongly depleted in Cr and Ni ( 21.4 -1470 μg/g and 7.79 -562 μg/g, respectively), and their transition element distribution curves are obviously of type-W. The ( 87 Sr/ 86 Sr)i ratios range from 0.704184 to 0.707539 ; ( 143 Nd / 144 Nd)i from 0.512265 to 0.512564 ; and ε Nd (t) from -6.3 to -0.4 . These geochemical features might suggest that the potential source of the high-K igneous rocks in the Liuhe-Xiangduo area is similar to the EM2, which may be similar to the material enriched K that is located under the crust-mantle mixed layer. The mafic deep-derived enclaves in the high-K igneous rocks belong to chance xenoliths. Their ( 87 Sr/ 86 Sr)i ratios range from 0.706314 to 0.707198 ; ( 143 Nd / 144 Nd)i from 0.512947 to 0.513046 ; and ε Nd (t) from +7.0 to +9.0 . These geochemical features might indicate that the enclaves probably came from the depleted mantle
7. Multidimensional classification of magma types for altered igneous rocks and application to their tectonomagmatic discrimination and igneous provenance of siliciclastic sediments
Science.gov (United States)
Verma, Surendra P.; Rivera-Gómez, M. Abdelaly; Díaz-González, Lorena; Pandarinath, Kailasa; Amezcua-Valdez, Alejandra; Rosales-Rivera, Mauricio; Verma, Sanjeet K.; Quiroz-Ruiz, Alfredo; Armstrong-Altrin, John S.
2017-05-01
A new multidimensional scheme consistent with the International Union of Geological Sciences (IUGS) is proposed for the classification of igneous rocks in terms of four magma types: ultrabasic, basic, intermediate, and acid. Our procedure is based on an extensive database of major element composition of a total of 33,868 relatively fresh rock samples having a multinormal distribution (initial database with 37,215 samples). Multinormally distributed database in terms of log-ratios of samples was ascertained by a new computer program DOMuDaF, in which the discordancy test was applied at the 99.9% confidence level. Isometric log-ratio (ilr) transformation was used to provide overall percent correct classification of 88.7%, 75.8%, 88.0%, and 80.9% for ultrabasic, basic, intermediate, and acid rocks, respectively. Given the known mathematical and uncertainty propagation properties, this transformation could be adopted for routine applications. The incorrect classification was mainly for the ;neighbour; magma types, e.g., basic for ultrabasic and vice versa. Some of these misclassifications do not have any effect on multidimensional tectonic discrimination. For an efficient application of this multidimensional scheme, a new computer program MagClaMSys_ilr (MagClaMSys-Magma Classification Major-element based System) was written, which is available for on-line processing on http://tlaloc.ier.unam.mx/index.html. This classification scheme was tested from newly compiled data for relatively fresh Neogene igneous rocks and was found to be consistent with the conventional IUGS procedure. The new scheme was successfully applied to inter-laboratory data for three geochemical reference materials (basalts JB-1 and JB-1a, and andesite JA-3) from Japan and showed that the inferred magma types are consistent with the rock name (basic for basalts JB-1 and JB-1a and intermediate for andesite JA-3). The scheme was also successfully applied to five case studies of older Archaean to
8. Unusual shape of pyrrhotite inclusions in scapolite of igneous rocks from the southernern Urals
Science.gov (United States)
Korinevsky, V. G.; Korinevsky, E. V.
2016-12-01
The unique igneous rock (scapolite-diopside gabbro) from the Ilmeny Mountains in the southern Urals is described. Gabbro fills a segment of dike 1.3 m thick that cuts through calcite-dolomite carbonatite. Medium-grain pyroxenite with scapolite that occurs at selvages gradually passes to scapolite-bearing gabbro in the central part of the dike. Scapolite crystals display surfaces of concurrent growth, which are evidence of their magmatic origin. Scapolite (Me 63-70%) contains numerous pyrrhotite inclusions as platelets 0.001 mm thick oriented parallel to the cleavage plane {100}. The calculated pyrrhotite formula is consistent with its stoichiometry (Fe1-xS). The morphology of the platelets (hexagonal sections) and their optical properties indicate a hexagonal symmetry of pyrrhotite. As follows from the insignificant difference between scapolite grains with and without pyrrhotite inclusions, scapolite and pyrrhotite should be regarded as products of synchronous magmatic melt crystallization.
9. Prospecting for Diverse Igneous Rock Types on Mars: Pixl on "black Beauty" Nwa 7533
Science.gov (United States)
Liu, Y.; Flannery, D.; Allwood, A.; Thompson, D. R.; Hodyss, R. P.; Clark, B. C.; Elam, W. T.; Hurowitz, J.
2015-12-01
In order to understand the evolution of the Martian crust and mantle, we need to acquire and analyze samples of igneous rocks other than the basaltic and ultramafic lithologies represented by the majority of Martian meteorites. Recent results from the Curiosity Rover demonstrate that diverse rock types exist in some Martian sedimentary environments in the form of conglomerate components or float, some of which shed light on the nature of early Martian crust (e.g., Sautter et al., 2015). We are developing investigation strategies for the in-situ instruments that will be flown on the Mars 2020 rover. These instruments will be used to inform the sampling campaigns required for future sample return missions. To achieve this, we applied PIXL (Planetary Instrument for X-ray Lithochemistry), an instrument for the Mars 2020 rover mission, to the meteorite NWA 7533. This meteorite is a pairing of NWA 7034, known informally as "Black Beauty", a new type of Martian meteorite that is broadly similar to the average composition of the Martian crust. This type of meteorite is essentially a 'conglomerate', with many diverse rock types, including mafic, feldspathic, and exotic rock fragments such as feldspar-ilmenite-phosphate clasts, as observed using higher-spatial resolution and higher sensitivity laboratory instruments (e.g., Agee et al., 2013; Humayun et al., 2014; Santos et al., 2015). Using PIXL, we analyzed a mm-scale cut and polished surface and applied algorithms developed by the PIXL team to semi-autonomously define and group regions containing similar lithological components (Thompson et al., 2015). PIXL data rapidly reveal distinctive zircon-bearing lithologies and feldspar-ilmenite-phosphate clasts similar to the detailed petrographic and mineralogical observations. Results suggest that PIXL readily identifies lithologies with minerals and elements (e.g., Rb and Sr) that are important for geochronology studies.
10. Finding of Neoproterozoic low-18O igneous rocks in the northern margin of the Dabie orogen
Institute of Scientific and Technical Information of China (English)
ZHENG Yongfei; WU Yuanbao; ZHAO Zifu; GONG Bing
2004-01-01
@@ It has been one of the most intriguing questions in the earth sciences whether the snowball Earth event is genetically associated with mantle superwelling, supercontinent assemblage and breakup, and rift magmatism during the Neoproterozoic[1-4]. In order to demonstrate the occurrence of significant interaction in energy and matter between the earth's interior and exterior in this period, it is critical to find coeval igneous rocks that contain the signature of surface water and thus form low-18O magma.Several investigations of U-Pb dating and O isotope analysis were carried out for zircons from ultrahigh pressure (UHP) metamorphic rocks in the Dabie-Sulu orogen,east-central China[5-8]. The results indicate that low δ18O zircons have U-Pb ages of 700-800 Ma as dated by either TIMS discordia upper-intercept or SIMS in-situ magmatic core, and the origin of low δ18O water is related to cold paleoclimate during the Sturtian ice age.
11. Radioactive occurrences in veins and igneous and metamorphic rocks of New Mexico with annotated bibliography. [Over 600 citations
Energy Technology Data Exchange (ETDEWEB)
McLemore, V. T.
1982-01-01
From an extensive literature search and field examination of 96 nonsandstone radioactive occurrences, the author compiled an annotated bibliography of over 600 citations and a list of 327 radioactive occurrences in veins and igneous and metamorphic rocks of New Mexico. The citations are indexed by individual radioactive occurrence, geographic area, county, fluorspar deposits and occurrences, geochemical analyses, and geologic maps. In addition, the geology, mineralization, and uranium and thorium potential of 41 geographic areas in New Mexico containing known radioactive occurrences in veins and igneous and metamorphic rocks or that contain host rocks considered favorable for uranium or thorium mineralization are summarized. A list of aerial-radiometric, magnetic, hydrogeochemical, and stream-sediment survey reports is included.
12. Thermobarometric studies on the Levack Gneisses: Footwall rocks to the Sudbury Igneous Complex
Science.gov (United States)
James, R. S.; Peredery, W.; Sweeny, J. M.
1992-01-01
Granulite and amphibolite facies gneisses and migmatites of the Levack Gneiss Complex occupy a zone up to 8 km wide around the northern part of the Sudbury Igneous Complex (SIC). Orthopyroxene- and garnet-bearing tonalitic and semipelitic assemblages of granulite facies grade occur within 3 km of the SIC together with lenses of mafic and pyroxenitic rock compositions normally represented by an amphibole +/- cpx-rich assemblage; amphibolite facies assemblages dominate elsewhere in this terrain. These 2.711-Ga gneisses were introduced by (1) the Cartier Granite Batholith during late Archaean to early Proterozoic time and (2) the SIC, at 1.85 Ga, which produced a contact aureole 1-1.5 km wide in which pyroxene hornfelses are common within 200-300 m of the contact. A suite of 12 samples including both the opx-gt and amphibole-rich rock compositions have been studied. Garnets in the semipelitic gneisses are variably replaced by a plg-bio assemblage. Thermobarometric calculations using a variety of barometers and thermometers reported in the literature suggest that the granulite facies assemblages formed at depths in the 21-28 km range (6-8 kbar). Textures and mineral chemistry in the garnet-bearing semipelitic rocks indicate that this terrain underwent a second metamorphic event during uplift to depth in the 5-11 km range (2-3 kbar) and at temperatures as low as 500-550 C. This latter event is distinct from thermal recrystallization caused by the emplacement of the SIC; it probably represents metamorphism attributable to intrusion of the Cartier Granite Batholith. These data allow two interpretations for the crustal uplift of the Levack Gneisses: (1) The gneisses were tectonically uplifted prior to the Sudbury Event (due to intrusion of the Cartier Batholith); or (2) the gneisses were raised to epizonal levels as a result of meteorite impact at 1.85 Ga.
13. Integrative method in lithofacies characteristics and 3D velocity volume of the Permian igneous rocks in H area, Tarim Basin
Institute of Scientific and Technical Information of China (English)
Yang Haijun; Liu Yongfu; Xie Huiwen; Xu Yongzhong; Sun Qi; Wang Shuangshuang
2013-01-01
This paper introduces horizon control,seismic control,logging control and facies control methods through the application of the least squares fitting of logging curves,seismic inversion and facies-controlled techniques.Based on the microgeology and thin section analyses,the lithology,lithofacies and periods of the Permian igneous rocks are described in detail.The seismic inversion and facies-controlled techniques were used to find the distribution characteristics of the igneous rocks and the 3D velocity volume.The least squares fitting of the logging curves overcome the problem that the work area is short of density logging data.Through analysis of thin sections,the lithofacies can be classified into eruption airfall subfacies,eruption pyroclastic flow subfacies and eruption facies.
14. PHASS99: A software program for retrieving and decoding the radiometric ages of igneous rocks from the international database IGBADAT
Science.gov (United States)
Al-Mishwat, Ali T.
2016-05-01
PHASS99 is a FORTRAN program designed to retrieve and decode radiometric and other physical age information of igneous rocks contained in the international database IGBADAT (Igneous Base Data File). In the database, ages are stored in a proprietary format using mnemonic representations. The program can handle up to 99 ages in an igneous rock specimen and caters to forty radiometric age systems. The radiometric age alphanumeric strings assigned to each specimen description in the database consist of four components: the numeric age and its exponential modifier, a four-character mnemonic method identification, a two-character mnemonic name of analysed material, and the reference number in the rock group bibliography vector. For each specimen, the program searches for radiometric age strings, extracts them, parses them, decodes the different age components, and converts them to high-level English equivalents. IGBADAT and similarly-structured files are used for input. The output includes three files: a flat raw ASCII text file containing retrieved radiometric age information, a generic spreadsheet-compatible file for data import to spreadsheets, and an error file. PHASS99 builds on the old program TSTPHA (Test Physical Age) decoder program and expands greatly its capabilities. PHASS99 is simple, user friendly, fast, efficient, and does not require users to have knowledge of programing.
15. End-to-End Models for Effects of System Noise on LIMS Analysis of Igneous Rocks
Energy Technology Data Exchange (ETDEWEB)
Clegg, Samuel M [Los Alamos National Laboratory; Bender, Steven [Los Alamos National Laboratory; Wiens, R. C. [Los Alamos National Laboratory; Carmosino, Marco L [MT. HOLYOKE COLLEGE; Speicher, Elly A [MT. HOLYOKE COLLEGE; Dyar, M. D. [MT. HOLYOKE COLLEGE
2010-12-23
The ChemCam instrument on the Mars Science Laboratory will be the first extraterrestial deployment of laser-induced breakdown spectroscopy (UBS) for remote geochemical analysis. LIBS instruments are also being proposed for future NASA missions. In quantitative LIBS applications using multivariate analysis techniques, it is essential to understand the effects of key instrument parameters and their variability on the elemental predictions. Baseline experiments were run on a laboratory instrument in conditions reproducing ChemCam performance on Mars. These experiments employed Nd:YAG laser producing 17 mJ/pulse on target and an with a 200 {micro}m FWHM spot size on the surface of a sample. The emission is collected by a telescope, imaged on a fiber optic and then interfaced to a demultiplexer capable of >40% transmission into each spectrometer. We report here on an integrated end-to-end system performance model that simulates the effects of output signal degradation that might result from the input signal chain and the impact on multivariate model predictions. There are two approaches to modifying signal to noise (SNR): degrade the signal and/or increase the noise. Ishibashi used a much smaller data set to show that the addition of noise had significant impact while degradation of spectral resolution had much less impact on accuracy and precision. Here, we specifically focus on aspects of remote LIBS instrument performance as they relate to various types of signal degradation. To assess the sensitivity of LIBS analysis to signal-to-noise ratio (SNR) and spectral resolution, the signal in each spectrum from a suite of 50 laboratory spectra of igneous rocks was variably degraded by increasing the peak widths (simulating misalignment) and decreasing the spectral amplitude (simulating decreases in SNR).
16. Chemical weathering on Mars - Thermodynamic stabilities of primary minerals /and their alteration products/ from mafic igneous rocks
Science.gov (United States)
Gooding, J. L.
1978-01-01
Chemical weathering on Mars is examined theoretically from the standpoint of thermodynamic equilibrium between primary rock-forming minerals and the atmospheric gases O2, H2O, and CO2. The primary minerals considered are those common to mafic igneous rocks and include olivine, pyroxene, plagioclase, magnetite, troilite, pyrrhotite, and apatite. The importance of kinetics and reaction mechanisms in controlling possible weathering processes on Mars is discussed within the limits of currently available data, and the possible influence of liquid water on Martian weathering processes is evaluated where appropriate. For gas-solid weathering of mafic igneous rocks at the Martian surface, it is concluded that upon attainment of thermodynamic equilibrium: (1) oxides and carbonates should dominate the mineral assemblage of weathering products; (2) hematite rather than goethite should be the stable mineral form of Fe (III); (3) FeSO4 or FeSO4.H2O could be the stable weathering product of iron sulfides in the absence of liquid water; and (4) kaolinite is apparently the only clay mineral that should be thermodynamically stable over all ranges of temperature and water-vapor abundance at the Martian surface.
17. Helium and argon isotopes of the Tertiary basic igneous rocks from Shandong Peninsula and implications for the magma origin
Institute of Scientific and Technical Information of China (English)
2007-01-01
Helium (He) and Argon (Ar) isotopic compositions of the Tertiary basic igneous rocks were determined by the high temperature melting extraction method. The selected samples for the studies included al-kaline basalts and diabases from the Jiyang basin,and the surrounding Shanwang and Qixia outcrops in the Shandong Peninsula,eastern China. The results show that the Paleogene basalts and diabases from the Jiyang basin yielded a wide range of P4 PHe abundance of (73.70-804.16)×10 P-8 Pcm P3 P STP·g P-1 P,with P3 PHe/ P4 PHe ratios of 0.374-2.959 Ra,which was lower than the MORB but evidently higher than the con-tinental crust value. The Neogene alkaline basalts from the Jiyang basin,Shanwang and Qixia outcrops have variable P4 PHe abundances ((42.34-286.72)×10-8 Pcm P3 P STP·g-1 P),and "continental crust-like" P3 PHe/ P4 PHe ratios (0.013-0.074 Ra). All of them contain atmospheric-like P40 PAr/ P36 PAr ratio (395.4-1312.7),reflecting the mantle sources with air components. Their low P3 PHe/ P4 PHe ratios are interpreted as the enrichment of the radiogenic P4 PHe mainly inherited from the mantle. He and Ar systematics show the mixing of MORB-type,air and a P4 PHe enriched member in the mantle source,suggesting that these igneous rocks originated from the depleted asthenospheric mantle mixed with an EMI component. Therefore,the present He and Ar isotopes do not support the viewpoints that the Cenozoic igneous rocks of Eastern North China were the products of mantle plume(s) activities.
18. Helium and argon isotopes of the Tertiary basic igneous rocks from Shandong Peninsula and implications for the magma origin
Institute of Scientific and Technical Information of China (English)
TANG HuaYun; ZHENG JianPing; CHEN HongHan; YE XianRen
2007-01-01
Helium (He) and Argon (Ar) isotopic compositions of the Tertiary basic igneous rocks were determined by the high temperature melting extraction method. The selected samples for the studies included alkaline basalts and diabases from the Jiyang basin, and the surrounding Shanwang and Qixia outcrops in the Shandong Peninsula, eastern China. The results show that the Paleogene basalts and diabases from the Jiyang basin yielded a wide range of 4 He abundance of (73.70-804.16)×10-8 cm3 STP·Gp-1, with 3He/4He ratios of 0.374-2.959 Ra, which was lower than the MORB but evidently higher than the continental crust value. The Neogene alkaline basalts from the Jiyang basin, Shanwang and Qixia outcrops have variable 4He abundances ((42.34-286.72)×10-8 cm3 STP·g-1), and "continental crust-like" 3He/4He ratios (0.013-0.074 Ra). All of them contain atmospheric-like 40Ar/36Ar ratio (395.4-1312.7), reflecting the mantle sources with air components. Their low 3He/4He ratios are interpreted as the enrichment of the radiogenic 4He mainly inherited from the mantle. He and Ar systematics show the mixing of MORB-type, air and a 4He enriched member in the mantle source, suggesting that these igneous rocks originated from the depleted asthenospheric mantle mixed with an EMI component. Therefore, the present He and Ar isotopes do not support the viewpoints that the Cenozoic igneous rocks of Eastern North China were the products of mantle plume(s) activities.
19. Geology and porphyry copper-type alteration-mineralization of igneous rocks at the Christmas Mine, Gila County, Arizona
Science.gov (United States)
Koski, Randolph A.
1979-01-01
The Christmas copper deposit, located in southern Gila County, Arizona, is part of the major porphyry copper province of southwestern North America. Although Christmas is known for skarn deposits in Paleozoic carbonate rocks, ore-grade porphyry-type copper mineralization also occurs in a composite granodioritic intrusive complex and adjacent mafic volcanic country rocks. This study considers the nature, distribution, and genesis of alteration-mineralization in the igneous rock environment at Christmas. At the southeast end of the Dripping Spring Mountains, the Pennsylvanian Naco Limestone is unconformably overlain by the Cretaceous Williamson Canyon Volcanics, a westward-thinning sequence of basaltic volcanic breccia and lava flows, and subordinate clastic sedimentary rocks. Paleozoic and Mesozoic strata are intruded by Laramide-age dikes, sills, and small stocks of hornblende andesite porphyry and hornblende rhyodacite porphyry, and the mineralized Christmas intrusive complex. Rocks of the elongate Christmas stock, intruded along an east-northeast-trending fracture zone, are grouped into early, veined quartz diorite (Dark Phase), biotite granodiorite porphyry (Light Phase), and granodiorite; and late, unveined dacite porphyry and granodiorite porphyry. Biotite rhyodacite porphyry dikes extending east and west from the vicinity of the stock are probably coeval with biotite granodiorite porphyry. Accumulated normal displacement of approximately 1 km along the northwest-trending Christmas-Joker fault system has juxtaposed contrasting levels (lower, intrusive-carbonate rock environment and upper, intrusive-volcanic rock environment) within the porphyry copper system. K-Ar age determinations and whole-rock chemical analyses of the major intrusive rock types indicate that Laramide calc-alkaline magmatism and ore deposition at Christmas evolved over an extended period from within the Late Cretaceous (~75-80 m.y. ago) to early Paleocene (~63-61 m.y. ago). The sequence of
20. Geodynamic setting and geochemical signatures of Cambrian?Ordovician rift-related igneous rocks (Ossa-Morena Zone, SW Iberia)
Science.gov (United States)
Sánchez-García, T.; Bellido, F.; Quesada, C.
2003-04-01
An important rifting event, accompanied by massive igneous activity, is recorded in the Ossa-Morena Zone of the SW Iberian Massif (European Variscan Orogen). It likely culminated in the formation of a new oceanic basin (Rheic ocean?), remnants of which appear presently accreted at the southern margin of the Ossa-Morena Zone. Rifting propagated diachronously across the zone from the Early Cambrian to the Late Ordovician, but by Early Ordovician time, the existence of a significant tract of new ocean is evidenced by a breakup unconformity. Although early stages of rifting were not accompanied by mantle-derived igneous activity, a pronounced increase of the geothermal gradient is indicated by partial melting of metasedimentary protoliths in the upper and middle crust, and by coeval core-complex formation. Geochemistry of the main volume of igneous rocks, emplaced some million years later during more mature stages of rifting, suggests an origin in a variably enriched asthenospheric source, similar to that of many OIB, from which subsequent petrogenetic processes produced a wide range of compositions, from basalt to rhyolite. A tectonic model involving collision with, and subsequent overriding of, a MOR is proposed to account for the overall evolution, a present-day analogue for which lies in the overriding of the East Pacific Rise by North America and the rifting of Baja California.
1. Petrografic description of some igneous rocks from the Cordillera of South Mendoza, in the Argentine
NARCIS (Netherlands)
Kuenen, Ph.H.
1926-01-01
Comparatively little is yet known of the intricate igneous history of the Cordillera of South Mendoza. Almost all the knowledge we have is due to the field- and stratigraphical work of Dr. H. Gerth of Leiden (bibl. 1 and 2), and the petrographic studies of Dr. H. G. Backlund (bibl. 3 and 4) on the
2. The superior analyses of igneous rocks from Roth's Tabellen, 1869 to 1884, arranged according to the quantitative system of classification
Science.gov (United States)
Washington, H.S.
1904-01-01
In Professional Paper No. 14 there were collected the chemical analyses of igneous rocks published from 1884 to 1900, inclusive, arranged according to the quantitative system of classification recently proposed by Cross, Iddings, Pirsson, and Washington. In order to supplement this work it has appeared advisable to select the more reliable and complete of the earlier analyses collected by Justus Roth and arrange them also in the same manner for publication. Petrographers would thus have available for use according to the new system almost the entire body of chemical work of real value on igneous rocks, the exceptions being a few analyses published prior to 1900 which may have been overlooked by both Roth and myself. The two collections would form a foundation as broad as possible for future research and discussion. I must express my sense of obligation to the United States Geological Survey for publishing the present collection of analyses, and my thanks to my colleagues in the new system of classification for their friendly advice and assistance.
3. A detailed paleomagnetic investigation of Cretaceous igneous rocks: New contributions from Colombia and Paraguay
Science.gov (United States)
Kapper, Lisa; Calvo-Rathert, Manuel; Cejudo Ruiz, Ruben; Sanchez Bettucci, Leda; Irurzun, Alicia; Carrancho, Ángel; Gogichaishvili, Avto; Morales, Juan; Sinito, Ana; Mejia, Victoria; Nivia Guevara, Alvaro
2016-04-01
We present rock magnetic results, paleodirections and -intensities from Cretaceous samples from two locations from South America. On the one hand we report paleomagnetic results from the Western Cordillera of Colombia from 15 sites north of Cali. These volcanic rock samples were related to age determinations from close localities of 92.5 ± 1.1 Ma on average, occuring during the Cretaceous Normal Superchron (CNS). On the other hand we show results from an alkaline dike swarm in the Asunción Rift, Eastern Paraguay. Previous investigations suggest that these dikes extruded in a rather short period of 126-127 Ma, during normal and reversed polarity field configuration, right before the onset of the CNS. Rock magnetic measurements of both sites show that the main magnetic component is a low-coercivity mineral, e.g., (titanium)magnetite, with a large range of grain sizes from multi- to single domain, or mixtures of several grain sizes in a sample. For the Colombian site we obtained an average Virtual Geomagnetic Pole (VGP), whose latitude compares well with those for South and North America of Besse and Courtillot (2002) with a similar age. For the determination of the Virtual Dipole Moments (VDMs) the Thellier-Coe method did not give successful results, probably due to minerals in the range of multidomain grain size. Therefore, we applied the multispecimen protocol on ten specimens. Six successful determinations produced an average VDM of 2.3 x 10-22 Am2. This value is rather low, but in good agreement with other data from the same time period. Directional investigation of the Eastern Paraguayan dike swarm show highly clustered promising results with six out of 22 sites having an α95 ≤ 10.0° . Most of these sites show a reversed polarity; however, one intermediate polarity site has a very reliable direction as well. This and the occurrence of normal polarity sites suggest that the dikes may have not appeared at the same time but rather during the transition from
4. New zircon data supporting models of short-lived igneous activity at 1.89 Ga in the western Skellefte District, central Fennoscandian Shield
Directory of Open Access Journals (Sweden)
P. Skyttä
2011-04-01
Full Text Available New U-Th-Pb zircon data (SIMS from three intrusive phases of the Palaeoproterozoic Viterliden intrusion in the western Skellefte District, central Fennoscandian Shield, dates igneous emplacement in a narrow time interval at about 1.89 Ga. A locally occurring quartz-plagioclase porphyritic tonalite, here dated at 1889 ± 3 Ma, is, based on the new age data and field evidence, considered the youngest of the intrusive units. This supports an existing interpretation of its fault-controlled emplacement after intrusion of the dominating hornblende-tonalite units, in this study dated at 1892 ± 3 Ma. The Viterliden magmatism was synchronous with the oldest units of the Jörn type early-orogenic intrusions in the eastern part of the district (1.89–1.88 Ga; cf. Gonzàles Roldán, 2010. A U-Pb zircon age for a felsic metavolcanic rock from the hanging-wall to the Kristineberg VMS deposit, immediately south of the Viterliden intrusion, is in this study constrained in the 1.89–1.88 Ga time interval. It provides a minimum age for the Kristineberg ore deposit and suggests contemporaneous igneous/volcanic activity throughout the Skellefte District. Furthermore, it supports the view that the Skellefte Group defines a laterally continuous belt throughout this "ore district". Tentative correlation of the 1889 ± 3 Ma quartz-plagioclase porphyritic tonalite with the Kristineberg "mine porphyry", which cuts the altered ore-hosting metavolcanic rocks, further constrain the minimum age for ore deposition at 1889 ± 3 Ma. Based on the new age determinations, the Viterliden intrusion may equally well have intruded into, or locally acted as a basement for the ore-hosting Skellefte Group volcanic rocks.
5. Isotopic ages for alkaline igneous rocks, including a 26 Ma ignimbrite, from the Peshawar plain of northern Pakistan and their tectonic implications
Science.gov (United States)
2013-01-01
New isotopic ages on zircons from rocks of the Peshawar Plain Alkaline Igneous Province (PPAIP) reveal for the first time the occurrence of ignimbritic Cenozoic (Oligocene) volcanism in the Himalaya at 26.7 ± 0.8 Ma. Other new ages confirm that PPAIP rift-related igneous activity was Permian and lasted from ˜290 Ma to ˜250 Ma. Although PPAIP rocks are petrologically and geochemically typical of rifts and have been suggested to be linked to rifting on the Pangea continental margin at the initiation of the Neotethys Ocean, there are no documented rift-related structures mapped in Permian rocks of the Peshawar Plain. We suggest that Permian rift-related structures have been dismembered and/or reactivated during shortening associated with India-Asia collision. Shortening in the area between the Main Mantle Thrust (MMT) and the Main Boundary Thrust (MBT) may be indicative of the subsurface northern extension of the Salt Range evaporites. Late Cenozoic sedimentary rocks of the Peshawar Plain deposited during and after Himalayan thrusting occupy a piggy-back basin on top of the thrust belt. Those sedimentary rocks have buried surviving evidence of Permian rift-related structures. Igneous rocks of the PPAIP have been both metamorphosed and deformed during the Himalayan collision and Cenozoic igneous activity, apart from the newly recognized Gohati volcanism, has involved only the intrusion of small cross-cutting granitic bodies concentrated in areas such as Malakand that are close to the MMT. Measurements on Chingalai Gneiss zircons have confirmed the occurrence of 816 ± 70 Ma aged rocks in the Precambrian basement of the Peshawar Plain that are comparable in age to rocks in the Malani igneous province of the Rajasthan platform ˜1000 km to the south.
6. Thermal conductivity of major rock types in western and central Anatolia regions, Turkey
Science.gov (United States)
Balkan, Elif; Erkan, Kamil; Şalk, Müjgan
2017-08-01
Thermal conductivity is a key parameter in heat flow and geothermal investigations as it controls the temperature distribution within the Earth. Turkey has a significant geothermal potential yet rock thermal conductivity studies have been very limited. Here, we report new thermal conductivity values collected from 240 rock samples in western and central Anatolia regions. The data were initially classified according to lithologic descriptions; then mean thermal conductivities were determined after applying corrections from dry to saturated conditions, if necessary. The major rock types encountered in these regions are igneous metamorphic, and sedimentary rocks. Limestone is the most common lithological unit encountered both in western and central Anatolia regions. The limestones in western Anatolia show a higher mean thermal conductivity than the limestones in central Anatolia. Dolomitization has a significant effect on the thermal conductivity of limestones. Neritic limestones show a higher mean thermal conductivity compared to lacustrine limestones. The results of this study reveal large contrasts in thermal conductivity values among different rock types that can have major implications for future heat flow and geothermal modeling studies in these regions.
7. Ages, geochemistry and tectonic implications of the Cambrian igneous rocks in the northern Great Xing'an Range, NE China
Science.gov (United States)
Feng, Zhiqiang; Liu, Yongjiang; Li, Yanrong; Li, Weimin; Wen, Quanbo; Liu, Binqiang; Zhou, Jianping; Zhao, Yingli
2017-08-01
The Xinlin-Xiguitu suture zone, located in the Great Xing'an Range, NE China, in the eastern segment of the Central Asian Orogenic Belt (CAOB), represents the boundary between the Erguna and Xing'an micro-continental blocks. The exact location of the Xinlin-Xiguitu suture zone has been debated, especially, the location of the northern extension of the suture zone. In this study, based on a detailed field, geochemical, geochronological and Sr-Nd-Hf isotope study, we focus our work on the Cambrian igneous rocks in the Erguna-Xing'an block. The Xinglong granitoids, mainly include ∼520 Ma diorite, ∼470 Ma monzogranite and ∼480 Ma pyroxene diorite. The granitoids show medium to high-K calc-alkaline series characteristics with post-collision granite affinity. The circa 500 Ma granitoids have low εHf (t) values (-16.6 to +2.2) and ancient two-stage model (TDM2) ages between 1317 Ma and 2528 Ma. These results indicate the primary magmas of the Xinglong granitoids were probably derived from the partial melting of a dominantly Paleo-Mesoproterozoic ;old; crustal source with possible different degrees of addition of juvenile materials, and formed in a post-collision tectonic setting after the amalgamation of the Erguna and Xing'an blocks. Compared with the Xinglong granitoids, the Duobaoshan igneous rocks are consisted of the approximately coeval rhyolitic tuffs (491 ± 5 Ma) and ultramafic intrusions (497 ± 5 Ma) within the Duobaoshan Formation. They are generally enriched in large ion lithophile elements (LILEs) and depleted in high field strength elements (HFSEs; e.g., Nb, Ta, and Ti), consistent with the geochemistry of igneous rocks from island arcs or active continental margins. The ultramafic rocks have high positive εHf (t) values (+1.3 to +15) and εNd (t) (+1.86 to +2.28), and relatively young two-stage model (TDM2) ages and low initial 87Sr/86Sr ratios (0.70628-0.70853), indicating the partial melting of a depleted mantle source from a subducted slab in
8. The Kenna ureilite - An ultramafic rock with evidence for igneous, metamorphic, and shock origin
Science.gov (United States)
Berkley, J. L.; Brown, H. G.; Keil, K.; Carter, N. L.; Mercier, J.-C. C.; Huss, G.
1976-01-01
Ureilites are a rare group of achondrites. They are composed mainly of olivine and pigeonite in a matrix of carbonaceous material, including graphite, lonsdaleite, diamond, and metal. In most respects Kenna is a typical ureilite with the requisite mineralogical and chemical properties of the group. Differences of the Kenna ureilite from previously studied ureilites are related to a greater density, the occurrence of exceedingly minute quantities of feldspar, and a very strong elongation lineation of the silicate minerals. A description is presented of a study which indicates a complex history for Kenna, including igneous, mild metamorphic, and shock processes.
9. New zircon data supporting models of short-lived igneous activity at 1.89 Ga in the western Skellefte District, central Fennoscandian Shield
Directory of Open Access Journals (Sweden)
P. Skyttä
2011-10-01
Full Text Available New U-Th-Pb zircon data (SIMS from three intrusive phases of the Palaeoproterozoic Viterliden intrusion in the western Skellefte District, central Fennoscandian Shield, dates igneous emplacement in a narrow time interval at about 1.89 Ga. A locally occurring quartz-plagioclase porphyritic tonalite, here dated at 1889 ± 3 Ma, is considered the youngest of the intrusive units, based on the new age data and field evidence. This supports an existing interpretation of its fault-controlled emplacement after intrusion of the dominating hornblende-tonalite units, in this study dated at 1892 ± 3 Ma. The Viterliden magmatism was synchronous with the oldest units of the Jörn type early-orogenic intrusions in the eastern part of the district (1.89–1.88 Ga; cf. Gonzàles Roldán, 2010. A U-Pb zircon age for a felsic metavolcanic rock from the hanging-wall to the Kristineberg VMS deposit, immediately south of the Viterliden intrusion, is constrained at 1883 ± 6 Ma in this study. It provides a minimum age for the Kristineberg ore deposit and suggests contemporaneous igneous/volcanic activity throughout the Skellefte District. Furthermore, it supports the view that the Skellefte Group defines a laterally continuous belt throughout this "ore district". Tentative correlation of the 1889 ± 3 Ma quartz-plagioclase porphyritic tonalite with the Kristineberg "mine porphyry" suggests that these units are coeval at about 1.89 Ga. Based on the new age determinations, the Viterliden intrusion may equally well have intruded into or locally acted as a basement for the ore-hosting Skellefte Group volcanic rocks.
10. Field Observation of Joint Structures in Various Types of Igneous Rocks
Science.gov (United States)
Kano, Shingo; Tsuchiya, Noriyoshi
2006-05-01
In this study, field observations of natural fracture network systems in some intrusive and extrusive rocks were undertaken, to clarify the fracturing mechanism in the rocks. Shallow intrusives, whose depth of emplacement was less than several hundred metres, include the Momo-iwa Dacite dome on Rebun Island (Hokkaido), and Jodogahama Rhyolite in Iwate prefecture. Extrusive complexes studied include the Tojinbo Andesite and Ojima Rhyodacite in Fukui prefecture. Rocks of granitic' composition were collected from the Takidani (Japan Alps) and Hijiori (Yamagata prefecture) plutons. The joint structure in Hijiori Granite was evaluated by analysis of core samples extracted from the HDR-3 geothermal production well. Based on detailed field observation, joint structures related to thermal contraction of a rock mass could be classified according to their inferred depth of formation. Joints from a near surface setting, such as shallow intrusive rocks and extrusives, tend to form pentagonal — hexagonal columnar structures (for a variety of rock types), whilst granitic rocks (from a deeper setting) typically exhibit a parallelepiped structure. The apparent differences in joint form are inferred to be dependent on the confining pressure, which acts on joint generation and propagation. In cases of non-confining pressure, such as the near-surface (shallow intrusive/extrusive) setting, joint networks typically form a columnar structure. On the contrary, confining pressure is considerably greater for deeper rock masses, and these form a parallelepiped joint structure.
11. Igneous phenocrystic origin of K-feldspar megacrysts in granitic rocks from the Sierra Nevada batholith
Science.gov (United States)
Moore, J.G.; Sisson, T.W.
2008-01-01
Study of four K-feldspar megacrystic granitic plutons and related dikes in the Sierra Nevada composite batholith indicates that the megacrysts are phenocrysts that grew in contact with granitic melt. Growth to megacrystic sizes was due to repeated replenishment of the magma bodies by fresh granitic melt that maintained temperatures above the solidus for extended time periods and that provided components necessary for K-feldspar growth. These intrusions cooled 89-83 Ma, are the youngest in the range, and represent the culminating magmatic phase of the Sierra Nevada batholith. They are the granodiorite of Topaz Lake, the Cathedral Peak Granodiorite, the Mono Creek Granite, the Whitney Granodiorite, the Johnson Granite Porphyry, and the Golden Bear Dike. Megacrysts in these igneous bodies attain 4-10 cm in length. All have sawtooth oscillatory zoning marked by varying concentration of BaO ranging generally from 3.5 to 0.5 wt%. Some of the more pronounced zones begin with resorption and channeling of the underlying zone. Layers of mineral inclusions, principally plagioclase, but also biotite, quartz, hornblende, titanite, and accessory minerals, are parallel to the BaO-delineated zones, are sorted by size along the boundaries, and have their long axes preferentially aligned parallel to the boundaries. These features indicate that the K-feldspar megacrysts grew while surrounded by melt, allowing the inclusion minerals to periodically attach themselves to the faces of the growing crystals. The temperature of growth of titanite included within the K-feldspar megacrysts is estimated by use of a Zr-in-titanite geothermometer. Megacryst-hosted titanite grains all yield temperatures typical of felsic magmas, mainly 735-760 ??C. Titanite grains in the granodiorite hosts marginal to the megacrysts range to lower growth temperatures, in some instances into the subsolidus. The limited range and igneous values of growth temperatures for megacryst-hosted titanite grains support the
12. Extra-terrestrial igneous granites and related rocks: A review of their occurrence and petrogenesis
Science.gov (United States)
Bonin, Bernard
2012-11-01
The telluric planets and the asteroid belt display the same internal structure with a metallic inner core and a silicate outer shell. Experimental data and petrological evidence in silicate systems show that granite can be produced by extreme igneous differentiation through various types of igneous processes. On Moon, 4.4-3.9 Ga granite clasts display dry mineral assemblages. They correspond to at least 8 discrete intrusive events. Large K/Ca enrichment and low REE abundances in granite relative to KREEP are consistent with silicate liquid immiscibility, a process observed in melt inclusions within olivine of lunar basalts and in lunar meteorites. Steep-sided domes identified by remote sensing can represent intrusive or extrusive felsic formations. On Mars, black-and-white rhythmic layers observed on the Tharsis rise along the flanks of the peripheral scarps of the Tharsis Montes giant volcanoes suggest the possible eruption of felsic pyroclastites. Though no true granites were found so far in the Martian SNC meteorites, felsic glasses and mesostases were identified and a component close to terrestrial continental (granitic) crust is inferred from trace element and isotope systematics. Venus has suffered extensive volcanic resurfacing, whereas folded and faulted areas resemble terrestrial continents. Near large shield volcanoes, with dominant basaltic compositions, steep-sided domes have been interpreted as non-degassed silicic extrusions. The hypothesis of a granitic component is "tantalising". Extra-terrestrial granite is frequently found as clasts and mesostases in asteroidal meteorites. Porphyritic textures, with alkali feldspar crystals up to several centimetres in size, were observed in silicate enclaves within iron meteorites. In the chondrite clan, polymict breccias can contain granitic clasts, whose provenance is debated. One clast from the Adzhi-Bogdo meteorite yields a 4.53 ± 0.03 Ga Pb-Pb age, making it the oldest known granite in the solar system. The
13. Frequency-Based Precursory Acoustic Emission Failure Sequences In Sedimentary And Igneous Rocks Under Uniaxial Compression
Science.gov (United States)
Colin, C.; Anderson, R. C.; Chasek, M. D.; Peters, G. H.; Carey, E. M.
2016-12-01
Identifiable precursors to rock failure have been a long pursued and infrequently encountered phenomena in rock mechanics and acoustic emission studies. Since acoustic emissions in compressed rocks were found to follow the Gutenberg-Richter law, failure-prediction strategies based on temporal changes in b-value have been recurrent. In this study, we extend on the results of Ohnaka and Mogi [Journal of Geophysical Research, Vol. 87, No. B5, p. 3873-3884, (1982)], where the bulk frequency characteristics of rocks under incremental uniaxial compression were observed in relation to changes in b-value before and after failure. Based on the proposition that the number of low-frequency acoustic emissions is proportional to the number of high-amplitude acoustic emissions in compressed rocks, Ohnaka and Mogi (1982) demonstrated that b-value changes in granite and andesite cores under incremental uniaxial compression could be expressed in terms of the percent abundance of low-frequency events. In this study, we attempt to demonstrate that the results of Ohnaka and Mogi (1982) hold true for different rock types (basalt, sandstone, and limestone) and different sample geometries (rectangular prisms). In order to do so, the design of the compression tests was kept similar to that of Ohnaka and Mogi (1982). Two high frequency piezoelectric transducers of 1 MHz and a 500 kHz coupled to the sides of the samples detected higher and lower frequency acoustic emission signals. However, rather than gathering parametric data from an analog signal using a counter as per Ohnaka and Mogi (1982), we used an oscilloscope as an analog to digital converter interfacing with LabVIEW 2015 to record the complete waveforms. The digitally stored waveforms were then processed, detecting acoustic emission events using a statistical method, and filtered using a 2nd order Butterworth filter. In addition to calculating the percent abundance of low-frequency events over time, the peak frequency of the
14. Rock mass condition, behaviour and seismicity in mines of the Bushveld igneous complex.
CSIR Research Space (South Africa)
Haile, AT
1995-12-01
Full Text Available This project report gives an overall view of the rock mass environment of the Bushveld complex and influence on the mine design practices. The main focus of the project was to survey the currently available data and conduct further analysis in order...
15. Geochemistry of igneous rocks from the Cerro Prieto geothermal field, northern Baja California, Mexico
Science.gov (United States)
Herzig, C. T.
1990-08-01
Fractional crystallization of basaltic magma, derived from an oceanic affinity source region present beneath the Salton Trough and emplaced into a pull-apart basin of this continental rift regime, produced a tholeiitic suite of hypabyssal rocks consisting of basalt, andesite and dacite within the Cerro Prieto geothermal field, located in northern Baja California, Mexico. Higher light-rare-earth-element abundances for a basalt from the Cerro Prieto geothermal field in comparison to basalts from the Gulf of California and the East Pacific Rise suggest partial assimilation of crustal materials into the parental magmas generated beneath the Salton Trough. The crustal contaminant may be present near the surface today in the form of granitoids of the Peninsular Ranges batholith, at deeper levels as hydrothermally altered materials near the base of the Salton Trough, or may be a relict feature of Tertiary subduction contained within the upper mantle beneath the Salton Trough. The Sr isotopic compositions of dacites from the nearby Cerro Prieto volcano range from 0.7029 to 0.7036, indicating an oceanic affinity source for these rocks. The suite of hypabyssal rocks of tholeiitic affinity present within the Cerro Prieto geothermal field, related by fractional crystallization, link the dacite volcano of Cerro Prieto to gabbroic plutons inferred to exist beneath the Cerro Prieto geothermal field.
16. Igneous phosphate rock solubilization by biofilm-forming mycorrhizobacteria and hyphobacteria associated with Rhizoglomus irregulare DAOM 197198.
Science.gov (United States)
Taktek, Salma; St-Arnaud, Marc; Piché, Yves; Fortin, J André; Antoun, Hani
2017-01-01
Biofilm formation on abiotic and biotic surfaces was studied with two hyphobacteria, strongly attached to the surface of the arbuscular mycorrhizal fungus (AMF) Rhizoglomus irregulare (Ri) DAOM 197198 and two mycorrhizobacteria, loosely attached to the roots of different mycorrhizal plants. When the sparingly soluble igneous phosphate rock (PR) from Quebec, or when the chemical hydroxyapatite were used as sole phosphorus (P) source, hyphobacteria Rhizobium miluonense Rm3 and Burkholderia anthina Ba8 produced significantly more biofilms than mycorrhizobacteria Rahnella sp. Rs11 and Burkholderia phenazinium Bph12, as indicated by the crystal violet assay or by quantifying biofilm exopolysaccharides. As previously observed with planktonic bacteria, biofilms mobilized P by lowering the pH and releasing gluconic acid. The high efficiency of P mobilization by the hyphobacteria Ba8 was linked to the presence of more viable cells in its biofilm as revealed by the hydrolysis of fluorescein diacetate. Scanning electron microscopy micrographs showed a high adherence of the best P-solubilizer hyphobacteria Ba8 on the surface of Quebec PR. Hydroxyapatite porous structure did not allow a good adherence of Ba8. Ba8 formed an important biofilm on the hyphae of Ri DAOM 197198 with low reactive Quebec PR while no biofilm was observed with the high reactive hydroxyapatite. Results confirm the possible presence of specificity between the Ri DAOM 197198 and the hyphobacteria and suggest that the interaction would be regulated by the availability of P.
17. Geochemistry of oceanic igneous rocks - Ridges, islands, and arcs - With emphasis on manganese, scandium, and vanadium
Science.gov (United States)
Doe, B.R.
1997-01-01
A database on a number of elements in oceanic volcanic rocks is presented, including the principal major-element oxides - SiO2, TiO2, Al2O3, Fe2O3(T), MnO, MgO, CaO, Na2O, K2O, and P2O5 (where T refers to total iron) - and the trace elements - Ba, Ce, Cr, Cu, Ni, Sc, Sr, V, Pb (mainly by isotope dilution), Yb, Zn, and Zr. Interpretations are given for transition metals, with emphasis on Mn, Sc, and V, in order to determine the concentration of the elements in primitive melts and assess their trends in magmatic differentiation. Transition metals are not enriched in plagioclase, so all are incompatible with pure plagioclase removal - that is, they become enriched in the melt. Both Cr and Ni are known to be highly compatible with olivine separation - i.e., they are depleted in the melt early in differentiation. Also, Sc is compatible with clinopyroxene (Cpx) removal from the melt and is depleted by separation of Cpx. Copper does not fit well in any of the principal silicates, but Cu, like Ni, is greatly enriched in sulfides that may remain in the source or separate from the magma. Decreasing Ni abundances and increasing Cu contents during differentiation are a sign of olivine separation. In the analysis presented herein, V - in the absence of Cpx separation - is found to behave remarkably like the moderately incompatible element Zn, and these two elements add to the list of element pairs of similar incompatibility whose ratios are insensitive to differentiation and to submarine weathering as well. Both are enhanced in titanomagnetite, so both would he compatible during titanomagnetite separation. When Cpx separates, however, V becomes compatible like Sc, but Zn remains incompatible. Thus, decreasing V (and Sc) contents and increasing Zn contents during differentiation are a sign of Cpx separation. Manganese often behaves much like Zn and therefore is moderately incompatible, but Mn is less compatible than Zn and V in titanomagnetite. Thus, decreasing Zn and V with
18. Yanshanian Magma-Tectonic-Metallogenic Belt in East China of Circum-Pacific Domain (Ⅰ):Igneous Rocks and Orogenic Processes
Institute of Scientific and Technical Information of China (English)
1999-01-01
Yanshanian igneous rocks in the East China, on an orogenic belt scale, are characterized by the continental marginal arc in petrology and geochemistry as Andes and West USA, except for the Hercyn-type biotite-two mica-muscovite granite belt in the Nanling region. Three segments of the Yanshanian igneous rocks along the belt are recognized. In terms of magma-tectonic event sequence, the north, middle and south segments have counter-clockwise (ccw), clockwise (cw) and ccw+cw pTt paths of the orogenic process, respectively. A genetic model of the lithospheric delamination (loss of the lithospheric root in about 120 km) in combination with the oceanic subduction for the Yanshanian Andes-like orogenic belt and both the crust and lithosphere thickening for the Yanshanian Hercyn-type Nanling orogenic belt in the East China is suggested.
19. Epithermal neutron activation, radiometric, correlation and principal component analysis applied to the distribution of major and trace elements in some igneous and metamorphic rocks from Romania
Energy Technology Data Exchange (ETDEWEB)
Cristache, C.I. [National Institute of Research and Development for Physics and Nuclear Engineering Horia-Hulubei, P.O. Box MG-6, 077125 Magurele, Ilfov (Romania); Duliu, O.G. [University of Bucharest, Department of Atomic and Nuclear Physics, P.O. Box MG-11, 077125 Magurele, Ilfov (Romania)], E-mail: duliu@b.astral.ro; Culicov, O.A.; Frontasyeva, M.V. [Joint Institute of Nuclear Research, 6, Joliot Curie str. 141980, Dubna (Russian Federation); Ricman, C. [Geological Institute of Romania, 1 Caransebes Street, 012271 Bucharest (Romania); Toma, M. [National Institute of Research and Development for Physics and Nuclear Engineering Horia-Hulubei, P.O. Box MG-6, 077125 Magurele, Ilfov (Romania)
2009-05-15
Six major (Na, Al, K, Ca, Ti, Fe) and 28 trace (Sc, Cr, V, Mn, Co, Zn, Cu, As, Br, Sr, Rb, Zr, Mo, Sn, Sb, Ba, Cs, La, Ce, Nd, Eu, Sm, Tb, Hf, Ta, W, Th and U) elements were determined by epithermal neutron activation analysis (ENAA) in nine Meridional Carpathian and Macin Mountains samples of igneous and metamorphic rocks. Correlation and principal factor analysis were used to interpret data while natural radionuclides radiometry shows a good correlation with ENAA results.
20. Epithermal neutron activation, radiometric, correlation and principal component analysis applied to the distribution of major and trace elements in some igneous and metamorphic rocks from Romania.
Science.gov (United States)
Cristache, C I; Duliu, O G; Culicov, O A; Frontasyeva, M V; Ricman, C; Toma, M
2009-05-01
Six major (Na, Al, K, Ca, Ti, Fe) and 28 trace (Sc, Cr, V, Mn, Co, Zn, Cu, As, Br, Sr, Rb, Zr, Mo, Sn, Sb, Ba, Cs, La, Ce, Nd, Eu, Sm, Tb, Hf, Ta, W, Th and U) elements were determined by epithermal neutron activation analysis (ENAA) in nine Meridional Carpathian and Macin Mountains samples of igneous and metamorphic rocks. Correlation and principal factor analysis were used to interpret data while natural radionuclides radiometry shows a good correlation with ENAA results.
1. Role of igneous rocks in the development of the gas outburst-prone nature of the black coal seams in the Mecsek area
Energy Technology Data Exchange (ETDEWEB)
Nemedi Varga, Z.
1986-01-01
In addition to the rank and structural conditions of coal seams the role of volcanic dykes is primordial from the point of view of the development of gas outburst of coal seams. The Mesco-Cenozoic volcanism of the Mecsek Mountains (South Transdanubia) is reviewed including the areal distribution of volcanics. The rock types and their frequency of occurrence are described with special emphasis to the contact metamorphism produced by the interaction of igneous and sedimentary rocks. The possibilities of gas migration as a function of the tectonic conditions are outlined exemplified by the Komlo region most famous for its gas outburst events.
2. Occurrence of uranium in rocks of the intrusive complex at Ekiek Creek, western Alaska
Science.gov (United States)
Wallace, Alan R.
1979-01-01
Uranium in the Ekiek Creek Complex of western Alaska is related to a niobium-rich pyrochlore in the nepheline syenite of the complex. The complex consists of an aegirine-phlogopite pyroxenite that has been intruded and partly replaced by nepheline syenite. The contact zone between the two igneous units varies from a sharp contact to a diffuse zone where the pyroxenite has been metasomatically replaced by the syenite. The entire complex was intruded into an older Cretaceous monzonite. The pyrochlore occurs as an accessory mineral in the syenite, and is visible in rocks containing over 50 ppm uranium. Chemical analyses indicate that, in all samples of syenite, there is a positive correlation between uranium and niobium; this suggests that the uranium-pyrochlore association persists even when pyrochlore is not readily visible in thin section. The small amount of pyrochlore, and its refractory nature, make the complex an unfavorable source for secondary uranium leaching or heavy-mineral concentration.
3. Common neuromusculoskeletal injuries amongst rock climbers in the Western Cape
Directory of Open Access Journals (Sweden)
Liezel Wegner
2015-04-01
Full Text Available Background: Rock climbing is an extreme sport that is fast gaining interest in the Western Cape. Due to the physical nature of the sport, climbers often suffer neuromusculoskeletal (NMS injuries. Physiotherapists are first-line practitioners who diagnose and treat NMS injuries, but no previous study has been conducted regarding common NMS injuries amongst rock climbers in the Western Cape.Objective: To determine the common NMS injuries amongst rock climbers, and the relationships between independent variables and injury.Method: A Quantitative, cross-sectional, retrospective descriptive study design utilised a self-developed survey based on the literature. This was completed by rock climbers from an indoor climbing gym in Cape Town and two outdoor crags in the Western Cape. Out of the total population of 650 climbers, 247 were conveniently sampled to complete the self-administered survey, making the results generalisable to the climbing population.Results: Finger flexor tendon pulley injuries were the most commonly diagnosed NMS injury. Injury to the fingers, hand and elbow regions were the most common self-reported injury by area. The risk of suffering climbing-related injuries was significantly correlated to gender, setting, grade and type of climbing, but not to frequency of climbing.Conclusion: The results of this study could assist physiotherapists to assess and manage the common NMS injuries that occur in this group of extreme athletes, as well as to raise awareness amongst rock climbers in the Western Cape about potential risk of injury.
4. Thermal effects of the Santa Eulália Plutonic Complex (southern Portugal on the meta-igneous and metasedimentary host rocks
Directory of Open Access Journals (Sweden)
Cruz, C.
2014-12-01
Full Text Available The Santa Eulália Plutonic Complex (SEPC is a late-Variscan granitic body located in the northern part of the Ossa Morena Zone, a inner zone of the Variscan Iberian Massif. The SEPC host rocks are composed of meta-igneous and metasedimentary units, from Upper Proterozoic to Paleozoic ages, with a NW-SE structure, cross-cut by the SEPC. The SEPC host rocks, with low grade metamorphism show well preserved primary sedimentary or igneous mineralogical, textural and structural features. The thermal effect induced by the SEPC is restricted to the roof pendants. At N and NE of the SEPC, textures and paragenesis resulting from thermal metamorphism, are not related to the SEPC intrusion but to a previous magmatism, controlled by the NW-SE regional anisotropies. The restriction of the thermal effects to the pluton roof may be caused by a combination of several interrelated factors: higher volume of granitic mass, thermal effect by advection of fluids and longer period of prevalence of high thermal conditions. The geochemical study of SEPC host rocks shows the heterogeneous character and diversity of metasedimentary, igneous and meta-igneous rocks. The whole rock geochemical data indicate that all the metasedimentary lithologies derived from an upper continental crustal source and the igneous and meta-igneous rocks show no evidence of metasomatic effects by the SEPC emplacement.El Complejo Plutónico de Santa Eulalia (CPSE es un cuerpo granítico tardi-Varisco situado en la parte norte de la Zona de Ossa Morena, en la zona interior del Macizo Ibérico Varisco. Las rocas encajantes del CPSE están compuestas por unidades meta-ígneas y metasedimentarias, de edades que van desde el Proterozoico Superior hasta el Paleozoico, con una estructura de dirección NW-SE, cortada por el CPSE. Las rocas encanjantes del CPSE, con metamorfismo de bajo grado conservan estructuras, mineralogía y textura primarias. El efecto térmicoinducido por el CPSE se limita a los
5. Acid neutralizing capacity and leachate results for igneous rocks, with associated carbon contents of derived soils, Animas River AML site, Silverton, Colorado
Science.gov (United States)
Yager, Douglas B.; Stanton, Mark R.; Choate, LaDonna M.; Burchell,
2009-01-01
Mine planning efforts have historically overlooked the possible acid neutralizing capacity (ANC) that local igneous rocks can provide to help neutralize acidmine drainage. As a result, limestone has been traditionally hauled to mine sites for use in neutralizing acid drainage. Local igneous rocks, when used as part of mine life-cycle planning and acid mitigation strategy, may reduce the need to transport limestone to mine sites because these rocks can contain acid neutralizing minerals. Igneous hydrothermal events often introduce moderately altered mineral assemblages peripheral to more intensely altered rocks that host metal-bearing veins and ore bodies. These less altered rocks can contain ANC minerals (calcite-chlorite-epidote) and are referred to as a propylitic assemblage. In addition, the carbon contents of soils in areas of new mining or those areas undergoing restoration have been historically unknown. Soil organic carbon is an important constituent to characterize as a soil recovery benchmark that can be referred to during mine cycle planning and restoration. This study addresses the mineralogy, ANC, and leachate chemistry of propylitic volcanic rocks that host polymetallic mineralization in the Animas River watershed near the historical Silverton, Colorado, mining area. Acid titration tests on volcanic rocks containing calcite (2 – 20 wt %) and chlorite (6 – 25 wt %), have ANC ranging from 4 – 146 kg/ton CaCO3 equivalence. Results from a 6-month duration, kinetic reaction vessel test containing layered pyritic mine waste and underlying ANC volcanic rock (saturated with deionized water) indicate that acid generating mine waste (pH 2.4) has not overwhelmed the ANC of propylitic volcanic rocks (pH 5.8). Sequential leachate laboratory experiments evaluated the concentration of metals liberated during leaching. Leachate concentrations of Cu-Zn-As-Pb for ANC volcanic rock are one-to-three orders of magnitude lower when compared to leached solution from
6. Estimation of the Primary Magma Compositions of an Igneous Rock Series Petrogenetically Associated with Fractional Crystallization with Special Reference to Element Abundance Relationships
Institute of Scientific and Technical Information of China (English)
汪云亮; 张万林; 等
1994-01-01
A primary magma not only represents the starting point of a fractional crystallization process, but also is the product of an equilibrium or fractional partial melting process in a mantle.Element abundance relationships in the primary magma obey both law of power function for fractional crystallization and the law of fractional linear function for equilibrium partial melting .Based on this double nature of the primary magma, the authors advanced a principle to restore the primary magma composition from that of an igneous rock series with petrogenesis of fractional crystallization and put forward an approach of estimating the element abundance of the primary magma, exempli-fied by the rar-earth elements in the Andes volcanic rock series.
7. Palaeointensity and palaeomagnetic study of Cretaceous and Palaeocene rocks from Western Antarctica
Science.gov (United States)
Shcherbakova, V. V.; Bakhmutov, V. G.; Shcherbakov, V. P.; Zhidkov, G. V.; Shpyra, V. V.
2012-04-01
A combined palaeodirectional and palaeointensity study of a representative collection of plutonic rocks from the Antarctic Peninsula batholith from the western part of the Antarctic Peninsula, near the Ukrainian Antarctic base 'Academik Vernadsky' were carried out. Petrographically, the collection includes gabbros, diorites and quartz diorites, tonalities, granodiorites and granites. The ages of igneous complex emplacement vary from 50 to 117 Ma with most of the rocks belonging to the Cretaceous Normal Superchron. The characteristic remanent magnetizations were isolated by stepwise thermal demagnetization over the temperature interval 440-590°C and their intensities amount to 95 per cent of the NRM. The geographic positions of palaeopoles do not contradict the 'key poles' of the Antarctic Peninsula between 90 and 60 Ma. A significant part of the collection was subjected to Coe-modified Thellier palaeointensity experiments with the pTRM checks, which yielded seven reliable palaeointensity determinations for seven different locations. The obtained VDMs are relatively low for all sites, being on average about half of the present day VDM. The analysis of available palaeointensity data for the Cretaceous, Miocene and Middle Jurassic indicates the existence of strong correlations between the mean VDM and VDM scatter versus the rate of reversals. However, due to the shortage of data, the correlations are not significant at the 5 per cent significance level.
8. Petrogenesis of Cretaceous adakitic and shoshonitic igneous rocks in the Luzong area, Anhui Province (eastern China): Implications for geodynamics and Cu Au mineralization
Science.gov (United States)
Wang, Qiang; Wyman, Derek A.; Xu, Ji-Feng; Zhao, Zhen-Hua; Jian, Ping; Xiong, Xiao-Lin; Bao, Zhi-Wei; Li, Chao-Feng; Bai, Zheng-Hua
2006-07-01
Both adakitic and shoshonitic igneous rocks in the Luzong area, Anhui Province, eastern China are associated with Cretaceous Cu-Au mineralization. The Shaxi quartz diorite porphyrites exhibit adakite-like geochemical features, such as light rare earth element (LREE) enrichment, heavy REE (HREE) depletion, high Al 2O 3, MgO, Sr, Sr / Y and La / Yb values, and low Y and Yb contents. They have low ɛNd( t) values (- 3.46 to - 6.28) and high ( 87Sr / 86Sr) i ratios (0.7051-0.7057). Sensitive High-Resolution Ion Microprobe (SHRIMP) zircon analyses indicate a crystallization age of 136 ± 3 Ma for the adakitic rocks. Most volcanic rocks and the majority of monzonites and syenites in the Luzong area are K-rich (or shoshonitic) and were also produced during the Cretaceous (140-125 Ma). They are enriched in LREE and large-ion lithophile elements, and depleted in Ti, and Nb and Ba and exhibit relatively lower ɛNd( t) values ranging from - 4.65 to - 7.03 and relatively higher ( 87Sr / 86Sr) i ratios varying between 0.7057 and 0.7062. The shoshonitic and adakitic rocks in the Luzong area have similar Pb isotopic compositions ( 206Pb / 204Pb = 17.90-18.83, 207Pb / 204Pb = 15.45-15.62 and 208Pb / 204Pb = 38.07-38.80). Geological data from the Luzong area suggest that the Cretaceous igneous rocks are distributed along NE fault zones (e.g., Tanlu and Yangtze River fault zones) in eastern China and were likely formed in an extensional setting within the Yangtze Block. The Shaxi adakitic rocks were probably derived by the partial melting of delaminated lower crust at pressures equivalent to crustal thickness of > 50 km (i.e., ˜1.5 GPa), possibly leaving rutile-bearing eclogitic residue. The shoshonitic magmas, in contrast, originated mainly from an enriched mantle metasomatized by subducted oceanic sediments. They underwent early high-pressure (> 1.5 GPa) fractional crystallization at the boundary between thickened (> 50 km) lower crust and lithospheric mantle and late low
9. Assess the toxycity and hazard class moldboard rocks Western Donbass
Directory of Open Access Journals (Sweden)
Kroyik H.A. О. М. , Т. D.
2011-11-01
Full Text Available Researches of the contents of water-soluble forms of heavy metals in different types of dumping mine rocks of the Western Donbass are executed. According to existing state sanitary rules and norms two methods calculate indexes of toxicity for lead, cadmium, zinc, cobalt, nickel, copper. The estimation of an opportunity of application of existing norms and rules at definition of a class of danger of firm waste of the coal-mining industry. ,,
10. Assess the toxycity and hazard class moldboard rocks Western Donbass
OpenAIRE
Kroyik H.A. О. М. , Т. D.; Demura V.I.; Vinokurtseva O.M.; Azanova-Frolova T.D.
2011-01-01
Researches of the contents of water-soluble forms of heavy metals in different types of dumping mine rocks of the Western Donbass are executed. According to existing state sanitary rules and norms two methods calculate indexes of toxicity for lead, cadmium, zinc, cobalt, nickel, copper. The estimation of an opportunity of application of existing norms and rules at definition of a class of danger of firm waste of the coal-mining industry. ,,
11. New Geochemical Data on Postcollisional Ultrapotassic Rocks in Western Tibet
Science.gov (United States)
Zhao, Z.; Mo, X.; Depaolo, D.; Owens, T.; Liao, Z.; Zhu, D.
2003-12-01
We studied the postcollisional ultrapotassic volcanic rocks in Gongmutang (N30° 48', E84° 26'), Zabuye salt lake (N31° 26', E84° 20'), Dangreyong lake (N30° 57', E86° 24'), and Xuru lake (N30° 4', E86° 31') in western Lhasa block. These rocks erupted during the time between 27 Ma and 12 Ma ago according to published dating work. They are strongly related to the north-south trending normal faults or valley in tectonic setting. These lavas (SiO2=45-62%, K2O=6.0-8.8%, K2O/Na2O=2.0-4.3%, MgO=2.5-10.9%, TiO2=0.8-1.6%) are very homogenous in trace element composition, with enriched LREE, Rb, Ba, Th, and U, and depleted Nb, Ta, and Ti. These samples, with ɛ Nd varies from -11 to -15 and 87Sr/86Sr from 0.718 to 0.736, show much different isotopic features to the postcollisional shoshonitic-dominated rocks in North Tibet (ɛ Nd varies from -5 to -9 and 87Sr/86Sr from 0.708 to 0.711). But they shift much close or even overlap the Himalayan basement and granitoid Nd-Sr field (ɛ Nd range from -12 to -25 and 87Sr/86Sr from 0.733 to 0.760). The geochemical characteristics of the rocks in our study are similar to the rocks from Shiquanhe (Turner et al., 1996, J. Petrol.), Xunba (Miller et al., 1999, J Petrol), and Pabbai Zong (Williams et al., 2001, Geology). If we take the widely-accepted origin hypotheses that the ultrapotassic lavas is firstly derived from small degree partial melting of subcontinental lithospheric mantle, we could conclude that an enriched mantle source should be responsible for the lavas in western Tibet. The Nd-Sr isotopic data suggest that at least two possibilities for the structure and composition of the lithosphere in western Tibet: (1) The Himalayan basement affinity of these lavas suggest that the Himalayan crustal materials in the northern margin of Indian plate maybe a reagent that enriched the upper mantle of the western Lhasa block. If this is the fact, the northern part of India would have subducted beneath Lhasa block that suggested by
12. Characterisation of sub-micron particle number concentrations and formation events in the western Bushveld Igneous Complex, South Africa
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A. Hirsikko
2012-05-01
Full Text Available South Africa holds significant mineral resources, with a substantial fraction of these reserves occurring and being processed in a large geological structure termed the Bushveld Igneous Complex (BIC. The area is also highly populated by informal, semi-formal and formal residential developments. However, knowledge of air quality and research related to the atmosphere is still very limited in the area. In order to investigate the characteristics and processes affecting sub-micron particle number concentrations and formation events, air ion and aerosol particle size distributions and number concentrations, together with meteorological parameters, trace gases and particulate matter (PM were measured for over two years at Marikana in the heart of the western BIC. The observations showed that trace gas (i.e. SO2, NOx, CO and black carbon concentrations were relatively high, but in general within the limits of local air quality standards. The area was characterised by very high condensation sink due to background aerosol particles, PM10 and O3 concentration. The results indicated that high amounts of Aitken and accumulation mode particles originated from domestic burning for heating and cooking in the morning and evening, while during daytime SO2-based nucleation followed by the growth by condensation of vapours from industrial, residential and natural sources was the most probable source for large number concentrations of nucleation and Aitken mode particles. Nucleation event day frequency was extremely high, i.e. 86% of the analysed days, which to the knowledge of the authors is the highest frequency ever reported. The air mass back trajectory and wind direction analyses showed that the secondary particle formation was influenced both by local and regional pollution and vapour sources. Therefore, our observation of the annual cycle and magnitude of the particle formation and growth rates during
13. Mineral texture based seismic properties of meta-sedimentary and meta-igneous rocks in the orogenic wedge of the Central Scandinavian Caledonides
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Almqvist, B. S. G.; Czaplinska, D.; Piazolo, S.
2015-12-01
Progress in seismic methods offers the possibility to visualize in ever greater detail the structure and composition of middle to lower continental crust. Ideally, the seismic parameters, including compressional (Vp) and shear (Vs) wave velocities, anisotropy and Vp/Vs-ratio, allow the inference of detailed and quantitative information on the deformation conditions, chemical composition, temperature and the amount and geometry of fluids and melts in the crust. However, such inferences regarding the crust should be calibrated with known mineral and rock physical properties. Seismic properties calculated from the crystallographic preferred orientation (CPO) and laboratory measurements on representative core material allow us to quantify the interpretations from seismic data. The challenge of such calibrations lies in the non-unique interpretation of seismic data. A large catalogue of physical rock properties is therefore useful, with as many constraining geophysical parameters as possible (including anisotropy and Vp/Vs ratio). We present new CPO data and modelled seismic properties for amphibolite and greenschist grade rocks representing the orogenic wedge in the Central Scandinavian Caledonides. Samples were collected from outcrops in the field and from a 2.5 km long drill core, which penetrated an amphibolite-grade allochthonous unit composed of meta-sedimentary and meta-igneous rocks, as well as mica and chlorite-rich mylonites. The textural data was acquired using large area electron backscatter diffraction (EBSD) maps, and the chemical composition of minerals obtained by energy dispersive x-ray (EDS). Based on the texture data, we compare and evaluate some of the existing methods to calculate texture-based seismic properties of rocks. The suite of samples consists of weakly anisotropic rocks such as felsic gneiss and calc-silicates, and more anisotropic amphibolite, metagabbro, mica-schist. The newly acquired dataset provides a range of seismic properties that
14. Western Alborz Volcanic Rocks, a new Geochemical Viewpoint
Science.gov (United States)
Ghorbani, M.
2001-12-01
Volcanic and pyroclastic rocks of Eocene age comprise vast outcrops of Alborz Mountain Range, a fold-thrusted structural unit extending across northern Iran for 2000 km in a curvilinear pattern. In his account of structural evolution of Iranian plateau, Berberian (1983; p. 55) ascribed these rocks to a subduction-type magmatism. Based on a tectonostratigraphic study, these rocks are attributed to an arc-type magmatism (Alavi; 1996, p. 29). Recently a new data set of major and trace element (including REE) analyses of volcanic rocks from western Alborz, some 50 km west of city of Qazvin, has been made available (Asiabanha, 2001). Careful examination of the data (i.e., those of basic-intermediate rocks) in present study revealed, for the first time, some geochemical characteristics which have important implications on the geodynamic synthesis of this structural unit. The rocks contain 50-60 wt% SiO2. They lie in the midalkaline-to-subalkaline domain of TAS diagram (Middlemost, 1997; p.216) and fall in the calcalkaline field of AFM diagram. The volcanic rocks display two distinct chondrite-normalized REE patterns, one is MREE-depleted while the other is a rather smooth uniform M-HREE pattern. These are called MREE-depleted and smooth M-HREE series. Basic rocks from the latter contain higher silica than the former (>53 vs. >50 wt%), yet they show lower incompatible elements (e.g., K and Rb) and HFSE contents. These features can not be explained by differentiation and might be interpreted as implying the involvement of two source regions. Chondrite-normalized trace element patterns of the MREE-depleted series is more akin to the island arc calcalkaline (IACA) basic rocks than the basic rocks from any other tectonic settings. However, island arc products, known for being depleted in HFSE relative to other incompatible elements, differ from the MREE-depleted series which is rich in both HFSE and incompatible elements. One may advocate the role of OIB-type mantle
15. Fast Drilling Technique through Igneous Rocks in Well Hashan 3%哈山3井火成岩地层快速钻井技术
Institute of Scientific and Technical Information of China (English)
马凤清
2014-01-01
A drilling technique combining PDC bit and torsional impact tool has been developed and applied in drilling through the igneous rocks of Junggar Basin w hich solves the technical difficulties such as high hard-ness ,poor drillability and serious well deviation ,etc in drilling through igneous rock formation .In view of the li-thologic characteristics and technical difficulties of igneous rocks ,PK6245MJD PDC bit for φ311.1 mm diame-ter borehole with strong wear resistance was developed ,which combined with SLTIT type torsional impact tool suitable for PDC’ s rock shear breaking mechanism ,forming a composite drilling technique .The technique showed effective performance in drilling igneous rocks in Well Hashan 3 .In field application ,φ311.1 mm PK6245MJD PDC bit and SLTIT type torsional impact tool reached a continuous working time of 649 h with 457.50 m of drilling footage in one trip .The ROP was 1.0 m/h ,and its roundtrip ROP was 0.7 m/h .Com-pared with the drilling situation of adjacent upper igneous rocks ,at least 11 trip times and bit cost were saved . At the same time well deviation dropped from 4.2° at 2 882 m down to 1.2° at 3 310 m .So the composite drilling technique with φ311.1 mm PK6245MJD PDC bit and SLTIT type torsional impact tool is an effective way to realize optimal and fast drilling in igneous rock formations of Junggar Basin .%为解决准噶尔盆地火成岩地层岩石坚硬、可钻性差、井斜问题突出等技术难点，进行了火成岩地层“PDC钻头＋扭转冲击工具”复合钻井技术研究。针对火成岩地层岩性特点和钻井技术难点，通过研制具有较强耐磨性的φ311.1 mm PK6245M JD型PDC钻头，与适合PDC钻头机械剪切破岩机理的SL T IT型扭转冲击工具配合形成了“高效PDC钻头＋SLTIT型扭转冲击工具”复合钻井技术，并在哈山3井火成岩地层取得了较好的应用效果。现场应用发现，“φ311.1 mm PK6245MJD型PDC钻头＋SLTIT型扭转冲
16. Mafic microgranular enclaves (MMEs) in amphibole-bearing granites of the Bintang batholith, Main Range granite province: Evidence for a meta-igneous basement in Western Peninsular Malaysia
Science.gov (United States)
Quek, Long Xiang; Ghani, Azman A.; Chung, Sun-Lin; Li, Shan; Lai, Yu-Ming; Saidin, Mokhtar; Amir Hassan, Meor H.; Muhammad Ali, Muhammad Afiq; Badruldin, Muhammad Hafifi; Abu Bakar, Ahmad Farid
2017-08-01
Mafic microgranular enclaves (MMEs) with varying sizes are a common occurrence in porphyritic amphibole-bearing granite of the Bintang batholith, which is part of the Main Range granite province. The MMEs of the amphibole-bearing granite are significant as they are related to the I-type granitoids within the Main Range granite province. Petrographic observations indicate the MMEs are mantled with coarse mafic crystals on the rim and contain similar minerals to the host (biotite + plagioclase + K-feldspar + pyroxene + amphibole), but in different proportions. Geochemical analyses indicate the MMEs are shoshonitic with mg# comparable to the granite host. Substantial similarities exist between the MMEs and granite with regards to the normalized rare earth element patterns and trace elements variation diagrams. The MMEs and granite are not completely coeval as the MME zircon U-Pb age (224.3 ± 1.2 Ma) is slightly older than its granite host zircon U-Pb age (216.2 ± 1.0 Ma). The age difference is also observed from the unusual 500 m-long Tiak MME and another amphibole-bearing granite sample from the south of the pluton, which yield 221.8 ± 1.1 Ma and 217.4 ± 1.0 Ma respectively. The oldest inherited zircons found in the MME and granite are 2.0 Ga and 1.3 Ga respectively, while the oldest xenocrystic zircons found in the MME and granite are 2.5 Ga and 1.5 Ga respectively. Identical negative εHf(t) values from zircon U-Pb and Lu-Hf analysis for a MME-granite pair indicates the rocks were generated from a similar, ancient source in the basement. Combining the results, we suggest that incongruent melting of an ancient protolith played an important part in the evolution of the MMEs and granite and the MMEs characteristics are best explained as restite. The zircon Hf model age (two-stage) and the I-type peritectic and restitic mineral assemblages in the MMEs further describe the protolith as Early Proterozoic-Late Archean (≈2.5 Ga) meta-igneous rock. This shows the
17. Primary uranium sources for sedimentary-hosted uranium deposits in NE China: insight from basement igneous rocks of the Erlian Basin
Science.gov (United States)
Bonnetti, Christophe; Cuney, Michel; Bourlange, Sylvain; Deloule, Etienne; Poujol, Marc; Liu, Xiaodong; Peng, Yunbiao; Yang, Jianxing
2016-05-01
Carboniferous-Permian, Triassic and Jurassic igneous basement rocks around the Erlian Basin in northeast China have been investigated through detailed mineralogical, whole-rock geochemistry, geochronological data and Sm-Nd isotope studies. Carboniferous-Permian biotite granites and volcanic rocks belong to a calc-alkaline association and were emplaced during the Late Carboniferous-Early Permian (313 ± 1-286 ± 2 Ma). These rocks are characterised by positive ɛNd(t) (3.3-5.3) and fairly young T DM model ages (485-726 Ma), suggesting a dominant derivation from partial melting of earlier emplaced juvenile source rocks. Triassic biotite granites belong to a high-K calc-alkaline association and were emplaced during the Middle Triassic (243 ± 3-233 ± 2 Ma). Their negative ɛNd(t) (-2 to -0.1) and higher T DM model ages (703-893 Ma) suggest a contribution from Precambrian crust during the magma generation processes, leading to a strong enrichment in K and incompatible elements such as Th and U. Highly fractionated magmas crystallised in U-rich biotite (up to 21 ppm U) and two-mica granites. In biotite granite, the major U-bearing minerals are uranothorite and allanite. They are strongly metamict and the major part of their uranium (90 %) has been released from the mineral structure and was available for leaching. Mass balance calculations show that the Triassic biotite granites may have, at least, liberated ˜14,000 t U/km3 and thus correspond to a major primary uranium source for the U deposits hosted in the Erlian Basin.
18. Primary uranium sources for sedimentary-hosted uranium deposits in NE China: insight from basement igneous rocks of the Erlian Basin
Science.gov (United States)
Bonnetti, Christophe; Cuney, Michel; Bourlange, Sylvain; Deloule, Etienne; Poujol, Marc; Liu, Xiaodong; Peng, Yunbiao; Yang, Jianxing
2017-03-01
Carboniferous-Permian, Triassic and Jurassic igneous basement rocks around the Erlian Basin in northeast China have been investigated through detailed mineralogical, whole-rock geochemistry, geochronological data and Sm-Nd isotope studies. Carboniferous-Permian biotite granites and volcanic rocks belong to a calc-alkaline association and were emplaced during the Late Carboniferous-Early Permian (313 ± 1-286 ± 2 Ma). These rocks are characterised by positive ɛNd( t) (3.3-5.3) and fairly young T DM model ages (485-726 Ma), suggesting a dominant derivation from partial melting of earlier emplaced juvenile source rocks. Triassic biotite granites belong to a high-K calc-alkaline association and were emplaced during the Middle Triassic (243 ± 3-233 ± 2 Ma). Their negative ɛNd( t) (-2 to -0.1) and higher T DM model ages (703-893 Ma) suggest a contribution from Precambrian crust during the magma generation processes, leading to a strong enrichment in K and incompatible elements such as Th and U. Highly fractionated magmas crystallised in U-rich biotite (up to 21 ppm U) and two-mica granites. In biotite granite, the major U-bearing minerals are uranothorite and allanite. They are strongly metamict and the major part of their uranium (90 %) has been released from the mineral structure and was available for leaching. Mass balance calculations show that the Triassic biotite granites may have, at least, liberated ˜14,000 t U/km3 and thus correspond to a major primary uranium source for the U deposits hosted in the Erlian Basin.
19. Multifractal magnetic susceptibility distribution models of hydrothermally altered rocks in the Needle Creek Igneous Center of the Absaroka Mountains, Wyoming
Science.gov (United States)
Gettings, M.E.
2005-01-01
Magnetic susceptibility was measured for 700 samples of drill core from thirteen drill holes in the porphyry copper-molybdenum deposit of the Stinkingwater mining district in the Absaroka Mountains, Wyoming. The magnetic susceptibility measurements, chemical analyses, and alteration class provided a database for study of magnetic susceptibility in these altered rocks. The distribution of the magnetic susceptibilities for all samples is multi-modal, with overlapping peaked distributions for samples in the propylitic and phyllic alteration class, a tail of higher susceptibilities for potassic alteration, and an approximately uniform distribution over a narrow range at the highest susceptibilities for unaltered rocks. Samples from all alteration and mineralization classes show susceptibilities across a wide range of values. Samples with secondary (supergene) alteration due to oxidation or enrichment show lower susceptibilities than primary (hypogene) alteration rock. Observed magnetic susceptibility variations and the monolithological character of the host rock suggest that the variations are due to varying degrees of alteration of blocks of rock between fractures that conducted hydrothermal fluids. Alteration of rock from the fractures inward progressively reduces the bulk magnetic susceptibility of the rock. The model introduced in this paper consists of a simulation of the fracture pattern and a simulation of the alteration of the rock between fractures. A multifractal model generated from multiplicative cascades with unequal ratios produces distributions statistically similar to the observed distributions. The reduction in susceptibility in the altered rocks was modelled as a diffusion process operating on the fracture distribution support. The average magnetic susceptibility was then computed for each block. For the purpose of comparing the model results with observation, the simulated magnetic susceptibilities were then averaged over the same interval as the
20. Multifractal magnetic susceptibility distribution models of hydrothermally altered rocks in the Needle Creek Igneous Center of the Absaroka Mountains, Wyoming
Directory of Open Access Journals (Sweden)
M. E. Gettings
2005-01-01
Full Text Available Magnetic susceptibility was measured for 700 samples of drill core from thirteen drill holes in the porphyry copper-molybdenum deposit of the Stinkingwater mining district in the Absaroka Mountains, Wyoming. The magnetic susceptibility measurements, chemical analyses, and alteration class provided a database for study of magnetic susceptibility in these altered rocks. The distribution of the magnetic susceptibilities for all samples is multi-modal, with overlapping peaked distributions for samples in the propylitic and phyllic alteration class, a tail of higher susceptibilities for potassic alteration, and an approximately uniform distribution over a narrow range at the highest susceptibilities for unaltered rocks. Samples from all alteration and mineralization classes show susceptibilities across a wide range of values. Samples with secondary (supergene alteration due to oxidation or enrichment show lower susceptibilities than primary (hypogene alteration rock. Observed magnetic susceptibility variations and the monolithological character of the host rock suggest that the variations are due to varying degrees of alteration of blocks of rock between fractures that conducted hydrothermal fluids. Alteration of rock from the fractures inward progressively reduces the bulk magnetic susceptibility of the rock. The model introduced in this paper consists of a simulation of the fracture pattern and a simulation of the alteration of the rock between fractures. A multifractal model generated from multiplicative cascades with unequal ratios produces distributions statistically similar to the observed distributions. The reduction in susceptibility in the altered rocks was modelled as a diffusion process operating on the fracture distribution support. The average magnetic susceptibility was then computed for each block. For the purpose of comparing the model results with observation, the simulated magnetic susceptibilities were then averaged over the same
1. Geochemical diversity in first rocks examined by the Curiosity Rover in Gale Crater: Evidence for and significance of an alkali and volatile-rich igneous source
Science.gov (United States)
Schmidt, M. E.; Campbell, J. L.; Gellert, R.; Perrett, G. M.; Treiman, A. H.; Blaney, D. L.; Olilla, A.; Calef, F. J.; Edgar, L.; Elliott, B. E.; Grotzinger, J.; Hurowitz, J.; King, P. L.; Minitti, M. E.; Sautter, V.; Stack, K.; Berger, J. A.; Bridges, J. C.; Ehlmann, B. L.; Forni, O.; Leshin, L. A.; Lewis, K. W.; McLennan, S. M.; Ming, D. W.; Newsom, H.; Pradler, I.; Squyres, S. W.; Stolper, E. M.; Thompson, L.; VanBommel, S.; Wiens, R. C.
2014-01-01
first four rocks examined by the Mars Science Laboratory Alpha Particle X-ray Spectrometer indicate that Curiosity landed in a lithologically diverse region of Mars. These rocks, collectively dubbed the Bradbury assemblage, were studied along an eastward traverse (sols 46-102). Compositions range from Na- and Al-rich mugearite Jake_Matijevic to Fe-, Mg-, and Zn-rich alkali-rich basalt/hawaiite Bathurst_Inlet and span nearly the entire range in FeO* and MnO of the data sets from previous Martian missions and Martian meteorites. The Bradbury assemblage is also enriched in K and moderately volatile metals (Zn and Ge). These elements do not correlate with Cl or S, suggesting that they are associated with the rocks themselves and not with salt-rich coatings. Three out of the four Bradbury rocks plot along a line in elemental variation diagrams, suggesting mixing between Al-rich and Fe-rich components. ChemCam analyses give insight to their degree of chemical heterogeneity and grain size. Variations in trace elements detected by ChemCam suggest chemical weathering (Li) and concentration in mineral phases (e.g., Rb and Sr in feldspars). We interpret the Bradbury assemblage to be broadly volcanic and/or volcaniclastic, derived either from near the Gale crater rim and transported by the Peace Vallis fan network, or from a local volcanic source within Gale Crater. High Fe and Fe/Mn in Et_Then likely reflect secondary precipitation of Fe3+ oxides as a cement or rind. The K-rich signature of the Bradbury assemblage, if igneous in origin, may have formed by small degrees of partial melting of metasomatized mantle.
2. Geology and genesis of the Toongi rare metal (Zr, Hf, Nb, Ta, Y and REE) deposit, NSW, Australia, and implications for rare metal mineralization in peralkaline igneous rocks
Science.gov (United States)
Spandler, Carl; Morris, Caitlin
2016-12-01
The Toongi Deposit, located in central NSW, Australia, hosts significant resources of Zr, Hf, Nb, Ta, Y and REE within a small (ca. 0.3 km2), rapidly cooled trachyte laccolith. Toongi is part of regional Late Triassic to Jurassic alkaline magmatic field, but is distinguished from the other igneous bodies by its peralkaline composition and economically significant rare metal content that is homogenously distributed throughout the trachyte body. The primary ore minerals are evenly dispersed throughout the rock and include lueshite/natroniobite and complex Na-Fe-Zr-Nb-Y-REE silicate minerals dominated by a eudialyte group mineral (EGM). The EGM occurs in a unique textural setting in the rock, commonly forming spheroidal or irregular-shaped globules, herein called "snowballs", within the rock matrix. The snowballs are often protruded by aegirine and feldspar phenocrysts and contain swarms of fine aegirine and feldspar grains that often form spiral or swirling patterns within the snowball. Secondary ore minerals include REE carbonates, Y milarite, catapleiite and gaidonnayite that fill fractures and vesicles in the rock. Based on bulk-rock geochemical and Nd isotope data, and thermodynamic modelling of magma fractionation, the alkaline rocks of the region are interpreted to represent extrusive to hyperbyssal products of mantle-derived magma that ponded at mid-crustal levels (ca. 0.3 GPa) and underwent extensive fractionation under low-oxygen fugacity conditions. The high Na2O, peralkaline nature of the Toongi Deposit trachyte developed via extensive fractionation of an alkali olivine basalt parental magma initially in the mid-crust and subsequently at shallow levels (ca. 0.1 GPa). This extended fractionation under low fO2 and relatively low H2O-activity conditions limited volatile release and allowed build-up of rare metal contents to ore grades. We speculate that the ore minerals may have originally formed from rare metal-rich sodic-silicate melt that formed immiscible
3. Stable (C, O, S isotopes and whole-rock geochemistry of carbonatites from Alto Paranaíba Igneous Province, SE Brazil
Directory of Open Access Journals (Sweden)
Caroline Siqueira Gomide
Full Text Available ABSTRACT: The present work investigates the relationship between whole-rock geochemistry and stable isotope composition from carbonatites belonging to the Tapira, Araxá, Salitre, Serra Negra, Catalão I, and Catalão II alkaline-carbonatite complexes of the Alto Paranaiba Igneous Province (APIP, central Brazil and from the Jacupiranga Complex, of the Ponta Grossa Province, southeast Brazil. The APIP complexes are ultrapotassic, comprising bebedourites, phoscorites, nelsonites, and carbonatites, whereas Jacupiranga is a sodic complex composed of ijolite-series rocks, syenites, carbonatites, and alkaline gabbros. The geochemistry data allied to mineralogical constraints allowed us to classify the carbonatites into five groups, and to devise a chemical index (BaO/(BaO+SrO to gauge the magmatic evolution of the studied carbonatites.The APIP carbonatites evolve from apatite-rich calciocarbonatites toward Ba-, Sr-, and rare earth element (REE-rich magnesiocarbonatites. This evolution is mostly driven by apatite, phlogopite, dolomite, and calcite fractionation and consequent enrichment in monazite, norsethite, and strontianite. Stable isotope data show a wide diversity of petrogenetic processes in play at the APIP, relatively to the Jacupiranga Complex, which is interpreted as a result of the shallower intrusion levels of the APIP complexes. Such shallower emplacement, at low lithostatic pressure, allowed for a complex interplay of fractional crystallization, liquid immiscibility, degassing, and interaction with hydrothermal and carbohydrothermal systems.
4. Nature and Significance of Igneous Rocks Cored in the State 2-14 Research Borehole: Salton Sea Scientific Drilling Project, California
Science.gov (United States)
Herzig, Charles T.; Elders, Wilfred A.
1988-11-01
The State 2-14 research borehole of the Salton Sea Scientific Drilling Project penetrated 3.22 km of Pleistocene to Recent sedimentary rocks in the Salton Sea geothermal system, located in the Salton Trough of southern California and northern Baja California, Mexico. In addition, three intervals of igneous rocks were recovered; a silicic tuff and two sills of altered diabase. The chemical composition of the silicic tuff at 1704 m depth suggests that it is correlative with the Durmid Hill tuff, cropping out 25 km NW of the geothermal system. In turn, both of these tuffs may be deposits of the Bishop Tuff, erupted from the Long Valley caldera of central California at 0.7 Ma. The diabases are similar to basaltic xenoliths found in the nearby Salton Buttes rhyolite domes. These diabase are interpreted as hypabyssal intrusions resulting from magmatism due to rifting of the Salton Trough as part of the East Pacific Rise/Gulf of California transtensional system. The sills apparently intruded an already developed geo-thermal system and were in turn altered by it.
5. Geology of crystalline rocks of northern Fiordland: details of the granulite facies Western Fiordland Orthogneiss and associated rock units
Science.gov (United States)
1990-01-01
A c. 700 km2 area of northern Fiordland (South Island, New Zealand) is described in which Early Cretaceous high-pressure metamorphic rocks and virtually unmetamorphosed plutonic rocks occur. The dominant rocks are orthogneisses developed from synmetamorphic basic-intermediate intrusive complexes, the youngest and most widespread of which is the Early Cretaceous Western Fiordland Orthogneiss (WFO). The latter has undergone granulite facies metamorphism and occurs throughout much of western Fiordland. WFO was emplaced synkinematically in a subduction-related magmatic arc. A collisional event during or immediately following magma emplacement resulted in crustal thickening equivalent to onloading of a 20 km thick section over rocks already buried at mid-crustal depths. This event was responsible for peak load pressures of c. 12-13 kbar. The steeply dipping Surprise Creek Fault juxtaposes high-pressure metamorphic rocks of western and central Fiordland against virtually unmetamorphosed gabbroic rocks of the Early Cretaceous Darran Complex. -from Author
6. Reactive transport modeling of ferroan dolomitization by seawater interaction with mafic igneous dikes and carbonate host rock at the Latemar platform, Italy
Science.gov (United States)
Blomme, Katreine; Fowler, Sarah Jane; Bachaud, Pierre
2017-04-01
The Middle Triassic Latemar carbonate platform, northern Italy, has featured prominently in the longstanding debate regarding dolomite petrogenesis [1-4]. Recent studies agree that ferroan and non-ferroan dolomite replaced calcite in limestone during reactive fluid flow at altered mafic igneous dikes that densely intrude the platform. A critical observation is that ferroan dolomite abundances increase towards the dikes. We hypothesize that seawater interacted with mafic minerals in the dikes, leading to Fe enrichment in the fluid that subsequently participated in dolomitization. This requires that dolomite formation was preceded by dike alteration reactions that liberated Fe and did not consume Mg. Another requirement is that ferroan and non-ferroan dolomite (instead of other Fe- and Mg-bearing minerals) formed during fluid circulation within limestone host rock. We present reactive transport numerical simulations (Coores-Arxim, [5]) that predict equilibrium mineral assemblages and the evolution of fluid dolomitizing potential from dike crystallization, through dike alteration by seawater, to replacement dolomitization in carbonate host rock. The simulations are constrained by observations. A major advantage of the simulations is that stable mineral assemblages are identified based on a forward modeling approach. In addition, the dominant igneous minerals (plagioclase, clinopyroxene olivine and their alteration products) are solid solutions. Most reactive transport simulations of carbonate petrogenesis do not share these benefits (e.g. [6]). Predicted alteration mineral assemblages are consistent with observations on dikes and with ferroan and non-ferroan dolomite genesis. The simulation results also show that fluid dolomitizing potential (Mg/Ca and Fe/Mg) increases during dissolution of igneous solid solution minerals. Enrichment in fluid Fe concentration is sufficient to stabilize ferroan replacement dolomite. Consistent with field observations, ferroan dolomite
7. Alteration processes in igneous rocks of the michilla mining area, coastal range, northern chile, and their relation with copper mineralisation
Science.gov (United States)
Oliveros, V.; Aguirre, L.; Townley, B.
2003-04-01
A 10 km thick homoclinal sequence of intermediate volcanic and sedimentary Jurassic rocks crops out in the Michilla mining area, Coastal Range, northern Chile (22-22°45S, 70-70°15W). Cretaceous plutons, intermediate to acid in composition, intrude this sequence together with numerous small basic to acid dykes and stocks. Main deposits are stratabound Cu-(Ag) with the ore minerals emplaced at the porous tops of the volcanic flows. However, some discordant orebodies, e.g. hydrothermal breccias, exist within the manto-type deposits. The volcanic sequence, and a minor part of the plutonic rocks, have been affected by three different alteration processes, each of them with their distinct mineral assemblages reflecting that every process was developed under different physicochemical conditions. The volcanic rocks far from the mining area are affected by a regional scale alteration process, basically isochemical. Its products are typical of a low-grade event: chl + ep +qtz + ttn (+- ab +- cal) with no ore minerals associated. The temperature interval, estimated by the chlorite geothermometer, ranges between 250 and 350°C. This alteration is either due to very low grade burial metamorphism or to hydrothermalism related to the Late Jurassic - Cretaceous plutonism. Inside the mining district the volcanic rocks are affected by a local scale alteration process originated by the intrusion of small stocks and dykes. This event is characterized by strong sodic metasomatism and minor Mg mobility. Two stages probably occurred as suggested by the two main mineral assemblages present, a propylitic (ab + ep + chl + act + ttn + qtz) and a quartz-sericitic one (ab + ser + qtz + tnn). They would reflect the changes in temperature, water/rock ratio and pH conditions during the whole process. Ore minerals related to this alteration are chalcopyrite, chalcocite and minor bornite and native silver. A temperature interval of 200-300°C is indicated by the chlorite geothermometer for the
8. Petrogenesis of the Neoproterozoic bimodal volcanic rocks along the western margin of the Yangtze Block: New constraints from Hf isotopes and Fe/Mn ratios
Institute of Scientific and Technical Information of China (English)
LI Xianhua; QI Changshi; LIU Ying; LIANG Xirong; TU Xianglin; XIE Liewen; YANG Yueheng
2005-01-01
High-precision major element and Hf isotope data are reported for the Neoproterozoic Suxiong volcanic rocks along the western margin of the Yangtze Block. These volcanic rocks have variable εHf(T) values and Fe/Mn ratios. The relatively primitive basalts have high Fe/Mn ratios and high Hf-Nd isotopic compositions, indicating that they were generated by partial melting of garnet clinopyroxene in mantle plume at high pressure. Thus, the Suxiong basalts are genetically related to the proposed Neoproterozoic superplume. On the contrary, a few differentiated basalts have low Fe/Mn ratios and low Hf-Nd isotopic compositions. They are likely to experience assimilation-fractional crystallization process. The Suxiong rhyolites have consistent Hf and Nd model ages of 1.3-1.4 Ga. They are likely generated by shallow dehydration melting of pre-existing young arc igneous rocks associated with the basaltic underplating/intrusion in a continental rift.
9. The Late Cretaceous igneous rocks of Romania (Apuseni Mountains and Banat): the possible role of amphibole versus plagioclase deep fractionation in two different crustal terranes
Science.gov (United States)
Vander Auwera, Jacqueline; Berza, Tudor; Gesels, Julie; Dupont, Alain
2016-04-01
We provide new whole-rock major and trace elements as well as 87Sr/86Sr and 143Nd/144Nd isotopic data of a suite of samples collected in the Late Cretaceous volcanic and plutonic bodies of the Apuseni Mts. (Romania) that belong to the Banatitic Magmatic and Metallogenic Belt, also called the Apuseni-Banat-Timok-Srednogorie belt. The samples define a medium- to high-K calc-alkaline differentiation trend that can be predicted by a three-step fractional crystallization process which probably took place in upper crustal magma chambers. Published experimental data indicate that the parent magma (Mg# = 0.47) of the Apuseni Mts. trend could have been produced by the lower crustal differentiation of a primary (in equilibrium with a mantle source) magma. The Late Cretaceous magmatic rocks of the Apuseni Mts. and Banat display overlapping major and trace element trends except that Sr is slightly lower and Ga is higher in the Apuseni Mts. parent magma. This difference can be accounted for by fractionating plagioclase-bearing (Apuseni Mts.) or amphibole-bearing (Banat) cumulates during the lower crustal differentiation of the primary magma to the composition of the parent magma of both trends. This, together with results obtained on the Late Cretaceous igneous rocks from the Timok area in Eastern Serbia, further suggests variation of the water content of the primary magma along and across the belt. The Apuseni Mts. versus the Banat samples display different isotopic compositions that likely resulted from the assimilation of two distinct crustal contaminants, in agreement with their emplacement in two separate mega-units of Alpine Europe.
10. Single Variable and Multivariate Analysis of Remote Laser-Induced Breakdown Spectra for Prediction of Rb, Sr, Cr, Ba, and V in Igneous Rocks
Energy Technology Data Exchange (ETDEWEB)
Clegg, Samuel M [Los Alamos National Laboratory; Wiens, Roger C. [Los Alamos National Laboratory; Speicher, Elly A [MT HOLYOKE COLLEGE; Dyar, Melinda D [MT HOLYOKE COLLEGE; Carmosino, Marco L [MT HOLYOKE COLLEGE
2010-12-23
Laser-induced breakdown spectroscopy (LIBS) will be employed by the ChemCam instrument on the Mars Science Laboratory rover Curiosity to obtain UV, VIS, and VNIR atomic emission spectra of surface rocks and soils. LIBS quantitative analysis is complicated by chemical matrix effects related to abundances of neutral and ionized species in the resultant plasma, collisional interactions within plasma, laser-to-sample coupling efficiency, and self-absorption. Atmospheric composition and pressure also influence the intensity of LIBS plasma. These chemical matrix effects influence the ratio of intensity or area of a given emission line to the abundance of the element producing that line. To compensate for these complications, multivariate techniques, specifically partial least-squares regression (PLS), have been utilized to predict major element compositions (>1 wt.% oxide) of rocks, PLS methods regress one or multiple response variables (elemental concentrations) against multiple explanatory variables (intensity at each pixel of the spectrometers). Because PLS utilizes all available explanatory variable and eliminates multicollinearity, it generally performs better than univariate methods for prediction of major elements. However, peaks arising from emissions from trace elements may be masked by peaks of higher intensities from major elements. Thus in PLS regression, wherein a correlation coefficient is determined for each elemental concentration at each spectrometer pixel, trace elements may show high correlation with more intense lines resulting from optical emissions of other elements. This could result in error in predictions of trace element concentrations. Here, results of simple linear regression (SLR) and multivariate PLS-2 regression for determination of trace Rb, Sr, Cr, Ba, and V in igneous rock samples are compared. This study focuses on comparisons using only line intensities rather than peak areas to highlight differences between SLR and PLS.
11. Testing of the recently developed tectonomagmatic discrimination diagrams from hydrothermally altered igneous rocks of 7 geothermal fields
OpenAIRE
PANDARINATH, Kailasa
2014-01-01
Recently developed multidimensional tectonomagmatic discrimination diagrams based on log-ratio variables of chemical elements, discordant outlier-free databases, and probability-based boundaries have been shown to work better than the earlier diagrams. Hydrothermally altered drilled well rock cuttings obtained from different depths of geothermal fields were used to test these diagrams to compare the inferred tectonic setting with the expected one. In spite of the hydrothermal alteration effec...
12. Testing the Mojave-Sonora megashear hypothesis: Evidence from Paleoproterozoic igneous rocks and deformed Mesozoic strata in Sonora, Mexico
Science.gov (United States)
Amato, J.M.; Lawton, T.F.; Mauel, D.J.; Leggett, W.J.; Gonzalez-Leon, C. M.; Farmer, G.L.; Wooden, J.L.
2009-01-01
U-Pb ages and Nd isotope values of Proterozoic rocks in Sonora, Mexico, indicate the presence of Caborca-type basement, predicted to lie only south of the Mojave-Sonora mega-shear, 40 km north of the postulated megashear. Granitoids have U-Pb zircon ages of 1763-1737 Ma and 1076 Ma, with ??Nd(t) values from +1.4 to -4.3, typical of the Caborca block. Lower Jurassic strata near the Proterozoic rocks contain large granitic clasts with U-Pb ages and ??Nd(t) values indistinguishable from those of Caborcan basement. Caborca-type basement was thus present at this location north of the megashear by 190 Ma, the depositional age of the Jurassic strata. The Proterozoic rocks are interpreted as parautochthonous, exhumed and juxtaposed against the Mesozoic section by a reverse fault that formed a footwall shortcut across a Jurassic normal fault. Geochronology, isotope geochemistry, and structural geology are therefore inconsistent with Late Jurassic megashear displacement and require either that no major transcurrent structure is present in Sonora or that strike-slip displacement occurred prior to Early Jurassic time. ?? 2009 The Geological Society of America.
13. Geochemistry of meta-igneous rocks from southern Ethiopia: a new insight into neoproterozoic tectonics of northeast Africa
Science.gov (United States)
Alene, Mulugeta; Barker, Andrew J.
1997-04-01
Utilising geochemical data, various discriminant diagrams have been employed to establish the magma type and original tectonic environment for some Neoproterozoic amphibolites, ultrabasic rocks and gabbros of the Moyale area, southern Ethiopia. The gneissic amphibolites are found to have mixed geochemical characteristics indicative of island arc and/or ocean ridge basalts with tholeiitic composition whereas the porphyritic amphibolites show alkalic features with no clear tectonic setting. The ultrabasic and gabbroic units of the Moyale area are described in terms of their relation with mantle melts and parental material. The majority of ultrabasics relate to a cumulate origin and the gabbroic rocks appear as more differentiated magma from the same source. The mainly dunite bodies in the eastern sub-area at Moyale probably represent refractory residues left after variable degree of partial melting of a periodotite mantle. It is concluded that the gneissic amphibolites were probably part of an accreting arc associated with closure of a pre-existing oceanic basin. The ultrabasic and gabbroic rocks (together with the porphyritic amphibolite) are considered to be remnants of oceanic crust.
14. Deciphering igneous and metamorphic events in high-grade rocks of the Wilmington complex, Delaware: Morphology, cathodoluminescence and backscattered electron zoning, and SHRIMP U-Pb geochronology of zircon and monazite
Science.gov (United States)
Aleinikoff, J.N.; Schenck, W.S.; Plank, M.O.; Srogi, L.A.; Fanning, C.M.; Kamo, S.L.; Bosbyshell, H.
2006-01-01
High-grade rocks of the Wilmington Complex, northern Delaware and adjacent Maryland and Pennsylvania, contain morphologically complex zircons that formed through both igneous and metamorphic processes during the development of an island-arc complex and suturing of the arc to Laurentia. The arc complex has been divided into several members, the protoliths of which include both intrusive and extrusive rocks. Metasedimentary rocks are interlayered with the complex and are believed to be the infrastructure upon which the arc was built. In the Wilmingto n Complex rocks, both igneous and metamorphic zircons occur as elongate and equant forms. Chemical zoning, shown by cathodoluminescence (CL), includes both concentric, oscillatory patterns, indicative of igneous origin, and patchwork and sector patterns, suggestive of metamorphic growth. Metamorphic monazites are chemically homogeneous, or show oscillatory or spotted chemical zoning in backscattered electron images. U-Pb geochronology by sensitive high resolution ion microprobe (SHRIMP) was used to date complexly zoned zircon and monazite. All but one member of the Wilmington Complex crystallized in the Ordovician between ca. 475 and 485 Ma; these rocks were intruded by a suite of gabbro-to-granite plutonic rocks at 434 ?? Ma. Detrital zircons in metavolcanic and metasedimentary units were derived predominantly from 0.9 to 1.4 Ga (Grenvillian) basement, presumably of Laurentian origin. Amphibolite to granulite facies metamorphism of the Wilmington Complex, recorded by ages of metamorphic zircon (428 ?? 4 and 432 ?? 6 Ma) and monazite (429 ?? 2 and 426 ?? 3 Ma), occurred contemporaneously with emplacement of the younger plutonic rocks. On the basis of varying CL zoning patterns and external morphologies, metamorphic zircons formed by different processes (presumably controlled by rock chemistry) at slightly different times and temperatures during prograde metamorphism. In addition, at least three other thermal episodes are
15. Geochronology, geochemistry, and Sr-Nd-Hf isotopes of the early Paleozoic igneous rocks in the Duobaoshan area, NE China, and their geological significance
Science.gov (United States)
Wu, Guang; Chen, Yuchuan; Sun, Fengyue; Liu, Jun; Wang, Guorui; Xu, Bei
2015-01-01
The Duobaoshan area of northwestern Heilongjiang Province is the most important copper resource concentration region in NE China. To date, the Duobaoshan superlarge Cu-Mo deposit and the Tongshan large Cu-Mo deposit have been discovered in the Duobaoshan area. Both the deposits are hosted by granodiorites and volcanic rocks. Zircon LA-ICP-MS U-Pb dating indicates that these granodiorites emplaced approximately 479 Ma ago and that those volcanic rocks erupted between 447 and 450 Ma. The early Ordovicain granodiorites belong to the high-K to medium-K calc-alkaline series and are characterized by high Al2O3 and Sr contents, low Yb and Y contents, and relatively low Mg# values and Na2O/K2O ratios, with positive Eu or slight negative Eu anomalies (averaging 1.18). All of these geochemical characters are similar to those of the adakites generated by partial melting of a thickened lower crust in the world. Moreover, the granodiorites have low initial 87Sr/86Sr ratios (varying from 0.703474 to 0.704436), very high zircon εHf(t) and whole-rock εNd(t) values (varying from 13.0 to 16.8 and 5.27 to 5.46, respectively), and young zircon Hf and whole-rock Nd single-stage and two-stage model ages. Taking these geochemical characteristics and Sr-Nd-Hf isotope compositions together, we suggest that the early Ordovician granodiorites in the Duobaoshan area occurred in a post-collision environment and were formed by partial melting of a juvenile thickened lower crust dominated by depleted mantle-derived material. These late Ordovician volcanic rocks, which are composed of basalt, basaltic andesite, and andesite, belong to the tholeiitic or calc-alkaline series. They are generally enriched in large ion lithophile elements (LILEs) and depleted in high field strength elements (HFSEs; e.g., Nb, Ta, Zr, Hf, P, and Ti), consistent with the geochemistry of igneous rocks from island arcs or active continental margins. Compared with the early Ordovician granodiorites, these volcanic rocks
16. Platinum group elements geochemistry of ultramafic and associated rocks from Pindar in Madawara Igneous Complex, Bundelkhand massif, central India
V Balaram; S P Singh; M Satyanarayanan; K V Anjaiah
2013-02-01
Ultramafic rocks comprising dunite, harburgite, lehzolite, olivine webserite and websterite occur as intrusives in the form of small hillocks at around Pindar into the granite–gneisses of Bundelkhand Gneissic Complex (BnGC). The peridotites are dominated by olivine cumulates where chromite and precious metal-bearing sulphides crystallized along with pyroxenes, subsequent to crystallization of olivine into the interstitial spaces of cumulates during cooling. Ultramafic rocks of Pindar are characterized by high MgO (up to 46.0 wt%) and FeO (up to 5.8 wt%); low SiO2 (40.8 to 48.0 wt%), TiO2 (0.2 to 0.5 wt%), Al2O3 (∼3.2 wt% av.), CaO(∼ 2.7 wt% av.) and Cu (11 to 73 g/g). Cr and Ni values range from 2297 to 3150 g/g and 2434 to 2767 g/g, respectively. Distribution of Ir (up to 20 ng/g), Ru (27 to 90 ng/g), Rh (3 to 14 ng/g), Pt (18 to 72 ng/g), Pd (10 to 27 ng/g) and Au (22 to 57 ng/g) indicate platinum group element (PGE) and associated gold mineralization in these ultramafic rocks. A mineral phase representing sperrylite (PtAs2) was also identified within the sulphides in Scanning electron microscopy with energy dispersive spectrometer (SEM–EDS) studies. The primitive mantle-normalized siderophile elements pattern shows platinum group element PGE (PPGE) enrichment (Rh, Pt, Pd). Discrimination diagrams of Pd/Ir vs. Ni/Cu, Pd/Pt vs. Ni/Cu, Cu/Pd vs. Pd, and Cu vs. Pd for the peridotites of Pindar attribute to affinity towards komatiite magma, derived from high degree of partial melting of prolonged depleted mantle, and the sulphur saturation condition incurred during the crystallization of chromite which was favourable for PGE mineralization.
17. Low Ni olivine in silica-undersaturated ultrapotassic igneous rocks as evidence for carbonate metasomatism in the mantle
Science.gov (United States)
Ammannati, Edoardo; Jacob, Dorrit E.; Avanzinelli, Riccardo; Foley, Stephen F.; Conticelli, Sandro
2016-06-01
Subduction drags a large amount of CO2 into the Earth's interior, which is partly returned to the atmosphere by arc volcanism. Processes involved in the recycling of subducted carbon within the upper mantle are mainly related to mineralogical transformation. Subducted CO2 may dramatically affect the equilibria among peridotitic minerals (olivine vs. pyroxenes) changing their stability fields and hence their modal abundances. This process is accompanied by a subduction-induced change in the budget of some incompatible trace and major elements (e.g., K, Ca, HFSE), whereas it has a minimal effect on the mass balance of compatible elements (e.g., Ni). We report trace elements in olivine in subduction-related mafic alkaline ultrapotassic rocks from Italy, which are used as a proxy to define mantle wedge mineralogy and metasomatic processes. Minor element concentrations, and in particular the high Li and low Ti of all the olivines, confirm a major role for recycled sediment in the generation of Italian ultrapotassic magmas. The distinct contents of Ni, Mn, and Ca in olivine reflect the bimodal character of silica-rich and silica-poor ultrapotassic Italian rocks and constrain two distinct mineralogical reactions between metasomatic agents and peridotite. Olivine chemistry from silica-saturated rocks reflects the reaction of silicate melts with the ambient mantle, with consequent consumption of olivine in favour of orthopyroxene. In contrast, the low-Ni, high-Mn/Fe of olivine crystallised from silica-undersaturated leucitites require a mantle source enriched in olivine (and clinopyroxene) compared to orthopyroxene, as a result of the interaction between the ambient peridotitic mantle and CaCO3-rich metasomatic agents. The change from silica-oversaturated lamproites to silica-undersaturated leucitites and thus the difference in the olivine composition is due to a change in composition of the subducting sediment from pelitic to carbonate-rich. The results of this study
18. Sr-Nd-Pb isotopic compositions of the lower crust beneath northern Tarim: insights from igneous rocks in the Kuluketage area, NW China
Science.gov (United States)
Zhang, Yan; Wei, Xun; Xu, Yi-Gang; Long, Xiao-Ping; Shi, Xue-Fa; Zhao, Jian-Xin; Feng, Yue-Xing
2016-09-01
The composition of lower crust of the Tarim Craton in NW China is essential to understand the petrogenesis of the ~290-275 Ma Tarim basalts and associated intermediate-felsic rocks. However, it remains poorly constrained because extremely sparse granulite terrains or granulite xenoliths have been found in the Tarim Craton. New trace element and Sr-Nd-Pb isotopic data are reported for the Neoarchean and Neoproterozoic igneous rocks widely distributed in the northern margin of the Tarim Craton. The Neoarchean granitic gneisses show fractionated REE (rare earth element) patterns [(La/Yb) N = 12-58, YbN = 10.6-36] with pronounced negative Nb-Ta and Ti anomalies. These features, together with negative ɛNdi (-0.7 to -3.2) suggest that they were derived from melting of mafic lower crust. The Neoproterozoic biotite granodiorites are strongly depleted in HREE with (La/Yb) N up to 55. They are characterized by high Sr (671-789 ppm) but very low Y (7.10-8.06 ppm) and Yb contents (0.47-0.58 ppm), showing typical features of adakitic rocks. The samples with different SiO2 contents display identical 87Sr/86Sri (0.7101-0.7103), ɛNdi (-14.1 to -15.7) and Pb isotopes (208Pb/204Pbi = 36.94-37.07). These features together with arc-like trace element patterns suggest that they were derived from melting of thickened lower crust. In comparison, the Neoproterozoic hornblende-biotite granodiorites have similar trace element compositions except for weaker depletion in HREE and have lower 87Sr/86Sri (0.7078) and initial Pb isotopes, and higher ɛNdi (-12.3 to -12.7). This suggests that they were formed by melting of old lower continental crust at a shallower depth than the biotite granodiorites. These rocks were derived from the lower crust, thus providing valuable information on the nature of the lower crust beneath northern Tarim. Combined with published data, the 87Sr/86Sri, ɛNdi, 206Pb/204Pbi and ɛHfi of the northern Tarim lower crust ranges from 0.7055 to 0.7103, from -12 to -17
19. Interlaboratory comparison of magnesium isotopic compositions of 12 felsic to ultramafic igneous rock standards analyzed by MC-ICPMS
Science.gov (United States)
Teng, Fang-Zhen; Yin, Qing-Zhu; Ullmann, Clemens V.; Chakrabarti, Ramananda; Pogge von Strandmann, Philip A. E.; Yang, Wei; Li, Wang-Ye; Ke, Shan; Sedaghatpour, Fatemeh; Wimpenny, Joshua; Meixner, Anette; Romer, Rolf L.; Wiechert, Uwe; Jacobsen, Stein B.
2015-09-01
To evaluate the interlaboratory mass bias for high-precision stable Mg isotopic analysis of natural materials, a suite of silicate standards ranging in composition from felsic to ultramafic were analyzed in five laboratories by using three types of multicollector inductively coupled plasma mass spectrometer (MC-ICPMS). Magnesium isotopic compositions from all labs are in agreement for most rocks within quoted uncertainties but are significantly (up to 0.3‰ in 26Mg/24Mg, >4 times of uncertainties) different for some mafic samples. The interlaboratory mass bias does not correlate with matrix element/Mg ratios, and the mechanism for producing it is uncertain but very likely arises from column chemistry. Our results suggest that standards with different matrices are needed to calibrate the efficiency of column chemistry and caution should be taken when dealing with samples with complicated matrices. Well-calibrated standards with matrix elements matching samples should be used to reduce the interlaboratory mass bias.
20. Trace element geochemistry of zircons from mineralizing and non-mineralizing igneous rocks related to gold ores at Yanacocha, Peru
Science.gov (United States)
Koleszar, A. M.; Dilles, J. H.; Kent, A. J.; Wooden, J. L.
2012-12-01
Zircons record important details about the evolution of magmatic systems, are relatively insensitive to alteration, and have been used to investigate the geochemistry, temperature, and oxidation state of volcanic and plutonic system. We examine zircons that span 6-7 m.y. of calc-alkaline volcanic activity in the Yanacocha district of northern Peru, where dacitic intrusions are associated with high-sulfidation gold deposits. The 14.5-8.4 Ma Yanacocha Volcanics include cogenetic lavas and pyroclastic rocks and are underlain by the andesites and dacites of the Calipuy Group, the oldest Cenozoic rocks in the region. We present data for magmatic zircons from the Cerro Fraile dacitic pyroclastics (15.5-15.1 Ma) of the Calipuy Group, and multiple eruptive units within the younger Yanacocha Volcanics: the Atazaico Andesite (14.5-13.3 Ma), the Quilish Dacite (~14-12 Ma), the Azufre Andesite (12.1-11.6 Ma), the San Jose Ignimbrite (11.5-11.2 Ma), and the Coriwachay Dacite (11.1-8.4 Ma). Epithermal high sulfidation (alunite-bearing) gold deposits are associated with the dacite intrusions of the Coriwachay and Quilish Dacites. Zircons from the non-mineralizing rocks typically have lower Hf concentrations and record Ti-in-zircon temperatures that are ~100°C hotter than zircons from the mineralizing intrusions. Temperatures recorded by zircons from the mineralizing intrusions are remarkably similar to those of the underlying Cerro Fraile dacite pyroclastics, but the zircons discussed here generally record SHRIMP-RG 206Pb/238U ages within error of previously published Ar-Ar eruption ages (eliminating antecrystic or xenocrystic origins). These observations suggest that zircons in the mineralizing intrusions form after greater extents of crystallization (and thus record elevated Hf concentrations and lower temperatures) than do zircons in the non-mineralized deposits. Unlike zircons from mineralized units associated with the porphyry Cu(Mo) deposits in Yerington, Nevada, which
1. Crystal populations of igneous rocks and their implications in genetic mineralogy%火成岩的晶体群与成因矿物学展望
Institute of Scientific and Technical Information of China (English)
罗照华; 杨宗锋; 代耕; 程黎鹿; 周久龙
2013-01-01
in igneous rocks are crystallized from their host magma. According to the ways of adding crystals to the magmatic system, the crystals in igneous rocks can be divided into three populations:solid-, melt- and fluid-crystal populations. The solid-crystal population means that the crystals exist in solid state before they are added into the magmatic system, including residual crystal sub-population and xenocryst sub-population. The melt-crystal population consists of the crystals crystallized from a melt, including crystals from the magma chambers at different depths (chamber crystal sub-population), crystals from magma conduits (channel crystal sub-population), crystals that have crystallized from progenitors of the final magma and have been 'reincorporated' into the final magma (antecryst sub-population), and crystals that have been crystallized after magma emplacement (matrix crystal sub-population). The fluid-crystal population is used to define crystals separated out from fluids, including crystals from the super -critical fluid (super -critical crystal sub -population), from vapor (condensation crystal sub -population), and from hydrothermal liquid (hydrothermal crystal sub-population). Such a division opens a new window for the future of genetic mineralogy of igneous rocks. Accordingly, an important duty of genetic mineralogy is to clarify the typical characteristics of various crystal populations and their forming conditions. Theoretically, the residual crystal is in thermodynamic equilibrium with the primary magma; the xenocryst is generally in disequilibrium with the host magma; the melt-crystal is in equilibrium with the magma produced at a special stage in the evolution of the magma system; the fluid-crystal is commonly in disequilibrium with magma, but a part of crystals from the super-critical crystal sub-population can be in equilibrium with the host magma. Therefore, the fluid-crystal is occasionally coexisting with the melt-crystals. The preservation of
2. Petrology and chemistry of late Cretaceous volcanic rocks from the southernmost segment of the Western Cordillera of Colombia (South America)
Science.gov (United States)
1996-03-01
This paper presents new data on the petrology and chemistry of the igneous rocks composing the Mesozoic basement of southernmost Western Cordillera of Colombia along the Ricaurte-Altaquer section. The studied sequence includes variably metamorphosed submarine lavas, breccias, tuffs and dykes of basalt to andesite composition, and minor, shallow quartz microdiorite intrusives. A Campanian age is recorded by radiolarian faunas from chert strata capping the lavas. Two different tholeiitic suites and a younger calc-alkaline suite, represented by hornblende andesite, are distinguished. One tholeiitic suite, represented by plagioclase and pyroxene phyric lavas, evolves from basalt to basaltic andesite. It is characterized by the occurrence of diopsidic pyroxene as early crystallising phase, by depletion in high-field strength elements, particularly Nb and by relative enrichment in light REE and Th. The second tholeiitic suite, which includes aphyric or poorly phyric lavas of basalt to dacite composition, differs from the first group in having moderately low {FeO tot}/{MgO} ratio and lower P 2O 5 content for a given SiO 2, and higher {Ti}/{Zr}and{Y}/{Zr} ratios. The pyroxene chemistry of the two suites also differs. The primary geochemical characteristics of the two suites suggest a similarity with tholeiitic suites generated in island-arc environment. The hornblende andesite has mineralogical and chemical characteristics of calc-alkaline lavas erupted in an oceanic setting in an evolved island-arc. Petrologic and geochemical evidence suggests that the volcanic rocks from the Ricaurte-Altraquer section are similar to the island-arc tholeiite volcanics from the upper Macuchi Formation of northern Ecuador and can be correlated partly with this unit. Conversely, they are petrochemically dissimilar from the typical Diabase Group volcanic rocks, characterized by transitional MORB lavas, extensively present to the north in the Western Cordillera of Colombia.
3. Geochronology and Geochemistry of Igneous Rocks from the Laoshankou District, North Xinjiang: Implications for the Late Paleozoic Tectonic Evolution and Metallogenesis of East Junggar
Science.gov (United States)
Liang, Pei; Chen, Huayong; Hollings, Pete; Wu, Chao; Xiao, Bing; Bao, Zhiwei; Xu, Deru
2016-12-01
arc. The northern margin of East Junggar was related to the southward subduction of the Kuerti-Erqis Ocean (a branch of the Paleo-Asian Ocean) between the Altay and the Dulate arcs in this period, consistent with the presence of Nb-enriched basalts and boninites in the north of the Dulate arc and the island arc rather than back arc setting of the igneous rocks in the Laoshankou district. For metallogenesis in the northern margin of East Junggar, arc-related Fe-Cu-Au and porphyry Cu mineralization was dominated. There is large potential to find several Late Paleozoic arc-related Fe-Cu-Au mineralizations in North Xinjiang.
4. Net Acid Production, Acid Neutralizing Capacity, and Associated Mineralogical and Geochemical Characteristics of Animas River Watershed Igneous Rocks Near Silverton, Colorado
Science.gov (United States)
Yager, Douglas B.; Choate, LaDonna; Stanton, Mark R.
2008-01-01
Formation, west and northwest of the Silverton caldera, and (b) the Picayune Megabreccia Member of Sapinero Mesa Tuff along the western San Juan caldera margin. Sultan Mountain stock, composed of granitoid intrusive rocks, was shown to have low ANC and moderate NAP. Sequential leachate analyses on a suite of whole-rock samples from the current and a previous study indicate that host rock composition and mineralogy control leachate compositions. The most mafic volcanic samples had high leachate concentrations for Mg, Fe, and Ca, whereas silicic volcanic samples had lower ferromagnesiun compositions. Samples with high chlorite abundance also had high leachable Mg concentrations. Trace-element substitution, such as Sr for Ca in plagioclase, controls high Sr concentrations in those samples with high plagioclase abundance. High Ti abundance in leachate was observed in those samples with high magnetite concentrations. This is likely due to samples containing intergrown magnetite-ilmenite. Whole rocks having high trace-element concentrations have relatively high leachate trace-element abundances. Some lavas of the San Juan Formation and Burns Member of the Silverton Volcanics had elevated Zn-, Cd-, and Pb-leachate concentrations. Manganese was also elevated in one San Juan Formation sample. Other San Juan Formation and Burns Member lavas had low to moderate trace-element abundances. One sample of the pyroxene andesite member of the Silverton Volcanics had elevated concentrations for As and Mo. Most other pyroxene andesite member samples had low leachate trace-element abundances. Mine-waste-leachate analyses indicated that one mine-waste sample had elevated concentrations of Cu (1.5 orders of magnitude), Zn (1 order of magnitude), As (1 order of magnitude), Mo (1.5 to 2 orders of magnitude), Cd (1 to 2 orders of magnitude), and Pb (2 to 3 orders of magnitude) compared to whole rocks. These data indicate the importance of whole-rock geochemistry or leachate analys
5. Chemical composition of igneous rocks expressed by means of diagrams, with reference to rock classification on a quantitative chemico-mineralogical basis
Science.gov (United States)
Iddings, J.P.
1903-01-01
The value of graphical methods for expressing relative quantities has been well established in all kinds of statistical exposition and discussion. Their use in conveying definite conceptions of relative quantities of chemical and mineral components of rocks is becoming more and more frequent, and the value of the results in some cases can not be overestimated. This is especially true when a series or group of rocks is being considered. The intricate variations in the amounts of numerous mineral components, or of chemical components, baffle most attempts to comprehend their interrelationships by simple contemplation or by study of the numbers in which they may be expressed. Many facts and relations are overlooked which arc readily observed when diagrams are used to represent numerical figures. Moreover, visual memory is sufficiently developed in most persons to enable them to carry in mind simple geometrical forms, where it does not permit them to recollect manifold assemblages of oft-repeated numbers. Mental impressions of simple diagrams are, therefore, more definite and lasting and enable the student to store up a much greater amount of quantitative data than he could otherwise acquire.
6. Chemostratigraphy of Flood Basalts in the Garzê-Litang Region and Zongza Block:Implications for Western Extension of the Emeishan Large Igneous Province, SW China
Institute of Scientific and Technical Information of China (English)
XIAO Long; XU Yigang; XU Jifeng; HE Bin; Pirajno FRANCO
2004-01-01
The Late Permian Emeishan Large Igneous Province (ELIP) is commonly regarded as being located in the western part of the Yangtze craton, SW China, with an asymmetrical shape and a small area. This area, however, is just amaximum estimation because some parts of the ELIP were not recognized or dismembered and destroyed during thebasalts in petrography and geochemistry. Flood basalts in the Sanjiangkou area are composed of the lower part of the lowTi (LT) tholeiite and the upper part of the high-Ti (HT) tholeiite, which is the same as the flood basalts on the western craton, consist of HT tholeiite only. This is the same as the flood basalts within the Yangtze craton. Therefore we argue that these contemporary basalts all originated from the Emeishan mantle plume, and the ELIP could have a significant westward extension with an outcropped area of over 500,000 km2. This new scenario shows that the LT tholeiite occurs on the westem margin of the Yangtze craton, while the HT tholeiite overlying the LT basalts occupies the whole area of the ELIP.
7. Structural observations and U-Pb mineral ages from igneous rocks at the Archaean-Palaeoproterozoic boundary in the Salahmi Schist Belt, central Finland: constraints on tectonic evolution
Directory of Open Access Journals (Sweden)
Pietikäinen, K.
1999-06-01
Full Text Available The study area in Vieremä, central Finland, contains part of Archaean-Palaeoproterozoic boundary. In the east, the area comprises Archaean gneiss and the Salahmi Schist Belt. The rocks of the schist belt are turbiditic metagreywackes, with well-preserved depositional structures, occurring as Proterozoic wedge-shaped blocks, and staurolite schists, the latter representing higher-strained and metamorphosed equivalents of the metagreywackes. In the west of the area there is an Archaean gneiss block, containing strongly elongated structures, and deformed Svecofennian supracrustal rocks, which are cut by deformed granitoids. These are juxtaposed with the schist belt. The boundaries of these tectonometamorphic blocks are narrow, highly strained mylonites and thrust zones. The metamorphic grade of the supracrustal rocks increases from east to west, the increase being stepwise across the mylonitic block boundaries. The rocks are more deformed from east to west with younger structures overprinting. In the staurolite schists of the Salahmi Schist Belt, the most prominent structure is a lineation (L2 that overprints the bedding and axial plane foliation. In Sorronmäki quarry, at the western boundary of the schist belt, this Palaeoproterozoic lineation dominates all the structures in tonalite gneiss, which gives a U-Pb age of 2731±6 Ma. Southeast of the quarry, at the same boundary, the Salahmi schists have been overturned towards the northeast, suggesting that the Archaean gneiss at Sorronmäki has been thrust towards the northeast over these rocks. In the western part of the study area, the Leppikangas granodiorite that intrudes the Svecofennian supracrustal rocks gives a U-Pb age of 1891+6 Ma. In the granodiorite, a strong lineation formed by the intersection of two foliations, which maybe L2 is associated with thrusting towards the northeast. The monazite age of the Archaean Sorronmäki gneiss is 1817+3 Ma, and the titanite age of the Svecofennian
8. Carbonate- and silicate-rich globules in the kimberlitic rocks of northwestern Tarim large igneous province, NW China: Evidence for carbonated mantle source
Science.gov (United States)
Cheng, Zhiguo; Zhang, Zhaochong; Santosh, M.; Hou, Tong; Zhang, Dongyang
2014-12-01
We report carbonate- and silicate-rich globules and andradite from the Wajilitage kimberlitic rocks in the northwestern Tarim large igneous province, NW China. The carbonate-rich globules vary in size from 1 to 3 mm, and most have ellipsoidal or round shape, and are composed of nearly pure calcite. The silicate-rich globules are elliptical to round in shape and are typically larger than the carbonate-rich globules ranging from 2 to several centimeters in diameter. They are characterized by clear reaction rims and contain several silicate minerals such as garnet, diopside and phlogopite. The silicate-rich globules, reported here for the first time, are suggested to be related to the origin of andradite within the kimberlitic rocks. Our results show that calcite in the carbonate-rich globules has a high XCa (>0.97) and is characterized by extremely high concentrations of the total rare earth elements (up to 1500 ppm), enrichment in Sr (8521-10,645 ppm) and LREE, and remarkable depletion in Nd, Ta, Zr, Hf and Ti. The calcite in the silicate-rich globules is geochemically similar to those in the carbonate-rich globules except the lower trace element contents. Garnet is dominantly andradite (And59.56-92.32Grs5.67-36.03Pyr0.36-4.61Spe0-0.33) and is enriched in light rare earth elements (LREEs) and relatively depleted in Rb, Ba, Th, Pb, Sr, Zr and Hf. Phlogopite in the silicate-rich globules has a high Mg# ranging from 0.93 to 0.97. The composition of the diopside is Wo45.82-51.39En39.81-49.09Fs0.88-0.95 with a high Mg# ranging from 0.88 to 0.95. Diopside in the silicate-rich globules has low total rare earth element (REE) contents (14-31 ppm) and shows middle REE- (Eu to Gd), slight light REE- and heavy REE-enrichment with elevated Zr, Hf and Sr contents and a negative Nb anomaly in the normalized diagram. The matrix of the kimberlitic rocks are silica undersaturated (27.92-29.31 wt.% SiO2) with low Al2O3 (4.51-5.15 wt.%) and high CaO (17.29-17.77 wt.%) contents. The
9. Large gravitational rock slope deformation in Romsdalen Valley (Western Norway
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Aline Saintot
2012-09-01
Full Text Available Large gravitational rock slope deformation affects Precambrian gneisses at four localities of the Romsdalen valley of Western Norway. At each locality, detailed studies have allowed to determine the mechanism of deformation and to assess the degree of susceptibility for failure. 1 Svarttinden is a 4.3 Mm³ translational rockslide. Its single basal detachment developed along a foliation-parallel cataclastic fault. Although a rockslide occurred along the same detachment and the deposits reached the edge of the plateau, no displacement of the current instability is detected. 2 At Flatmark distinct 2-25 Mm³ blocks detached from the edge of the plateau by an opening along the steep foliation. The collapse of the blocks is explained by a complex mechanism of sliding and toppling. No displacement is actually detected on the instabilities. 3 At Børa blocks located at the edge of the plateau deformed by the same mechanism as at Flatmark. They have a maximum volume of 0.5 Mm3 and displacement rates of 0.2-2 cm/year. The deformation at Børa has affected a large part of the plateau and the entire deformed volume would be of 50-200 Mm³ but it is currently inactive. 4 A wedge failure at the edge of Mannen plateau is inferred to allow the 4-5 cm/year downward displacement of a 2-3.5 Mm³ instability. The high susceptibility of failure led to a permanent monitoring of the site since 2009.
10. GRAPHITIZATION OF METASEDIMENTARY ROCKS IN THE WESTERN KONYA
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Hüseyin KURT
2000-01-01
Full Text Available The Paleozoic-Mesozoic metasedimentary rocks in the study area are metacarbonate, metachert, metapelite, metasandstone and metaconglomerate. Graphite layers are 1cm to 2m thick, extend laterally for tens of meters and are intercalated with metasedimentary rocks. Generally, the graphite is black in color, with a well developed cleavage which is concordant with the cleavage of the host rocks. In addition, the crystal and flake graphites formed in metasedimentary rocks are mostly aligned parallel to the cleavage planes. These metamorphic rocks are subjected to shearing and granulation providing structural control for the development of graphite. It was probably this phenomenon that first led to emphasize the relationship between graphite and metasedimentary rocks. Graphite mineralization has been controlled by bedding, microfractures and granulations. Briefly, the metamorphism has converted carbonaceous matter into graphite .
11. IGNEOUS PETROLOGY
Institute of Scientific and Technical Information of China (English)
2011-01-01
<正>20110832 Cui Yurong(School of Earth and Space Sciences,University of Science and Technology of China,Hefei 230026,China);Xie Zhi SHRIMP U-Pb Dating of Zircons from the Late Mesozoic Basalts in Eastern Zhejiang Province and Its Geological Significance(Geological Journal of China Universities,ISSN1006-7493,CN32-1440/P,16(2),2010,p.198-212,5 illus.,1 table,39 refs.)Key words:basalts,U-Pb dating,Zhejiang Province The zircon U-Pb ages were dated by SHRIMP method for eight basaltic rocks occurred in the eastern area of Zhejiang Province,which were erupted during the Late Mesozoic and named as Lower and Upper rock series(LRS&URS). The data suggest that the zircons from both rock series are of magmatic origin and represent the formation times of the basalts of LRS and URS.Thus,it can be concluded that the formation time of the URS and LRS is
12. IGNEOUS PETROLOGY
Institute of Scientific and Technical Information of China (English)
2015-01-01
20150781 Bai Daoyuan(Hunan Institute of Geological Survey,Changsha 410016,China);Zhong Xiang Zircon SHRIMP U-Pb Dating and Geochemistry of Caledonian Miao’ershan Pluton in the Western Part of the Nanling Mountains and Their Tectonic Significance(Acta Petrologica et Mineralogica,ISSN1000-6524,CN11-1966/P,33(3),2014,p.407
13. IGNEOUS PETROLOGY
Institute of Scientific and Technical Information of China (English)
2016-01-01
20160156Bai Daoyuan(Hunan Institute of Geology Survey,Changsha 410016,China);Zhong Xiang The Zircon SHRIMP U-Pb Dating,Geochemical Characteristics and Tectonic Setting of Caledonian Yuechengling Pluton in the Western Segment of the Nanling Mountains(Geochimica,ISSN0379-1726,CN44-1398/P,44(1),2015,p.27-42,15illus.,5
14. Silicic Large Igneous Provinces
Institute of Scientific and Technical Information of China (English)
Scott Bryan
2007-01-01
@@ Large Igneous Provinces (LIPs) are the end-product of huge additions of magma to the continental crust both at the surface and at depth. Since the first categorisation of LIPs by Coffin & Eldholm (1994), it has been recognised that LIPs are more varied inform, age and character, and this includes the recognition of Silicic LIPs. Silicic LIPs are the largest accumulations of primary volcaniclastic rocks at the Earth's surface with areal extents >0.1 Mkm2 and extrusive and subvolcanic intrusive volumes >0.25 Mkm3. The Late Palaeozoic to Cenozoic Silicic LIP events are the best recognised and are similar in terms of their dimension, crustal setting, volcanic architecture and geochemistry.
15. Tertiary foraminiferal rock samples from the western Solomon Sea
Science.gov (United States)
Haig, David W.
1986-12-01
Rock fragments dredged from four R/VNatsushima stations contain Tertiary foraminifera. The oldest sample is an upper bathyal biomicrite of Early Eocene age (52 to 53.5 Ma) from the the Trobriand Platform. Upper Oligocene-Lower Miocene neritic limestones were located off the Trobriand Platform and on the inner wall of the New Britain Trench. Miocene bathyal sediments come from the Trobriand Platform; similar Pliocene rocks were recovered here as well as from the inner wall of the New Britain Trench and the central part of the Solomon Sea Basin. No reworked pre-Tertiary foraminifera are present in any sample.
16. A multi-isotope approach to understanding the evolution of Cenozoic magmatism in the northeastern Basin and Range: Results from igneous rocks in the Albion-Raft River-Grouse Creek metamorphic core complex
Science.gov (United States)
Konstantinou, A.; Strickland, A.; Miller, E. L.
2012-12-01
Deep crustal rocks exposed by extensional processes in metamorphic core complexes provide a unique opportunity to address the magmatic and isotopic evolution of the crust and assess the relative crust versus mantle contributions in Cenozoic igneous rocks exposed in the complexes. The Albion-Raft River-Grouse Creek metamorphic core complex exposes mid-crustal rocks that resided at depths of ~15-20 km before the onset of Cenozoic extension. Three major Cenozoic magmatic events are represented in the complex and have been studied using multiple isotopic systems (whole rock Sr and Nd coupled with the Oxygen isotopes in zircon). These three major events are: (1) 42-31 Ma intrusion of a composite plutonic complex of calc-alkaline composition that intrudes both upper crustal rocks (~5-10 km depth) and deeper rocks. (2) A 32-25 Ma plutonic complex, with evolved calc-alkaline composition that intruded in the middle crust (~12-15 km depth), and (3) A 10-8 Ma bimodal (basalt-rhyolite) suite of volcanic rocks that contain high-T anhydrous mineral assemblages erupted across the complex. The pre-extensional crust consisted of an upper crust composed primarily of Neoproterozoic through Triassic metasedimentary rocks (schist and quartzite at its base and limestone at its top). The middle crust consists of late Archean orthogneiss with evolved composition (metamorphosed peraluminous granite) with average 87Sr/86Sr40~0.800, ɛNd40~ -43.4 and δ18Ozirc ~5.7‰. The lower crust is inferred to have been composed of Precambrian intermediate composition igneous rocks with average 87Sr/86Sr40~0.750, ɛNd40~ -37.5 and δ18Ozirc ~5.9‰, and Precambrian mafic rocks with average 87Sr/86Sr40~0.717, ɛNd40~ -25 and δ18Ozirc ~7.0‰. Existing and new data indicate that the 42-31 Ma upper crustal plutonic complex ranges in isotopic composition from 87Sr/86Sri=0.709-0.712, ɛNdi=-15 to -25 and δ18Ozirc 4.7-6.5‰. The composition of the 32-25 Ma middle crustal plutonic complex ranges from 87Sr
17. ChemRock: a lithogeochemical data analysis and interpretation system as a tool to the petrological study of igneous rocks and their tectonic setting; ChemRock: um sistema de analise e interpretacao de dados litogeoquimicos como ferramenta para o estudo petrologico de rochas igneas e seu contexto tectonico
Energy Technology Data Exchange (ETDEWEB)
Alves, Daisy Barbosa [PETROBRAS S.A., Rio de de Janeiro, RJ (Brazil). Centro de Pesquisas (CENPES). Gerencia de Sedimentologia e Petrologia], E-mail: daisy@petrobras.com.br; Biondi, Mauro; Leta, Fabiana Rodrigues; Lima, Leonardo Pereira de; Valente, Sergio de Castro; Corval, Arthur
2005-11-15
Petrology of igneous rocks is strongly based on calculations of whole-rock geochemical data, which applied to a large number of samples can be very time-consuming. This paper presents ChemRock, a computer-based system used to analyze, interpret and visualize lithogeochemical data in a petrologic and geodynamic approach. It operates in a Windows platform and offers a simple and user-friendly interface. Within the same environment it is able to gather rock classification graphs used to discriminate series of tectonic paleo environments, and modules used to interpret normative (CIPW and mesonorm) and isotopic data. Besides, normalization and partition coefficients tables proposed by different authors, quantification modules of partial melting processes, crystal fractionation and binary mixture have been provided. It is capable of generating hundreds of graphs and pre-formatted tables that can be inserted in digital reports, and it is also provided with a module to generate its own reports. ChemRock is a tool to speed up petrogenetic analysis by offering methods and functionalities used in current literature. (author)
18. Technological characteristics of glauconite rocks in Bakchar deposit (Western Siberia
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Rudmin M.A.
2016-01-01
Full Text Available Glauconite-containing rocks found within the boundaries of the Bakchar deposit includethe following: glauconite ores (glauconitolite, glauconite sandstone, hydrogoethite-chlorite, iron ores with glauconite. Glauconite content in glauconite ores is 50…70 %, in glauconite sandstone – 20…40 %, in hydrogoethite-chlorite ores- 10…20 %. This paper describes the technological characteristics of glauconite rocks. The authors proposed the optimal technological scheme of producing glauconite concentrate. It has been defined that the most highly-qualified product with commercial components 90…100 % is recovered from glauconite ores. It has been evaluated that Bakchar glauconite is applicable as a favorable mineral fertilizer based on the concentrate produced from enriched hydrogoethite-chlorite ores. Experimentally, it has been proved that this concentrate has a positive effect on the growth of oats (Avéna satíva. This is a direct indicator of its practical applicability. Obtained results indicate the fact that the extraction and application of Bakchar glauconite could be widely used in agriculture.
19. Burial metamorphism in rocks of the Western Andes of Peru
Science.gov (United States)
Offler, R.; Aguirre, L.; Levi, B.; Child, S.
1980-01-01
An unconformity bound, episodic pattern of burial metamorphism is preserved in marine and terrestrial volcanic and sedimentary rocks which were deposited in the West Peruvian Trough during the Mesozoic and Cenozoic Eras. A particular metamorphic facies series is developed in each of the stratigraphic-structural units bounded by unconformities. In each unit, grade increases with stratigraphic depth and covers part or all of the range from zeolite to greenschist facies. At every unconformity a mineralogic break occurs where higher grade assemblages on top of the unconformity plane overlie lower grade assemblages. The presence of wairakite and the development of a wide range of metamorphic facies in thin sequences suggest high geothermal gradients, possibly related to generation of magma at depth.
20. Habitat surrounding patch reefs influences the diet and nutrition of the western rock lobster
Science.gov (United States)
In this study the influence of habitat on the diet and nutrition of a common reef-associated generalist consumer, the western rock lobster Panulirus cygnus, was tested. Stable isotopes (13C/12C and 15N/14N) and gut contents were used to assess the diet of lobsters collected from ...
1. Early-Middle Paleozoic subduction-collision history of the south-eastern Central Asian Orogenic Belt: Evidence from igneous and metasedimentary rocks of central Jilin Province, NE China
Science.gov (United States)
Pei, Fu-Ping; Zhang, Ying; Wang, Zhi-Wei; Cao, Hua-Hua; Xu, Wen-Liang; Wang, Zi-Jin; Wang, Feng; Yang, Chuan
2016-09-01
To constrain the Early-Middle Paleozoic tectonic evolution of the south-eastern segment of the Central Asian Orogenic Belt (CAOB), we undertook zircon U-Pb dating and analyzed major and trace elements and zircon Hf isotope compositions of Late Cambrian to Middle Devonian igneous and metasedimentary rocks in central Jilin Province, NE China. LA-ICP-MS zircon U-Pb dating indicates that the Early-Middle Paleozoic magmatism in central Jilin Province can be divided into four episodes: Late Cambrian (ca. 493 Ma), Middle Ordovician (ca. 467 Ma), Late Ordovician-Early Silurian (ca. 443 Ma), and Late Silurian-Middle Devonian (425-396 Ma). The progression from subduction initiation to maturity is recorded by Late Cambrian low-K tholeiitic meta-diabase, Middle Ordovician medium-K calc-alkaline pyroxene andesite, and Late Ordovician to Early Silurian low-K tonalite, which all have subduction-related characteristics and formed in an evolving supra-subduction zone setting. Late Silurian to Middle Devonian calc-alkaline igneous rocks, with the lithological association of granodiorite, monzogranite, rhyolite, dacite, and trachydacite, show progressively increasing K2O contents from medium K to shoshonite series. Furthermore, the Early-Middle Devonian monzogranites are characterized by high K2O, Sr/Y, and [La/Yb]N values, indicating they were generated by the melting of thickened lower crust. These results suggest a transition from subduction to post-orogenic setting during the Late Silurian-Middle Devonian. Our interpretation is supported by the maximum age of molasse deposition in the Zhangjiatun member of the Xibiehe Formation. Overall, we suggest that Late Cambrian tholeiitic meta-diabase, Middle Ordovician pyroxene andesite, and Late Ordovician-Early Silurian tonalite formed above the northward-subducting and simultaneously seaward-retreating of Paleo-Asian Ocean plate. Subsequently, the northern arc collided with the North China Craton and post-orogenic extension occurred
2. Characteristics and geological significance of olivine xenocrysts in Cenozoic volcanic rocks from western Qinling
Institute of Scientific and Technical Information of China (English)
SU Benxun; ZHANG Hongfu; XIAO Yan; ZHAO Xinmiao
2006-01-01
Cenozoic volcanic rocks from the Haoti, Dangchang County of the western Qinling Mountains, contain a few clearlyzoned olivines. These olivines are relatively big in grain sizes and usually have cracks or broken features. Their cores have similar compositions (Mg# = 90.4- 91.0) to those for the peridotitic xenoliths entrained in host volcanic rocks and their rims are close to the compositions of olivine phenocrysts (Mg# = 85.5 81.9). The CaO contents in these zoned olivines are lower than 0.1%. These features demonstrate that the clearly zoned olivines are xenocrysts and disaggregated from mantle peridotites. The zoned texture was the result of the interaction between the olivine and host magma. Available data show that the volcanic rocks would have been derived from the mantle source metasomatized by subducted hydrathermally-altered oceanic crust. The formation of these Cenozoic volcanic rocks was perhaps related to the rapid uplift of the Tibetan Plateau.
3. Evolution of the Mazatzal province and the timing of the Mazatzal orogeny: Insights from U-Pb geochronology and geochemistry of igneous and metasedimentary rocks in southern New Mexico
Science.gov (United States)
Amato, J.M.; Boullion, A.O.; Serna, A.M.; Sanders, A.E.; Farmer, G.L.; Gehrels, G.E.; Wooden, J.L.
2008-01-01
New U-Pb zircon ages, geochemistry, and Nd isotopic data are presented from three localities in the Paleoproterozoic Mazatzal province of southern New Mexico, United States. These data help in understanding the source regions and tectonic setting of magmatism from 1680 to 1620 Ma, the timing of the Mazatzal orogeny, the nature of postorogenic maginatism, Proterozoic plate tectonics, and provide a link between Mazatzal subblocks in Arizona and northern New Mexico. The data indicate a period from 1680 to 1650 Ma in which juvenile felsic granitoids were formed, and a later event between 1646 and 1633 Ma, when these rocks were deformed together with sedimentary rocks. No evidence of pre-1680 Ma rocks or inherited zircons was observed. The igneous rocks have ENd(t) from -1.2 to +4.3 with most between +2 and +4, suggesting a mantle source or derivation from similar-aged crust. Nd isotope and trace element concentrations are consistent with models for typical are magmatism. Detrital zircon ages from metasedimentary rocks indicate that sedimentation occurred until at least 1646 Ma. Both local and Yavapai province sources contributed to the detritus. All of the samples older than ca. 1650 Ma are deformed, whereas undeformed porphyroblasts were found in the contact aureole of a previously dated 1633 Ma gabbro. Regionally, the Mlazatzal orogeny occurred mainly between 1654 and 1643 Ma, during final accretion of a series of island arcs and intervening basins that may have amalgamated offshore. Rhyolite magmatism in the southern Mazatzal province was coeval with gabbro intrusions at 1633 Ma and this bimodal magmatism may have been related to extensional processes following arc accretion. ?? 2007 Geological Society of America.
4. Decoupling of surface and subsurface sutures in the Dabie orogen and a continent-collisional lithospheric-wedging model:Sr-Nd-Pb isotopic evidences of Mesozoic igneous rocks in eastern China
Institute of Scientific and Technical Information of China (English)
2003-01-01
There are significant differences of Nd and Pb isotopic compositions between Mesozoic mafic igneous rocks from the North China Block (NCB) and the South China Block (SCB). Mesozoic mantle-derived igneous rocks from the North China Block have very low εNd values (-15 to -21), and 206Pb/204Pb ratios ( -10 and 206Pb/204Pb > 18.3. The very low εNd values (-16 to -20) and 206Pb/204Pb ratios (< 17.3) of the early Cretaceous mafic-ultramafic intrusions developed in the north part of the Dabie orogen (NDZ) suggest that the deep lithosphere underneath the NDZ belongs to the NCB but not the SCB. Therefore, although the surface suture between the NCB and SCB is located on the north side of the NDZ, the subsurface suture between the NCB and SCB should be located to the south side of the NDZ. This is consistent with the previous suggestion that the subsurface suture in the Sulu terrane east of the Tanlu fault was the south displacement, but contradictory to northward continental subduction of the SCB. A continent-collisional lithospheric- wedging model can interpret the decoupling of the surface and subsurface sutures in the Dabie-Sulu orogen. After slab break-off, the continuing convergence of two continental blocks must increase the compression force acting on the suture zone, which might induce the lithosphere splitting of SCB. Thus, the lower crust and lithospheric mantle on the south margin of the NCB can wedge into the north margin of the lithosphere of the SCB along the Dabie-Sulu collision zone. This process caused the overthrust of the mid-upper continental crust with exhumed ultrahigh pressure metamorphic (UHPM) rocks and underthrust of the deep lithosphere of the SCB. It could be an important mechanism responsible for the second rapid cooling and uplifting of the UHPM rocks and lithospheric delamination as well as the corresponding magmatism in Jurassic in the Dabie orogen. The southward movement of subsurface suture in the Dabie-Sulu orogen may also provide a
5. THE GEOCHEMISTRY AND AGES OF ROCKS IN THE FOOTWALL OF THE BUTULIYN-NUR AND ZAGAN METAMORPHIC CORE COMPLEXES (NORTH MONGOLIA – WESTERN TRANSBAIKALIA)
OpenAIRE
T. V. Donskaya; A.M. MAZUKABZOV
2015-01-01
This article reviews data on ages of rocks in the footwall of the Butuliyn-Nur and Zagan metamorphic core complexes (MCC) and provides new data on the geochemistry of the rock complexes. It is noted that the oldest rocks are mylonitized gneisses on rhyolites (554 Ma) in the footwall of the Butuliyn-Nur MCC. The Late Permian – Triassic (249–211 Ma) igneous rocks are ubiquitous in the footwall of the Butuliyn-Nur and Zagan MCC. The youngest rocks in the studied MCC are the Jurassic granitoids (...
6. Three-dimensional distribution of igneous rocks near the Pebble porphyry Cu-Au-Mo deposit in southwestern Alaska: constraints from regional-scale aeromagnetic data
Science.gov (United States)
Anderson, Eric D.; Zhou, Wei; Li, Yaoguo; Hitzman, Murray W.; Monecke, Thomas; Lang, James R.; Kelley, Karen D.
2014-01-01
Aeromagnetic data helped us to understand the 3D distribution of plutonic rocks near the Pebble porphyry copper deposit in southwestern Alaska, USA. Magnetic susceptibility measurements showed that rocks in the Pebble district are more magnetic than rocks of comparable compositions in the Pike Creek–Stuyahok Hills volcano-plutonic complex. The reduced-to-pole transformation of the aeromagnetic data demonstrated that the older rocks in the Pebble district produce strong magnetic anomaly highs. The tilt derivative transformation highlighted northeast-trending lineaments attributed to Tertiary volcanic rocks. Multiscale edge detection delineated near-surface magnetic sources that are mostly outward dipping and coalesce at depth in the Pebble district. The total horizontal gradient of the 10-km upward-continued magnetic data showed an oval, deep magnetic contact along which porphyry deposits occur. Forward and inverse magnetic modeling showed that the magnetic rocks in the Pebble district extend to depths greater than 9 km. Magnetic inversion was constrained by a near-surface, 3D geologic model that is attributed with measured magnetic susceptibilities from various rock types in the region. The inversion results indicated that several near-surface magnetic sources with moderate susceptibilities converge with depth into magnetic bodies with higher susceptibilities. This deep magnetic source appeared to rise toward the surface in several areas. An isosurface value of 0.02 SI was used to depict the magnetic contact between outcropping granodiorite and nonmagnetic sedimentary host rocks. The contact was shown to be outward dipping. At depths around 5 km, nearly the entire model exceeded the isosurface value indicating the limits of nonmagnetic host material. The inversion results showed the presence of a relatively deep, northeast-trending magnetic low that parallels lineaments mapped by the tilt derivative. This deep low represents a strand of the Lake Clark fault.
7. Genetic aspects of barite mineralization related to rocks of the teschenite association in the Silesian Unit, Outer Western Carpathians, Czech Republic
Science.gov (United States)
Jirásek, Jakub; Dolníček, Zdeněk; Matýsek, Dalibor; Urubek, Tomáš
2017-04-01
Barite is a relatively uncommon phase in vein and amygdule mineralizations hosted by igneous rocks of the teschenite association in the Silesian Unit (Western Carpathians). In macroscopically observable sizes, it has been reported from 10 sites situated only in the Czech part of the Silesian Unit. Microscopic barite produced by the hydrothermal alteration of rock matrix and also by the supergene processes is more abundant. We examined four samples of barite by mineralogical and geochemical methods. Electron microprobe analyses proved pure barites with up to 0.038 apfu Sr and without remarkable internal zonation. Fluid inclusion and sulphur isotope data suggests that multiple sources of fluid components have been involved during barite crystallization. Barite contains primary and secondary aqueous all-liquid (L) or less frequent two-phase (L+V) aqueous fluid inclusions with variable salinity (0.4-2.9 wt. % NaCl eq.) and homogenization temperatures between 77 and 152 °C. The higher-salinity fluid endmember was probably Cretaceous seawater and the lower-salinity one was probably diagenetic water derived from surrounding flysch sediments during compaction and thermal alteration of clay minerals. The δ34S values of barite samples range between -1.0 ‰ and +16.4 ‰ CDT suggesting participation of two sources of sulphate, one with a near-zero δ34S values probably derived from wall rocks and another with high δ34S values being most probably sulphate from the Cretaceous seawater. All results underline the role of externally derived fluids during post-magmatic alteration of bodies of rock of the teschenite association.
8. Genetic aspects of barite mineralization related to rocks of the teschenite association in the Silesian Unit, Outer Western Carpathians, Czech Republic
Directory of Open Access Journals (Sweden)
Jirásek Jakub
2017-04-01
Full Text Available Barite is a relatively uncommon phase in vein and amygdule mineralizations hosted by igneous rocks of the teschenite association in the Silesian Unit (Western Carpathians. In macroscopically observable sizes, it has been reported from 10 sites situated only in the Czech part of the Silesian Unit. Microscopic barite produced by the hydrothermal alteration of rock matrix and also by the supergene processes is more abundant. We examined four samples of barite by mineralogical and geochemical methods. Electron microprobe analyses proved pure barites with up to 0.038 apfu Sr and without remarkable internal zonation. Fluid inclusion and sulphur isotope data suggests that multiple sources of fluid components have been involved during barite crystallization. Barite contains primary and secondary aqueous all-liquid (L or less frequent two-phase (L+V aqueous fluid inclusions with variable salinity (0.4-2.9 wt. % NaCl eq. and homogenization temperatures between 77 and 152 °C. The higher-salinity fluid endmember was probably Cretaceous seawater and the lower-salinity one was probably diagenetic water derived from surrounding flysch sediments during compaction and thermal alteration of clay minerals. The δ34S values of barite samples range between -1.0 ‰ and +16.4 ‰ CDT suggesting participation of two sources of sulphate, one with a near-zero δ34S values probably derived from wall rocks and another with high δ34S values being most probably sulphate from the Cretaceous seawater. All results underline the role of externally derived fluids during post-magmatic alteration of bodies of rock of the teschenite association.
9. Rock-slope failure activity and geological crises in western Norway
Science.gov (United States)
Hilger, Paula; Hermanns, Reginald L.; Myhra, Kristin S.; Gosse, John C.; Ivy-Ochs, Susan; Etzelmüller, Bernd
2017-04-01
In Norway a compilation of terrestrial cosmogenic nuclide (TCN) ages of rock-avalanche deposits suggests a close link of rock-slope failures related to deglaciation. Although ages spread over several thousand years at the end of the Late Pleistocene, 50% of all documented events occurred within 1000 years after deglaciation. It is therefore likely that debuttressing triggered most of the events. The same data set suggests that 25% of the events occurred during a period stretching until the Holocene thermal maximum (HTM). These events might be interpreted as possible reactions to additional factors such as the thawing of high-altitude permafrost. An example of a geological crisis following deglaciation and before the HTM are seven lobate rock-avalanche deposits mapped under the slope of the Vora mountain (1450 m asl.) in the Nordfjord area of western Norway. Three events of this rock-slope failure cluster date within a short time period of 2000 years, where modelling studies indicate that high-altitude permafrost was present. After the HTM rock-slope failures are distributed temporally and spatially rather evenly throughout the Holocene and western Norway. But there are two independent local clusters with frequent rock slides during a short time span. (1) At the active Mannen rock-slope instability several rock-avalanche and rockslide deposits were mapped on the valley bottom. Stratigraphic relations combined with TCN dating suggest that at least one event occurred when the valley bottom was below the marine limit. TCN ages of further four lobes cluster around 5.2 ka BP, which does not coincide with any other rock-avalanche occurrence in the region. The top of the north facing 1295 m high unstable slope concurs with the currently estimated permafrost boundary. Preliminary TCN ages of the sliding surface indicate that larger parts of the mountain did not become active until the climate maximum. It is likely that due to structural complexity not allowing for any easy
10. African dust phosphorus fertilizing the Amazon and the Atlantic Ocean is derived from marine sediments and igneous rocks - no indication for Bodélé diatomite contribution
Science.gov (United States)
Gross, Avner; Castido, Danilo; Pio, Casimero; Angert, Alon
2013-04-01
Dust eroded from West Africa is blown across the Atlantic Ocean towards the tropics and constitutes a major external source of phosphorus (P) to the Amazon and marine surface waters. It is usually assumed that the P concentration in dust is ~700 µg P g/dust based on the average concentrations in crust material. In addition, previous studies have claimed that diatomites from the Bodélé depression in Chad are a major source of P to the equatorial Atlantic Ocean and the Amazon. In this study we have utilized the oxygen isotopes in resin extractable inorganic phosphate (δ18OP) of dust particles to identify their P sources. The data presented here is from over 100 PM10 dust samples, collected during major dust events in October- April 2011 and 2012, as part of the CV-DUST project in Cape-Verde. This archipelago is located downwind of the Sahara and Sahel dust producing areas, and is thus well suited for collecting dust blown out from Africa. Air mass back trajectories computations show that the dust origin can be classified to 3 sectors: the north and west Saharan sector, south and central Saharan sector and the Sahel sector. Dust particles approaching from these 3 sectors shows distinct resin-P concentrations (in the range of 1160 µg P g/dust to 7260 µg P g/dust) and distinct δ18OP values which ranges from 7.2‰ to 21.7‰. Major elements concentrations also showed distinct pattern. Dust particles approaching from the north and west Saharan sector shows the lowest P concentrations and a δ18OP values of ~21‰ which are typical for P originating from marine sediments at the Sahara area. Dust particles from the south west Saharan sector are richest in P and have the lowest δ18OP values of 7.2‰ , which are typical for P originated from igneous source. Dust approaching from the Sahel sector shows mid-range P concentrations and δ18OP values of ~14‰ , and fall on isotopic mixing line (R2=0.91) between the dust samples with igneous and marine sedimentary
11. In-situ zircon U-Pb age and Hf-O isotopic constraints on the origin of the Hasan-Robat A-type granite from Sanandaj-Sirjan zone, Iran: implications for reworking of Cadomian arc igneous rocks
Science.gov (United States)
Honarmand, Maryam; Li, Xian-Hua; Nabatian, Ghasem; Neubauer, Franz
2017-01-01
The Lower Permian Hasan-Robat syenogranite occurs as a single pluton and intruded the Upper Carboniferous-Lower Permian sandstones and dolomitic limestones in the central part of the Sanandaj-Sirjan zone. This syenogranitic intrusion shows A-type granitic affinity and is a good representative of Early Permian igneous activity in Iran. SIMS U-Pb zircon analyses indicate a crystallization age of 294.2 ± 2.5 Ma for the Hasan-Robat A-type granite. In-situ Lu-Hf and oxygen isotope analyses of magmatic zircons were carried out to infer the magma sources and evolution of the Hasan-Robat A-type syenogranite. The Hf-O zircon isotopic compositions are relatively homogeneous, with nearly chondritic ɛHf(t) values of -0.8 to +2.4 corresponding to two-stage zircon Hf model ages of 1.15-1.36 Ga. The δ18O values of zircon range from +7.6 to +8.6‰. The Hf model ages of the Hasan-Robat zircons is within the range of those reported from the Cadomian granitoids in Iran. The isotopic features of the Hasan-Robat syenogranite are in good agreement with Hf isotopic values and Hf and Nd model ages reported from the Cadomian arc magmatic suites in Iran. Thus, partial melting of these Cadomian igneous rocks would be the favorite source for the Hasan-Robat syenogranitic magma during the opening of the Neotethys Ocean and separation of Iranian terranes from the northern margin of Gondwana.
12. Provenance and tectonic setting of siliciclastic rocks associated with the Neoproterozoic Dahongliutan BIF: Implications for the Precambrian crustal evolution of the Western Kunlun orogenic belt, NW China
Science.gov (United States)
Hu, Jun; Wang, He; Wang, Min
2017-10-01
The Late Neoproterozoic Dahongliutan BIF is associated with siliciclastic rocks in the Tianshuihai terrane of the Western Kunlun orogenic belt (WKO), NW China. The sedimentary rocks have various weathering indices (e.g., CIA = 57-87, PIA = 61-96 and Th/U = 4.85-12.45), indicative of varying degrees of weathering in the source area. The rocks have trace element ratios, such as Th/Sc = 0.60-1.21 and Co/Th = 0.29-1.67, and light rare earth element (LREE) enriched chondrite-normalized REE patterns, suggesting that they were mainly sourced from intermediate and felsic rocks. Available U-Pb ages of detrital zircon from these rocks reveal that the detrital sources may have been igneous and metamorphic rocks from the WKO and the Tarim Block. Our study suggests that the Dahongliutan BIF and hosting siliciclastic rocks may have deposited in a setting transitional from a passive to active continental margin, probably related to the Late Neoproterozoic-Early Cambrian seafloor spreading and subduction of the Proto-Tethys Ocean. U-Pb dating of 163 detrital zircons defines five major age populations at 2561-2329 Ma, 2076-1644 Ma, 1164-899 Ma, 869-722 Ma and 696-593 Ma. These age groups broadly correspond to the major stages of supercontinent assembly and breakup events widely accepted for Columbia, Rodinia and Gondwana. Some zircons have TDM2 model ages of 3.9-1.8 Ga and negative εHf(t) values, suggesting that the Archean to Paleoproterozoic (as old as Eoarchean) crustal materials were episodically reworked and incorporated into the late magmatic process in the WKO. Some Neoproterozoic zircons have TDM2 model ages of 1.47-1.07 Ga and 1.81-1.53 Ga and positive εHf(t) values, indicating juvenile crustal growth during the Mesoproterozoic. Our new results, combined with published data, imply that both the Tianshuihai terrane in the WKO and the Tarim Block share the same Precambrian tectonic evolution history.
13. Petrochemistry of igneous rocks of the California-Vetas mining district, Santander, Colombia: Implications for northern Andean tectonics and porphyry Cu (-Mo, Au) metallogeny
Science.gov (United States)
Bissig, Thomas; Mantilla Figueroa, Luis Carlos; Hart, Craig J. R.
2014-07-01
Porphyry Mo and Cu mineralization in the California-Vetas mining district is contemporaneous with 10.9 to 8.4 Ma granodiorite porphyry stocks and overprinted by Au-Ag mineralization of epithermal affinity. Mineralization is hosted by Grenvillian aged paragneisses (Bucaramanga Gneiss of the Santander Massif) and late Triassic to early Jurassic granitic rocks. All intrusive rocks are high-K calc-alkaline. Late Triassic to early Jurassic rocks include peraluminous granites with more than 70 wt.% SiO2 as well as metaluminous diorites, tonalites and granodiorites with SiO2 between 54.9 and 60.4 wt.%. Late Miocene rocks are weakly peraluminous granodiorite porphyries with SiO2 between 61 and 67 wt.% SiO2. Late Miocene rocks share some characteristics with adakite-like rocks which are widely associated with porphyry and epithermal style mineralization elsewhere in the Andes. They have high Ba (930 to 1500 ppm) and high Ba/La (28 to 50), high Sr (850 to 1100 ppm) and Sr/Y (48-78) and depleted middle rare earth elements (MREE) compared to the Mesozoic granites, which have 400 to 700 ppm Ba (Ba/La 14 to 25) and 80 to 150 ppm Sr (Sr/Y 2.5 to 14), and Mesozoic diorites and tonalites, which have ~ 900 to 1200 ppm Ba (Ba/La 20 to 32) and ~ 610 to 750 ppm Sr (Sr/Y 22 to 25). Miocene granodiorite porphyries, in contrast to Mesozoic intrusive rocks have only weak negative Eu anomalies. The Miocene rocks have 87Sr/86Sr ratios of 0.7052 to 0.7067 and εNd of - 1.9 to - 5.4 and are significantly more isotopically primitive than all other rocks in the study area including the Mesozoic diorites to tonalites (87Sr/86Sr = 0.7082 and 0.7092; εNd = - 6.7 and - 7.2), granites (87Sr/86Sr = 0.730 (n = 2); εNd = - 8.2 and - 8.3) and Bucaramanga Gneiss (0.718 to 0.743; εNd = - 10.8 to - 14.1). Lead isotope data are broadly consistent with the Sr and Nd isotope data and the Miocene porphyries have the lowest 207Pb/204Pb ratios but overlap with the Mesozoic diorites to tonalites in their 206Pb
14. DETECTION OF IGNEOUS BODIES IN HUAIBEI COAL MINESBY HIGH RESOLUTION MAGNETIC SURVEY
Institute of Scientific and Technical Information of China (English)
WangSilong; NingShunian; YangXiaoqin; HouXiaoqiang; LiuBo; LiuDonglin
1996-01-01
The present paper investigates the application of high resolution magnetic survey to detecting igneous bodies. The slight difference in magnetism between ig-neous bodies and their surrounding rocks is measured first and then the magnetic survey data are processed to determine whether there exist igneous bodies by analog among several measuring lines, and finally the modified Marquart inversion was used to determine the occurrence and distribution of the igneous bodies.
15. Stratigraphy, geochemistry and tectonic significance of the Oligocene magmatic rocks of western Oaxaca, southern Mexico
Science.gov (United States)
Martiny, B.; Martinez-Serrano, R. G.; Moran-Zenteno, D. J.; MacIas-Romo, C.; Ayuso, R.A.
2000-01-01
In Western Oaxaca, Tertiary magmatic activity is represented by extensive plutons along the continental margin and volcanic sequences in the inland region. K-Ar age determinations reported previously and in the present work indicate that these rocks correspond to a relatively broad arc in this region that was active mainly during the Oligocene (~ 35 to ~ 25 Ma). In the northern sector of western Oaxaca (Huajuapan-Monte Verde-Yanhuitlan), the volcanic suite comprises principally basaltic andesite to andesitic lavas, overlying minor silicic to intermediate volcaniclastic rocks (epiclastic deposits, ash fall tuffs, ignimbrites) that were deposited in the lacustrine-fluvial environment. The southern sector of the volcanic zone includes the Tlaxiaco-Laguna de Guadalupe region and consists of intermediate to silicic pyroclastic and epiclastic deposits, with silicic ash fall tuffs and ignimbrites. In both sectors, numerous andesitic to dacitic hypabyssal intrusions (stocks and dikes) were emplaced at different levels of the sequence. The granitoids of the coastal plutonic belt are generally more differentiated than the volcanic rocks that predominate in the northern sector and vary in composition from granite to granodiorite. The studied rocks show large-ion lithophile element (LILE) enrichment (K, Rb, Ba, Th) relative to high-field-strength (HFS) elements (Nb, Ti, Zr) that is characteristic of subduction-related magmatic rocks. On chondrite-normalized rare earth element diagrams, these samples display light rare earth element enrichment (LREE) and a flat pattern for the heavy rare earth elements (HREE). In spite of the contrasting degree of differentiation between the coastal plutons and inland volcanic rocks, there is a relatively small variation in the isotopic composition of these two suites. Initial 87Sr/86Sr ratios obtained and reported previously for Tertiary plutonic rocks of western Oaxaca range from 0.7042 to 0.7054 and ??Nd values, from -3.0 to +2.4, and for
16. Approximate western limit of glaciation within the Standing Rock Indian Reservation, Sioux County, North Dakota, and Corson County, South Dakota
Data.gov (United States)
U.S. Geological Survey, Department of the Interior — This coverage contains information about the western limit of glaciation within the Standing Rock Indian Reservation, Sioux County, North Dakota, and Corson County,...
17. Uranium-Lead Zircon Ages and Sr, Nd, and Pb Isotope Geochemistry of Selected Plutonic Rocks from Western Idaho
Science.gov (United States)
Unruh, Daniel M.; Lund, Karen; Kuntz, Mel A.; Snee, Lawrence W.
2008-01-01
Across the Salmon River suture in western Idaho, where allochthonous Permian to Cretaceous oceanic rocks are juxtaposed against Proterozoic North American rocks, a wide variety of plutonic rocks are exposed. Available data indicate much variation in composition, source, and structural state of these plutons. The plutonic rocks were long described as the western border zone of the Cretaceous Idaho batholith but limited pre-existing age data indicate more complicated origins. Because the affinity and age of the plutonic rocks cannot be reliably determined from field relations, TIMS U-Pb dating in conjunction with Sr, Nd, and Pb isotopic studies of selected plutons across the suture in western Idaho were undertaken. The data indicate three general groups of plutons including (1) those that intruded the island arc terranes during the Triassic and Jurassic, those that intruded near the western edge of oceanic rocks along the suture in the Early Cretaceous, and the plutons of the Idaho batholith that intruded Proterozoic North American rocks in the Late Cretaceous. Plutons that intruded Proterozoic North American rocks commonly include xenocrystic zircons and in several cases, ages could not be determined. The least radiogenic Sr and most radiogenic Nd are found among the Blue Mountains superterrane island arc samples. Suture-zone plutons have isotopic characteristics that span the range between Idaho batholith and island arc samples but mostly follow island arc signatures. Plutons of the Idaho batholith have the most radiogenic initial Pb and Sr ratios and the least radiogenic Nd of the samples analyzed.
18. SHRIMP U-Pb zircon dates from igneous rocks from the Fontana Lake region, Patagonia: Implications for the age of magmatism, Mesozoic geological evolution and age of basement
Directory of Open Access Journals (Sweden)
A.P. Rolando
2004-12-01
Full Text Available In the eastern margin of the Patagonian Andes and between 44° 30´S and 45° 30´S (Fontana Lake region, Middle Jurassic to Early Cretaceous volcanic and sedimentary rocks were intruded by granitic bodies during the Cretaceous. The reconstruction of the Jurassic-Cretaceous magmatic evolution in the Fontana Lake region and in the adjacent Patagonian Batholith was made possible by the consideration of the following characteristics: distribution in time and space of several intrusive bodies, retro-arc basin formation and volcanic intensity. U-Pb SHRIMP dating of zircon crystals from an ignimbrite, a dacitic porphyry and two granitoid rocks yielded dates of 148.7 ± 2.3, 144.5 ± 1.6, 117 ± 1.7 and 99.6 ± 2.8 Ma, respectively. The Cerro Bayo Ignimbrite (148.7 ± 2.3 Ma, Late Jurassic was included in the Lago La Plata Formation; this unit hosts an epithermal ore deposit. The Laguna Escondida dacitic porphyry (144.5 ± 1.6 Ma, Jurassic-Cretaceous boundary intruded metasedimentary rocks of the Lago La Plata Formation; this sub-volcanic body can chronologically be linked to the Patagonian Batholith. After the Jurassic volcanic events, a retro-arc basin formed in the eastern sector of the Patagonian Range at about 140-115 Ma (Late Berriasian-Barremian and magmatism ceased during this event. The dating of granitoids (117 ± 1.7 and 99.6 ± 2.8 Ma in the Fontana Lake region confirms a temporal magmatic continuity with the Patagonian Batholith. These dates also are in agreement with the volcanic rocks of the Divisadero Group and epithermal deposits in the region (La Ferrocarrilera deposit. One of the analyzed granitoids (Dedo Chico, 99.6 ± 2.8 Ma has inherited zircon crystals of about 2,100 and 3,410 Ma, in agreement with other previous isotopic evidence for the occurrence of an underlying Precambrian basement in the region.
19. Geochemical evaluation of oils and source rocks from the Western Siberian basin, U. S. S. R
Energy Technology Data Exchange (ETDEWEB)
Peters, K.E.; Huizinga, B.J. (Chevron Overseas Petroleum, Inc., San Ramon, CA (United States)); Moldowan, J.M. (Chevron Oil Field Research Co., Richmond, CA (United States)); Kontorovich, A.E.; Stasova, O. (Siberian Scientific Research Institute for Geology, Geophysics and Mineral Resources, Novobsibirsk (Russian Federation)); Demaison, G.J.
1991-03-01
Although the Western Siberian basin is among the most prolific in the world, there has been disagreement among Soviet geoscientists on the origin of the petroleum within this basin. Screening geochemical analyses were used to select several oils and potential source rocks for a preliminary study using detailed biomarker and supporting geochemistry. Possible sources for this petroleum include rocks of Middle Jurassic, Upper Jurassic, and Lower Cretaceous age. Results indicate that most of the analyzed Western Siberian oils, occurring in reservoirs from Middle Jurassic to Late Cretaceous in age, are derived from the Upper Jurassic Bazhenov Formation. The locations of the samples in the study generally correspond to the distribution of the most effective oil-generative parts of the Bazhenov Formation. Analyses show that the Bazhenov rock samples contain abundant marine algal and bacterial organic matter, preserved under anoxic depositional conditions. Biomarkers show that thermal maturities of the samples range from the early to late oil-generative window and that some are biodegraded. For example, the Salym No. 114 oil, which flowed directly from the Bazhenov Formation, shows a maturity equivalent to the late oil window. The Van-Egan no. 110 oil shows maturity equivalent to the early oil window and is biodegraded. This oil shows preferential microbial conversion of lower homologs of the 17{alpha}, 21{beta}(H)-hopanes to 25-nor-17{alpha}(H)-hopanes.
20. Major and minor elements and traces in igneous rocks from crystalline basement of Parana by X-ray fluorescence; Elementos maiores, menores e tracos, em rochas igneas do escudo cristalino paranaense por fluorescencia de raios-X
Energy Technology Data Exchange (ETDEWEB)
Ferreira, Ademar O.; Pecequilo, Brigitte R.S.; Scapin, Marcos A.; Salvador, Vera L.R., E-mail: aoferreira@ipen.br, E-mail: brigitte@ipen.br, E-mail: mascapin@ipen.br, E-mail: vsalvado@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)
2015-07-01
Major and minor components of 30 acid and basic igneous rocks (granites, syenites, riolites and a basalt) of the Parana state crystalline basement were determined by X-ray fluorescence spectrometry (WDXRF), in order to evaluate the similarity in terms of the compositional content. The corrections of interelements effects (absorption/intensification) were performed by means of the fundamental parameters (FP) method. The methodology was validated using a certificated reference material. The main oxides found associated with the quantified elements are SiO{sub 2}, Al{sub 2}O{sub 3}, Na{sub 2}O, K{sub 2}O, Fe{sub 2}O{sub 3}, CaO, MgO, TiO{sub 2}, P{sub 2}O{sub 5}, MnO, SO{sub 3}, NiO, ZnO, Rb{sub 2}O. Through statistical analysis, the studied samples were organized in 3 groups of similar compositions: syenites, light granites and basalt and dark granites. The results show that the WDXRF technique is a robust tool that enables distinction even between similar geological samples. (author)
1. Geochemistry of oil in fluid inclusions in a middle Proterozoic igneous intrusion: implications for the source of hydrocarbons in crystalline rocks
Energy Technology Data Exchange (ETDEWEB)
Dutkiewicz, A. [Sydney Univ., NSW (Australia). School of Geosciences; Sydney Univ., NSW (Australia). Inst. of Marine Science; Volk, H.; George, S.C. [CSIRO Petroleum, North Ryde, NSW (Australia); Ridley, J. [Macquarie Univ., Sydney, NSW (Australia). Dept. of Earth and Planetary Sciences
2004-08-01
The ca. 1280 Ma dolerite sill within the Mesoproterozoic Roper Group in the Roper Superbasin, Australia, contains evidence for at least two episodes of hydrocarbon migration represented, respectively, by solid bitumen with a ketone-rich extract, and a mixture of a high maturity gas-condensate and a lower maturity oil within oil-bearing fluid inclusions. The ketone isomers are formed by flash pyrolysis of kerogen during the intrusion of the dolerite sill [Org.Geochem. 21(1994) 829] and represent the first and oldest phase of hydrocarbon migration. The gas condensate and oil were subsequently trapped as a mixture within fluid inclusions at diagenetic temperatures and pressures of around 110 {sup o}C and 250 bars, significantly after cooling of the sill and likely during the Neoproterozoic reactivation of the Roper Superbasin. Either (1) these fluids migrated together and mixed in the reservoir or (2) an earlier oil charge was flushed by a later condensate charge and the oil-condensate mixture was trapped within single fluid inclusions. Oil inclusions occur chiefly within albitised zones of labradorite laths within the dolerite matrix, and within transcrystalline microfractures cutting vein calcite and rarely vein quartz. Oil inclusions trapped in the vein calcite are accompanied by hypersaline Ca/Mg brines. Gas chromatography-mass spectrometry of oil extracted from inclusions within the dolerite matrix shows that the oil is non-biodegraded and was therefore trapped relatively quickly within the host minerals. Trace amounts of biomarkers indicate that the inclusion oil is of a biogenic origin and excludes any abiotic processes that are apparent sources of hydrocarbons in many crystalline rocks. Monomethylalkanes, pentacyclic terpanes chiefly comprising hopanes and diahopanes, and very low concentrations of steranes and diasteranes indicate input from cyanobacterial organic matter with a minor contribution from eukaryotes. The hydrocarbons are likely derived from
2. Geochemistry of Late Triassic pelitic rocks in the NE part of Songpan-Ganzi Basin, western China: Implications for source weathering, provenance and tectonic setting
Directory of Open Access Journals (Sweden)
Yan Tang
2012-09-01
Full Text Available Major, trace and rare earth element (REE concentrations of Late Triassic sediments (fine-grained sandstones and mudstones from Hongcan Well 1 in the NE part of the Songpan-Ganzi Basin, western China, are used to reveal weathering, provenance and tectonic setting of inferred source areas. The Chemical Index of Alteration (CIA reflects a low to moderate degree of chemical weathering in a cool and somewhat dry climate, and an A-CN-K plot suggests an older upper continental crust provenance dominated by felsic to intermediate igneous rocks of average tonalite composition. Based on the various geochemical tectonic setting discrimination diagrams, the Late Triassic sediments are inferred to have been deposited in a back-arc basin situated between an active continental margin (the Kunlun-Qinling Fold Belt and a continental island arc (the Yidun Island Arc. The Triassic sediments in the study area underwent a rapid erosion and burial in a proximal slope-basin environment by the petrographic data, while the published flow directions of Triassic turbidites in the Aba-Zoige region was not supported Yidun volcanic arc source. Therefore, we suggest that the Kunlun-Qinling terrane is most likely to have supplied source materials to the northeast part of the Songpan-Ganzi Basin during the Late Triassic.
3. Deformation Along the Southeast Extension of the Lake Mead Fault System Evaluated with Paleomagnetic Data From Miocene Igneous Rocks, Hoover Dam area, Nevada and Arizona
Science.gov (United States)
Geissman, J. W.
2002-12-01
At and near Hoover Dam, southeast of Las Vegas, Cenozoic left-slip offset along the NE-SW trending Lake Mead fault system (LMFS) has resulted in the apparent rotation of structures and total displacement of up to 65 km. Defining any rotation of blocks within and near the LMFS is critical to assessing the kinematics of strike-slip faulting and attending extension. Paleomagnetic data from Miocene volcanic and some sedimentary rocks and intrusions (over 160 sites) deposited on Precambrian basement show that part of the Hoover Dam locality has experienced counterclockwise rotation . The middle Miocene (ca. 14.2 Ma)Tuff of Hoover Dam (THD)(sampled at over 90 sites) yields a well-grouped characteristic magnetization (ChRM); about 5 km south and east of the dam, gently east-dipping, north-striking rocks of the THD yield a corrected ChRM of moderate positive inclination and northwest declination (D=324.8°, I=27.4°, a95=10.7°, k=24, N=9 sites). Structural corrections, based on compaction fabrics in the THD are consistent with stratigraphic contacts. The anomalous shallow inclination for the THD ChRM implies that it was emplaced over a short period of time during a field instability. contact and conglomerate test results are interpreted to show that the THD ChRM is primary. Corrected data from north and west of the dam (D=289.7°, I=30.2°,a95=8.6°,k=32, N=10) are interpreted to indicate about 35° of counterclockwise rotation (R= -35.1°, delR= 12.4, F= -2.8°, delF = 10.8, relative to data from south of the dam) of crust across the dam site, consistent with progressive changes in strike of tilted fault blocks. The transition from apparently unrotated crust to rotated crust occurs over a zone about 1 km wide, where blocks of THD and older strata have been tilted up to 50°, probably concurrent with rotation. Rotation of crust northwest of Hoover Dam may reflect differential extension northwest of the LMFS (e.g.,River Mountains area) as strain is partitioned into west to
4. Geophysical anatomy of counter-slope scarps in sedimentary flysch rocks (Outer Western Carpathians)
Science.gov (United States)
Tábořík, P.; Lenart, J.; Blecha, V.; Vilhelm, J.; Turský, O.
2017-01-01
A multidisciplinary geophysical survey, consisting of electrical resistivity tomography (ERT), ground penetrating radar (GPR), shallow seismic refraction (SSR) and gravity survey (GS), was used to investigate the counter-slope scarps, one of the typical manifestations of the relaxed zones of rock massifs, and the possible initial stages of deep-seated landslides (DSLs). Two upper parts of the extensive DSLs within the Moravskoslezské Beskydy Mountains (Outer Western Carpathians - OWC) built by the sedimentary flysch rock were chosen as the testing sites. A combined geophysical survey on the flysch rocks was performed on both localities to enhance our present findings. The survey revealed that the ERT is able to reliably detect underground discontinuities, which are manifested at the ground surface by one of the typical landforms (tension cracks, trenches, pseudokarst sinkholes, double-crested ridges and counter-slope scarps). Previous studies suggested that bedrock discontinuities should be depicted by high-resistivity features within ERT surveying. According to SSR and GS, expected zones of weakened rock massif were not confirmed directly underneath the superficial landforms, but they were shifted. Based on the SSR and GS measurements, the depicted high-contrast transitions between high- and low-resistivity domains within the ERT profiles were newly identified as possible manifestation of bedrock discontinuities. The results of GPR measurements give only limited information on the sedimentary flysch rocks, due to shallow penetrating depth and locally strong signal attenuation. The combined results of multidisciplinary geophysical surveying confirmed an importance of employing more than one geophysical technique for integrated interpretations of measured data. Integrated interpretations of the measured geophysical data provided a new insight into massif disintegration and the geomorphic origin of the landforms related to the DSL.
5. The Emeishan large igneous province: A synthesis
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J. Gregory Shellnutt
2014-05-01
Full Text Available The late Permian Emeishan large igneous province (ELIP covers ∼0.3 × 106 km2 of the western margin of the Yangtze Block and Tibetan Plateau with displaced, correlative units in northern Vietnam (Song Da zone. The ELIP is of particular interest because it contains numerous world-class base metal deposits and is contemporaneous with the late Capitanian (∼260 Ma mass extinction. The flood basalts are the signature feature of the ELIP but there are also ultramafic and silicic volcanic rocks and layered mafic-ultramafic and silicic plutonic rocks exposed. The ELIP is divided into three nearly concentric zones (i.e. inner, middle and outer which correspond to progressively thicker crust from the inner to the outer zone. The eruptive age of the ELIP is constrained by geological, paleomagnetic and geochronological evidence to an interval of ≤3 Ma. The presence of picritic rocks and thick piles of flood basalts testifies to high temperature thermal regime however there is uncertainty as to whether these magmas were derived from the subcontinental lithospheric mantle or sub-lithospheric mantle (i.e. asthenosphere or mantle plume sources or both. The range of Sr (ISr ≈ 0.7040–0.7132, Nd (ɛNd(t ≈ −14 to +8, Pb (206Pb/204Pb1 ≈ 17.9–20.6 and Os (γOs ≈ −5 to +11 isotope values of the ultramafic and mafic rocks does not permit a conclusive answer to ultimate source origin of the primitive rocks but it is clear that some rocks were affected by crustal contamination and the presence of near-depleted isotope compositions suggests that there is a sub-lithospheric mantle component in the system. The silicic rocks are derived by basaltic magmas/rocks through fractional crystallization or partial melting, crustal melting or by interactions between mafic and crustal melts. The formation of the Fe-Ti-V oxide-ore deposits is probably due to a combination of fractional crystallization of Ti-rich basalt and fluxing of CO2-rich fluids
6. Geochronology and geochemistry of early Paleozoic igneous rocks of the Lesser Xing'an Range, NE China: Implications for the tectonic evolution of the eastern Central Asian Orogenic Belt
Science.gov (United States)
Wang, Zhi-wei; Xu, Wen-liang; Pei, Fu-ping; Wang, Feng; Guo, Peng
2016-09-01
This paper presents new zircon U-Pb, Hf isotope, and whole-rock major and trace element data for early Paleozoic igneous rocks of the Lesser Xing'an Range, NE China, in order to constrain the early Paleozoic tectonic evolution of the eastern Central Asian Orogenic Belt (CAOB). Zircon U-Pb dating indicates that early Paleozoic magmatic events within the northern Songnen-Zhangguangcai Range Massif (SZM) can be subdivided into four stages: Middle Cambrian (~ 505 Ma), Late Cambrian (~ 490 Ma), Early-Middle Ordovician (~ 470 Ma), and Late Ordovician (460-450 Ma). The Middle Cambrian monzogranites are K-rich, weakly to strongly peraluminous, and characterized by pronounced heavy rare earth element (HREE) depletions, high Sr/Y ratios, low Y concentrations, low primary zircon εHf(t) values (- 6.79 to - 1.09), and ancient two-stage model (TDM2) ages (1901-1534 Ma). These results indicate derivation from partial melting of thickened ancient crustal materials that formed during the amalgamation of the northern SZM and the northern Jiamusi Massif (JM). The Late Cambrian monzonite, quartz monzonite, and monzogranite units are chemically similar to A-type granites, and contain zircons with εHf(t) values of - 2.59 to + 1.78 and TDM2 ages of 1625-1348 Ma. We infer that these rocks formed from primary magmas generated by partial melting of Mesoproterozoic accreted lower crustal materials in a post-collisional extensional environment. The Early-Middle Ordovician quartz monzodiorite, quartz monzonite, monzogranite, and rhyolite units are calc-alkaline, relatively enriched in light REEs (LREEs) and large ion lithophile elements (LILEs; e.g., Rb, Th, and U), depleted in HREEs and high field strength elements (HFSEs; e.g., Nb, Ta, and Ti), and contain zircons with εHf(t) values of - 7.33 to + 4.98, indicative of formation in an active continental margin setting. The Late Ordovician alkali-feldspar granite and rhyolite units have A-type granite affinities that suggest they formed in
7. Oxygen isotope exchange kinetics of mineral pairs in closed and open systems: Applications to problems of hydrothermal alteration of igneous rocks and Precambrian iron formations
Science.gov (United States)
Gregory, R.T.; Criss, R.E.; Taylor, H.P.
1989-01-01
The systematics of stable-isotope exchange between minerals and fluids are examined in the context of modal mineralogical variations and mass-balance considerations, both in closed and in open systems. On mineral-pair ??18O plots, samples from terranes that have exchanged with large amounts of fluid typically map out steep positively-sloped non-equilibrium arrays. Analytical models are derived to explain these effects; these models allow for different exchange rates between the various minerals and the external fluids, as well as different fluid fluxes. The steep arrays are adequately modelled by calculated isochron lines that involve the whole family of possible exchange trajectories. These isochrons have initially-steep near-vertical positive slopes that rotate toward a 45?? equilibrium slope as the exchange process proceeds to completion. The actual data-point array is thus analogous to the hand of an "isotopic clock" that measures the duration of the hydrothermal episode. The dimensionless ratio of the volumetric fluid flux to the kinetic rate parameter ( u k) determines the shape of each individual exchange trajectory. In a fluid-buffered system ( u k ??? 1), the solutions to the equations: (1) are independent of the mole fractions of the solid phases; (2) correspond to Taylor's open-system water/rock equation; and (3) yield straight-line isochrons that have slopes that approach 1 f, where f is the fraction reacted of the more sluggishly exchanging mineral. The isochrons for this simple exchange model are closely congruent with the isochrons calculated for all of the more complex models, thereby simplifying the application of theory to actual hydrothermal systems in nature. In all of the models an order of magnitude of time (in units of kt) separates steep non-equilibrium arrays (e.g., slope ??? 10) from arrays approaching an equilibrium slope of unity on a ??-?? diagram. Because we know the approximate lifetimes of many hydrothermal systems from geologic and
8. Was the Devonian geomagnetic field dipolar or multipolar? Palaeointensity studies of Devonian igneous rocks from the Minusa Basin (Siberia) and the Kola Peninsula dykes, Russia
Science.gov (United States)
Shcherbakova, V. V.; Biggin, A. J.; Veselovskiy, R. V.; Shatsillo, A. V.; Hawkins, L.; Shcherbakov, V. P.; Zhidkov, G. V.
2017-02-01
Defining variations in the behaviour of the geomagnetic field through geological time is critical to understanding the dynamics of Earth's core and its response to mantle convection and planetary evolution. Furthermore, the question of whether the axial dipole dominance of the recent palaeomagnetic field persists through the whole of Earth's history is fundamental to determining the reliability of palaeogeographic reconstructions and the efficacy of the magnetosphere in shielding Earth from solar wind radiation. Previous palaeomagnetic directional studies have suggested that the palaeofield had a complex configuration in the Devonian period (419-359 Ma). Here we present new palaeointensity determinations from rocks aged between 408 and 375 Ma from the Minusa Basin (southern Siberia), and the Kola Peninsula to investigate the strength of the field during this enigmatic period. Palaeointensity experiments were performed using the thermal Thellier, microwave Thellier, and Wilson methods on 165 specimens from 25 sites. Six out of eight successful sites from the Minusa Basin and all four successful sites from the Kola Peninsula produced extremely low palaeointensities (uniformitarian view of the palaeomagnetic field: field intensities of nearly an order of magnitude lower than Neogene values (except during relatively rare geomagnetic excursions and reversals) together with the widespread appearance of strange directions found in the Devonian suggest that the Earth's field during this time may have had a dominantly multipolar geometry. A persistent, low intensity multipolar magnetic field and associated diminished magnetosphere would increase the impact of solar particles on the Earth's magnetosphere, ionosphere and atmosphere with potential major implications for Earth's climate and biosphere.
9. Igneous Rocks of the East Pacific Rise: The alkali volcanic suite appear to be differentiated from a tholeiitic basalt extruded from the mantle.
Science.gov (United States)
Engel, A E; Engel, C G
1964-10-23
The apical parts of large volcanoes along the East Pacific Rise (islands and seamounts) are encrusted with rocks of the alkali volcanic suite (alkali basalt, andesine- and oligoclase-andesite, and trachyte). In contrast, the more submerged parts of the Rise are largely composed of a tholeiitic basalt which has low concentrations of K, P, U, Th, Pb, and Ti. This tholeiitic basalt is either the predominant or the only magma generated in the earth's mantle under oceanic ridges and rises. It is at least 1000-fold more abundant than the alkali suite, which is probably derived from tholeiitic basalt by magmatic differentiation in and immediately below the larger volcanoes. Distinction of oceanic tholeiites from almost all continental tholeiites is possible on the simple basis of total potassium content, with the discontinuity at 0.3 to 0.5 percent K(2)O by weight. Oceanic tholeiites also are readily distinguished from some 19 out of 20 basalts of oceanic islands and seamount cappings by having less than 0.3 percent K(2)O by weight and more than 48 percent SiO(2). Deep drilling into oceanic volcanoes should, however, core basalts transitional between the oceanic tholeiites and the presumed derivative alkali basalts. The composition of the oceanic tholeiites suggests that the mantle under the East Pacific Rise contains less than 0.10 percent potassium oxide by weight; 0.1 part per million of uranium and 0.4 part of thorium; a potassium:rubidium ratio of about 1200 and a potassium: uranium ratio of about 10(4).
10. Geochemistry of Mesoproterozoic Volcanic Rocks in the Western Kunlun Mountains:Evidence for Plate Tectonic Evolution
Institute of Scientific and Technical Information of China (English)
ZHANG Chuanlin; DONG Yongguan; ZHAO Yu; WANG Aiguo; GUO Kunyi
2003-01-01
Mesoproterozoic volcanic rocks occurring in the north of the western Kunlun Mountains can be divided into two groups. The first group (north belt) is an reversely-evolved bimodal series. Petrochemistry shows that the alkalinity of the rocks decreases from early to late: alkaline→calc-alkaline→tholeiite, and geochemistry proves that the volcanic rocks were formed in rifting tectonic systems. The sedimentary facies shows characteristics of back-arc basins. The second (south belt) group, which occurs to the south of Yutian-Minfeng-Cele, is composed of calc-alkaline island arc (basaltic) andesite and minor rhyolite. The space distribution, age and geochemistry of the two volcanite groups indicate that they were formed in a back-arc basin (the first group) and an island arc (the second group) respectively and indicate the plate evolution during the Mesoproterozoic. The orogeny took place at ～1.05 Ga, which was coeval with the Grenville orogeny. This study has provided important geological data for exploring the position of the Paleo-Tarim plate in the Rodinia super-continent.
11. Classification scheme for acid rock drainage detection - the Hamersley Basin, Western Australia
Science.gov (United States)
Skrzypek, Grzegorz; Dogramaci, Shawan; McLean, Laura
2017-04-01
In arid environment where precipitation and surface water are very limited, groundwater is the most important freshwater resource. For this reasons it is intensively exploited and needs to be managed wisely and protected from pollutants. Acid rock drainage often constitutes a serious risk to groundwater quality, particularly in catchments that are subject to mining, large scale groundwater injection or abstraction. However, assessment of the potential acid rock drainage risk can be challenging, especially in carbonate rich environment, where the decreasing pH that usually accompanies pyrite oxidation, can be masked by the high pH-neutralisation capacity of carbonate minerals. In this study, we analysed 73 surface and groundwater samples from different water bodies and aquifers located in the Hamersley Basin, Western Australia. Although the majority of samples had a neutral pH, there was a large spatial variability in the dissolved sulphate concentrations that ranged from 1 mg/L to 15,000 mg/L. Waters with high dissolved sulphate concentration were found in areas with a high percentage of sulphide minerals (e.g. pyrite) located within the aquifer matrix and were characterised by low δ34SSO4 values (+1.2‰ to +4.6) consistent with signatures of aquifer matrix pyritic rock samples (+1.9‰ to +4.4). It was also found that the SO4 concentrations and acidity levels were not only dependent on δ34SSO4 values and existence of pyrite but also on the presence of carbonate minerals in the aquifer matrix. Based on the results from this study, a classification scheme has been developed for identification of waters impacted by acid rock drainage that also encompasses numerous concomitant geochemical processes that often occur in aqueous systems. The classification uses five proxies: SO4, SO4/Cl, SI of calcite, δ34SSO4 and δ18OSO4 to improve assessment of the contribution that oxidation of sulphide minerals has to overall sulphate ion concentrations, regardless of acidity
12. Evaluation of geochemical mobility of heavy metals in the dump mine rocks Western Donbass
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Yatsechko N.Y.
2014-12-01
Full Text Available Typification of turn mine rocks of Western Donbas is conducted after a size acid-lye the index of water-soluble complex. It is set that exactly rocks with the low value of it an index characterized the most sizes of middle content of water-soluble forms of heavy metals. It is well-proven that exactly mine dumps are the generating source of contamination of objects of environment of this region by heavy metals. The significant impact on the environment inflicted not only directly in the process of coal mining, but for many years after its completion. The source of contamination of environmental objects are dumps that occupy large areas of fertile land. Every year in the dumps is stored about 40 million. m3 moldboard mine rock. Most of the waste coal industry have potential toxic and mutagenic properties as containing a significant amount of heavy metals, which are practically not biodegradable in the environment and is therefore especially dangerous for living organisms paramount importance score geochemical mobility of heavy metals, ie their property to move from solid to liquid phase, migrate to the natural landscape and absorbed by vegetation. This applies particularly to water-soluble forms of metals, as in warehousing surface mine dump piles of rocks, the priority factor that regulates the processes of migration of heavy metals are leaching precipitation of solid phase wastes. It is the existence and content of heavy metals in water-soluble complex characterized by their solubility and migration activity and can be used to assess the real extent of possible contamination of the hydrosphere.
13. Mechanism of rock deformation and failure and monitoring analysis in water-rich soft rock roadway of western China
Institute of Scientific and Technical Information of China (English)
MENG Qing-bin; HAN Li-jun; QIAO Wei-guo; LIN Deng-ge; YANG Ling
2012-01-01
Aiming to get the strata behavior and stability rules of surrounding rock of the main return airway of Yushujing Coal Mine,convergence deformation of two sides and force of U-shaped steel yieldable support and bolt were monitored,and deformation of surrounding rock and mechanical characteristics of support structure were timely obtained to guide the information construction and optimize supporting parameters in water-rich soft rock roadway.The field monitoring results indicate the following.(1) Convergence displacement of rock surface increases with time continuity and shows surrounding rock's intense rheological behavior.The original support scheme cannot control the large deformation and strongly rheological behavior;(2) Without backfilling,the U-shaped steel support begins to bear load after erecting for 4-7 days and increases rapidly in the first 30 days.The U-shaped steel support at the right shoulder and top of roadway bears a larger force and the left side and shoulder bears a smaller force; (3) The stress of bolt increasing over time and at the right shoulder of roadway has larger growth and value.The mechanism of rock deformation and the failure and strata behavior in water-rich soft rock roadway are revealed based on the results of the measured relaxation zone of surrounding rock,measured stresses,and the rock mechanics tests.
14. Igneous-sedimentary petroleum systems; Sistemas petroliferos igneo-sedimentares
Energy Technology Data Exchange (ETDEWEB)
Eiras, Jaime Fernandes [Para Univ., Belem, PA (Brazil)]. E-mail: eiras@ufpa.br; Wanderley Filho, Joaquim Ribeiro [PETROBRAS S.A., Manaus, AM (Brazil). Unidade de Negocios-BSOL]. E-mail: jwand@petrobras.com.br
2003-07-01
Igneous-sedimentary petroleum systems are mixed systems in which one or more essential elements or processes are related to magmatic events. Many examples worldwide are presented to show the importance of igneous rocks in the exploratory activities, as well as in the petroleum occurrence. Volcanic ash layers are of great importance in stratigraphic correlation and elucidation of structures, particularly when they occur in thick nonfossiliferous strata. They are also good indicators of turbidite deposition where turbidity currents are related to earthquakes generated by magmatic events. Unconventional reservoirs can be created by volcanic eruptions or intrusions, crystallization, reworking, and fracturing. Unaltered igneous rocks can seal vertically and laterally conventional reservoirs due to its excellent cap capacity. Abnormal thermal effect of igneous rocks can compensate the lack of overburden in shallow basins. Structural or combined traps can be formed due to intrusions, such as folded, faulted, and unconformity traps. Porosity can be either primary or secondary, or both. Primary porosity mainly consists of cavities produced by gas volatilization during eruption and cooling. Secondary porosity refers to those pores that result from hydrothermal alteration, recrystallization, and dissolution by groundwater, and tectonic stress. It includes intercrystalline pores formed by crystallization of various secondary minerals, dissolution pores, and tectonic fractures. New technologies of petroleum development and production are encouraging to search for oil and gas within igneous rocks, and new discoveries are expected. (author)
15. Cosmogenic helium in a terrestrial igneous rock
Science.gov (United States)
Kurz, M. D.
1986-01-01
New helium isotopic measurements on samples from the Kula formation of Haleakala volcano of Hawaii are presented that are best explained by an in situ cosmogenic origin for a significant fraction of the He-3. Results from crushing and stepwise heating experiments, and consideration of the exposure age of the sample at the surface and the cosmic ray fluxes strongly support this hypothesis. Although crustal cosmogenic helium has been proposed previously, this represents its first unambiguous identification in a terrestrial sample.
16. SNC meteorites - Igneous rocks from Mars
Science.gov (United States)
Wood, C. A.; Ashwal, L. D.
1982-01-01
It is argued that SNC (shergottite, nakhlite, chassignite) meteorites are ejecta from Mars. The mineralogy and chemistry of these objects is discussed, including rare earth element content, potassium/uranium ratios, oxidation state, oxygen isotopes, ages and isotopic evolution, magnetism, shock and texture. The possibility of SNC's deriving from Mercury, Venus, earth, moon, or a eucrite parent body is argued against. Mercury is too volatile-poor and anhydrous, Venus's atmosphere too thick and hot and its gravitational field too large, earth's oxygen isotope content too different from that of SNC's, the moon too different isotopically and chemically, and the ages of eucrites too different. Models suggest that SNC's could have escaped from Mars's gravitational field, and their composition supports Martian origin. Statistically, they could have reached the earth within their measured shock ages. Objections to the hypothesis are also discussed.
17. Basement rocks of Western Galicia as sources for the minerals in the Ría de Arosa
NARCIS (Netherlands)
Floor, P.
1966-01-01
The geology of the hercynian orogen in western Galicia is briefly outlined with special reference to the drainage area of the Ría de Arosa. The possible host rocks of translucent heavy minerals found in unconsolidated sediments within and around the ria are tabulated and discussed.
18. Basement rocks of Western Galicia as sources for the minerals in the Ría de Arosa
NARCIS (Netherlands)
Floor, P.
1966-01-01
The geology of the hercynian orogen in western Galicia is briefly outlined with special reference to the drainage area of the Ría de Arosa. The possible host rocks of translucent heavy minerals found in unconsolidated sediments within and around the ria are tabulated and discussed.
19. Amphibolites and other metamorphic mafic rocks of the blastomylonitic graben in Western Galicia, NW Spain: field relations and petrography
NARCIS (Netherlands)
Arps, C.E.S.
1981-01-01
Within the strongly migmatized axial zone of the Hesperian massif in western Galicia a graben-like structure has been distinguished, characterized essentially by the presence of non-migmatic rocks that comprise orthogneisses with blastomylonitic textures, leucocratic gneisses, plagioclase-blastbeari
20. Geochemistry Characteristics and Tectonic Significance of the Igneous Rocks from the Eastern Tianshan Mountains%东天山觉罗塔格一带晚古生代岩浆岩地球化学特征及构造意义
Institute of Scientific and Technical Information of China (English)
杨震; 古力巴哈尔·阿布都热西提; 木合塔尔·扎日; 舍建忠
2015-01-01
通过对东天山觉罗塔格一带晚古生代岩浆岩地质特征、岩石化学特征等系统研究，认为该晚古生代岩浆岩主要由早石炭世至中二叠世的火山岩和侵入岩组成，其形成与康古尔洋向北俯冲有关。早石炭世岩浆岩为康古尔洋初始俯冲而成的钙碱性岛弧火山岩及具有低压、低温特征的高钾钙碱性 I 型花岗岩；晚石炭世岩浆岩为后碰撞弧火山岩；早二叠世岩浆岩为具有后碰撞弧和板内双重特征的火山岩及高温、高压特征的 I 型花岗岩；中二叠世发育具有低压、高温特征的高钾钙碱性 A 型花岗岩。综合前人资料及本文研究成果，初步认为觉罗塔格一带晚古生代经历了俯冲碰撞—碰撞造山—造山后陆内伸展的构造演化过程。%This paper systematically summarized the geochemical characteristics of late Paleozoic igneous rocks in the Jueluotage area of Eastern Tianshan.The igneous rockis mainly formed by early Carboniferous to middle Permian volcanic and intrusive rocks,and its formation is relevant with the northward subduction of Kangguer ocean.The igneous rock of early Carboniferous is composed of calc-alkaline island arc volcanics formed in the initial stage of slab subduction and high-potassium calc-alkalineI-type granite with a characteristic of low temperature and low pres-sure.The igneous rock of late Carboniferous is post-collision arc volcanics.The igneous rock of early Permian is composed of the volcanic in the post-collision arc and intraplate environment,andI-type granite with a characteristic of high temperature and high pressure.The igneous rock of middle Permian is high-potassium calc-alkaline A-type granite with characteristics of high temper-ature and low pressure.The results of previous studies and this paper suggest that this region experienced a tectonic evolution from subduction-collision to collision-orogenesis and post-orogen-ic intracontinental extension in late
1. Attempts of whole-rock K/Ar dating of mesozoic volcanic and hypabissal igneous rocks from the Central Subbetic (Southern Spain: A case of differential Argon loss related to very low-grade metamorphism
Directory of Open Access Journals (Sweden)
Sanz de Galdeano, C.
1988-04-01
Full Text Available 12 samples of basic intrusives within Triassic rocks «ophites» and 11 samples of volcanic and associated intrusives within Jurassic to Early Cretaceous sequences of the Subbetic Zone were subjected to whole-rock K/Ar dating in combination with chemical/petrological analysis. Satisfactory results were obtained only from a number of samples of volcanic rocks, however, analytical ages commonly agree, within about 10 relative percent, with those deduced from stratigraphic location. «Ophite» samples, on the other hand, may reveal considerably lower analytic ages than the volcanics and show much stronger scattering, even among samples collected within a small area. It is argued that the inferred loss of Ar results from very-low-grade alpine metamorphic alteration, which affected the «ophites» more intensely than the higher volcanic rocks. Other post-emplacement chemical changes, such as the degree of secondary oxidation of Fe, are also distintive among the two groups of samples, and are to some extent consistent with the above view in that the alteration environment of the ophites should have produced conditions for more penetrative fluid-rock interactions and homogeneous recrystallization. Overall, the magmatic activity from which the ophitic rocks originated might have started in the Late Triassic and continued in the Lower Jurassic. 80th, the «ophites» and the volcanics are though to be the result of magmatic events Collowing tensional to transtensive crustal movements affecting the external basins of the Betic Cordilleras Crom Late Triassic to Early Cretaceous times.Doce muestras de cuerpos básicos intrusivos en rocas triásicas («ofitas» y 11 muestras de volcanitas y rocas intrusivas asociadas en secuencias jurásico-cretáceas de la zona Subbética han sido objeto de datación radiométrica K/Ar (roca total en combinación con análisis químico-petrográfico. Las edades analíticas obtenidas son 's
2. Teaching the Rock Cycle with Ease.
Science.gov (United States)
Bereki, Debra
2000-01-01
Describes a hands-on lesson for teaching high school students the concept of the rock cycle using sedimentary, metamorphic, and igneous rocks. Students use a rock cycle diagram to identify pairs of rocks. From the rock cycle, students explain on paper how their first rock became the second rock and vice versa. (PVD)
3. Geochemistry of Coesite-Bearing Pyrope Quartzites and Related Rocks From the Dora Maira Massif, Western Alps: New Results and the Enigma of the Jadeite-Rocks
Science.gov (United States)
Schertl, H.
2008-12-01
demonstrate that the whiteschist-type pyrope quartzites can be clearly distinguished chemically from metasedimentary whiteschists of former evaporite environments. Field relations of trails of pyrope quartzites, now forming lensoid inclusions within a former granite intrusion, would also make a metasedimentary origin rather unlikely. On the other hand, consistent genetical relationships between pyrope quartzites and their adjacent granitic country rocks were obtained, which virtually match those of Mg-metasomatic leucophyllites from the Eastern Alps occurring along shear zones within granitic gneisses. Similar Mg-rich rocks to be found within the Tauern Window and the Monte Rosa and Gran Paradiso Massivs of the Western Alps indicate that throughout the entire range of the Alps local processes of Mg-metasomatism occurred. References Chopin, C. (1984): Coesite and pure pyrope in high-grade blueschists of the Western Alps: a first record and some consequences. Contrib. Mineral. Petrol., 86, 107-118. Compagnoni, R. and Hirajima, T. (2001): Superzoned garnets in the coesite-bearing Brossasco-Isasca Unit, Dora-Maira massif, Western Alps, and the origin of the whiteschists. Lithos, 57, 219- 236. Schertl, H.-P. and Schreyer, W. (2008): Geochemistry of coesite-bearing "pyrope quartzites" and related rocks from the Dora-Maira Massif, Western Alps. Eur. J. Mineral., in press.
4. Mesozoic magmatism and timing of epigenetic Pb-Zn-Ag mineralization in the western Fortymile mining district, east-central Alaska: Zircon U-Pb geochronology, whole-rock geochemistry, and Pb isotopes
Science.gov (United States)
Dusel-Bacon, Cynthia; Aleinkoff, J.N.; Day, W.C.; Mortensen, J.K.
2015-01-01
The Mesozoic magmatic history of the North American margin records the evolution from a more segmented assemblage of parautochthonous and allochthonous terranes to the more cohesive northern Cordilleran orogenic belt. We characterize the setting of magmatism, tectonism, and epigenetic mineralization in the western Fortymile mining district, east-central Alaska, where parautochthonous and allochthonous Paleozoic tectonic assemblages are juxtaposed, using sensitive high-resolution ion microprobe (SHRIMP) U-Pb zircon geochronology, whole-rock geochemistry, and feldspar Pb isotopes of Mesozoic intrusions and spatially associated mineral prospects. New SHRIMP U-Pb zircon ages and published U-Pb and 40Ar/39Ar ages indicate four episodes of plutonism in the western Fortymile district: Late Triassic (216-208 Ma), Early Jurassic (199-181 Ma), mid-Cretaceous (112-94 Ma), and Late Cretaceous (70-66 Ma). All age groups have calc-alkalic arc compositions that became more evolved through time. Pb isotope compositions of feldspars from Late Triassic, Early Jurassic, and Late Cretaceous igneous rocks similarly became more radiogenic with time and are consistent with the magmas being mantle derived but extensively contaminated by upper crustal components with evolving Pb isotopic compositions. Feldspar Pb isotopes from mid-Cretaceous rocks have isotopic ratios that indicate magma derivation from upper crustal sources, probably thickened mid-Paleozoic basement. The origin of the mantle component in Late Cretaceous granitoids suggested by Pb isotopic ratios is uncertain, but we propose that it reflects asthenospheric upwelling following slab breakoff and sinking of an inactive inner subduction zone that delivered the previously accreted Wrangellia composite terrane to the North American continental margin, after the outer Farallon subduction zone was established.
5. Potash-rich volcanic rocks and lamprophyres in western Shandong Province: 40Ar39Ar dating and source tracing
Institute of Scientific and Technical Information of China (English)
2002-01-01
Highly precise 40Ar39Ar dating results demonstrate that the ages of potash-rich volcanic rocks in western Shandong Province are 114.7-124.3 Ma, and that of the lamprophyres is 119.6 Ma. The potash-rich volcanic rocks have relatively high (87Sr/86Sr)i ratios ( 0.708715-0.711418)and distinctly negative εNd values ( -11.47 - -17.54), and are enriched in radiogenic lead (206Pb/204pb=17.341-17.622,207pb/204Pb=15.525-15.538, 208Pb/204pb = 37.563-37.684).Similarly, the lamprophyres also have quite low εNd values ( -11.57 - -19.64). Based on the fact that the Sr, Nd and Pb isotopic compositions of potash-rich volcanic rocks are very consistent with that of the clinopyroxene separates, and by integrating comprehensive analyses of their tectonic settings,and extensive comparisons of the Sr, Nd isotopic compositions with that of the related simultaneous rocks, it is concluded that the potash-rich volcanic rocks and lamprophyres in western Shandong Province were most possibly derived from the partial melting of enriched mantle which was caused by source contamination and metasomatism of subducted continental crustal materials.
6. Contrasting styles of (U)HP rock exhumation along the Cenozoic Adria-Europe plate boundary (Western Alps, Calabria, Corsica)
Science.gov (United States)
Malusà, Marco G.; Faccenna, Claudio; Baldwin, Suzanne L.; Fitzgerald, Paul G.; Rossetti, Federico; Balestrieri, Maria Laura; Danišík, Martin; Ellero, Alessandro; Ottria, Giuseppe; Piromallo, Claudia
2015-06-01
Since the first discovery of ultrahigh pressure (UHP) rocks 30 years ago in the Western Alps, the mechanisms for exhumation of (U)HP terranes worldwide are still debated. In the western Mediterranean, the presently accepted model of synconvergent exhumation (e.g., the channel-flow model) is in conflict with parts of the geologic record. We synthesize regional geologic data and present alternative exhumation mechanisms that consider the role of divergence within subduction zones. These mechanisms, i.e., (i) the motion of the upper plate away from the trench and (ii) the rollback of the lower plate, are discussed in detail with particular reference to the Cenozoic Adria-Europe plate boundary, and along three different transects (Western Alps, Calabria-Sardinia, and Corsica-Northern Apennines). In the Western Alps, (U)HP rocks were exhumed from the greatest depth at the rear of the accretionary wedge during motion of the upper plate away from the trench. Exhumation was extremely fast, and associated with very low geothermal gradients. In Calabria, HP rocks were exhumed from shallower depths and at lower rates during rollback of the Adriatic plate, with repeated exhumation pulses progressively younging toward the foreland. Both mechanisms were active to create boundary divergence along the Corsica-Northern Apennines transect, where European southeastward subduction was progressively replaced along strike by Adriatic northwestward subduction. The tectonic scenario depicted for the Western Alps trench during Eocene exhumation of (U)HP rocks correlates well with present-day eastern Papua New Guinea, which is presented as a modern analog of the Paleogene Adria-Europe plate boundary.
7. Processes and mechanisms governing hard rock cliff erosion in western Brittany, France
Science.gov (United States)
Laute, Katja; Letortu, Pauline; Le Dantec, Nicolas
2017-04-01
The evolution of rocky coasts is controlled by the interplay between subaerial, marine as well as biological processes, and the geological context. In times of ongoing climate change it is difficult to predict how these erosional landscapes will respond for example to anticipated sea-level rise or to an increase in storminess. However, it can be expected that changes in the morphodynamics of rocky coasts will have a noticeable effect on society and infrastructure. Recent studies have proven that monitoring cliff micro-seismic ground motion has been very effective in exploring both marine and atmospheric actions on coastal cliffs. But only few studies have focused so far on the effects of wave loading and water circulation (runoff, infiltration, water table variations) on cliff stability and subsequent erosion, considering the interaction between subaerial and marine processes. This project focuses on the identification and quantification of environmental controls on hard rock cliff erosion with an emphasis on discriminating the relative contributions of subaerial and marine processes. We aim at relating different sources of mechanical stress (e.g. wave loading, direct wave impact, hydrostatic pressure, thermal expansion) to cliff-scale strain (cliff-top swaying and shaking) and micro-fracturing (generation, expansion and contraction of micro-cracks) with the objective to unravel and discriminate triggering mechanisms of cliff failure. A four-month monitoring field experiment during the winter period (February-May) of 2017 is carried out at a cliff face located in Porsmilin beach (western Brittany, France). The selected cliff section is exposed to Atlantic swell from the south/southwest with a significant wave height of ca. 1.5 m on average and, reaching up to 4 m during storm events. The cliff rises ca. 20 m above the beach and is mainly formed of orthogneiss with intrusions of granodiorite. The entire cliff is highly fractured and altered, which can promote slope
8. Diverse Igneous Protolith Contributions to Sediments in Gale Crater: Variable Metasomatism of the Mars Mantle
Science.gov (United States)
Schmidt, M. E.; Izawa, M. R. M.; Thomas, A. P.; Thompson, L.; Gellert, R.
2016-08-01
Igneous float rocks and least altered basaltic sedimentary bedrock examined in Gale Crater provide insight to the petrogenesis of the crystalline basement and suggest the mantle source was alkali and Ni-enriched by an oxidizing metasomatic event.
9. Palaeomagnetic, rock-magnetic and mineralogical investigations of metadolerites from Western Svalbard : A preliminary report
Science.gov (United States)
Michalski, Krzysztof; Nejbert, Krzysztof; Domańska-Siuda, Justyna; Manby, Geoffrey
2014-05-01
A group of 42 independently oriented palaeomagnetic samples from 7 sites located in central part of the West Spitsbergen Thrust and Fault Belt has been investigated. The samples were collected from 5 distinct metadolerite sheets intruded into the Proterozoic - Lower Paleozoic metamorphic complex of Western Oscar II Land (Western Svalbard Caledonian Terrane - Harland, 1997 division). All analyzed metadolerite samples were metamorphosed under greenschist facies metamorphism. The metamorphic assemblage consist of hornblende, biotite, actinolite, chlorite, epidote, stilpnomelane, titanite, albite, and quartz. Calcite, associated with pyrrhotite, pyrite chalcopyrite, sphalerite, and covellite, that occurs as irregular intergrowths or thin veins, document high activity of H2O-CO2-rich fluids during metamorphism. Primary magmatic phases represented by clinopyroxene occur rarely, and only in thick metadolerite dykes. Accessory oxides change their mineralogical and chemical composition during metamorphism. In all examined samples primary Ti-magnetite and oxy-exsolved hematite break-down completely into titanite or have been dissolved. The ilmenite are also replaced by titanite, but in metadolerites at contact with host metapelites, slightly altered ilmenite grains with preserved hematite exsolution were documented. Basing on mineralogical observations it should be expected that metamorphic processes have almost completely reset the paleomagnetic data record from the time of dolerite crystallization. This stage can document only rare hematite oxy-exsolution preserved within ilmenite, and presumably small inclusion of magnetite still preserved within unaltered clinopyroxene. The paleomagnetic record of metamorphic stage is probably recorded by pyrrhotite, hematite, goethite, and late Ti-free magnetite that can grow during breakdown of pyrrhotite to pyrite (Ramdohr. 1980). The NRM (Natural Remanent Magnetisation) intensities of the palaeomagnetic samples exceed the minimum 10
10. Depositional settings, correlation, and age carboniferous rocks in the western Brooks Range, Alaska
Science.gov (United States)
Dumoulin, J.A.; Harris, A.G.; Blome, C.D.; Young, L.E.
2004-01-01
The Kuna Formation (Lisburne Group) in northwest Alaska hosts the Red Dog and other Zn-Pb-Ag massive sulfide deposits in the Red Dog district. New studies of the sedimentology and paleontology of the Lisburne Group constrain the setting, age, and thermal history of these deposits. In the western and west-central Brooks Range, the Lisburne Group includes both deep- and shallow-water sedimentary facies and local volcanic rocks that are exposed in a series of thrust sheets or allochthons. Deep-water facies in the Red Dog area (i.e., the Kuna Formation and related rocks) are found chiefly in the Endicott Mountains and structurally higher Picnic Creek allochthons. In the Red Dog plate of the Endicott Mountains allochthon, the Kuna consists of at least 122 m of thinly interbedded calcareous shale, calcareous spiculite, and bioclastic supportstone (Kivalina unit) overlain by 30 to 240 m of siliceous shale, mudstone, calcareous radiolarite, and calcareous lithic turbidite (Ikalukrok unit). The Ikalukrok unit in the Red Dog plate hosts all massive sulfide deposits in the area. It is notably carbonaceous, is generally finely laminated, and contains siliceous sponge spicules and radiolarians. The Kuna Formation in the Key Creek plate of the Endicott Mountains allochthon (60-110 m) resembles the Ikalukrok unit but is unmineralized and has thinner carbonate layers that are mainly organic-rich dolostone. Correlative strata in the Picnic Creek allochthon include less shale and mudstone and more carbonate (mostly calcareous spiculite). Conodonts and radiolarians indicate an age range of Osagean to early Chesterian (late Early to Late Mississippian) for the Kuna in the Red Dog area. Sedimentologic, faunal, and geochemical data imply that most of the Kuna formed in slope and basin settings characterized by anoxic or dysoxic bottom water and by local high productivity. Shallow-water facies of th e Lisburne Group in the Red Dog area are present locally in the Endicott Mountains
11. Western rock lobsters ( Panulirus cygnus) in Western Australian deep coastal ecosystems (35-60 m) are more carnivorous than those in shallow coastal ecosystems
Science.gov (United States)
Waddington, Kris I.; Bellchambers, Lynda M.; Vanderklift, Mathew A.; Walker, Diana I.
2008-08-01
The western rock lobster ( Panurilus cygnus George.) is a conspicuous consumer in the coastal ecosystems of temperate Western Australia. We used stable isotope analysis and gut content analysis to determine the diet and trophic position of western rock lobsters from mid-shelf coastal ecosystems (35-60 m depth) at three locations. Lobsters were primarily carnivorous, and no consistent differences in diet were detected with varying lobster size, sex or among locations. The main components of the diet were bait (from the fishery) and small crustaceans - crabs and amphipods/isopods. Foliose red algae, bivalves/gastropods and sponges were minor contributors to diet. The diet of lobsters in deep coastal ecosystems differed from the results of previous studies of diets of lobsters from shallow coastal ecosystems. In particular, coralline algae and molluscs - important prey in studies of lobsters from shallow coastal ecosystems - were minor components of the diet. These differences are likely to reflect differences in food availability between these systems and potentially, differences in choice of prey by lobsters that inhabit deeper water. Given the high contribution of bait to lobster diet, bait is likely to be subsidizing lobster production in deep coastal ecosystems during the fishing season.
12. The age and tectonic environment of the rhyolitic rocks on the western side of Wuyi Mountain, South China
Institute of Scientific and Technical Information of China (English)
SHU LiangShu; DENG Ping; YU JinHai; WANG YanBin; JIANG ShaoYong
2008-01-01
During the geological survey of the metamorphic rocks in Xingning-Wuhua region on the western side of Wuyi Mountain, South China, we discovered the Neoproterozoic rhyolite and rhyolitic greywacke for the first time that outcrop in the Proterozoic metamorphic rocks near Jingnan Town of Xingning County,eastern Guangdong Province. A systematic research on petrology, geochemistry and geochronology of rhyolitic rocks was conducted to understand their tectonic setting and formation age. The Jingnan rhyolite is interbedded with a coeval greywacke, with a total thickness of 60 m; both rhyolite and greywacke display a similar folding and metamorphic pattern. Meta-rhyolite consists of groundmass and phenocrystals including sanidine, orthoclase, and quartz with distinct undulose extinction; the groundmass has been re-crystallized into fine-grain feldspar, quartz and sericite aggregation.Meta-greywacke is composed of crystallinoclastic grains (sanidine, orthoclase, quartz and oligoclase)and clay groundmass. Zircon grains used for the SHRIMP U-Pb analysis are light brown-colored and euhedral or sub-euhedral. Dating data suggest two age groups; eight grains of magma-type zircon with an idiomorphic form yield an age of 972±8 Ma, and the other seven weakly corroded grains of zircon with euhedral to subeuhedral shape construct an average age of 1097±11 Ma, which were captured from older rocks by an uplifting magma, implying that a late Mesoproterozoic basement exists in the Nanling region. In addition, one Paleoproterozoic age, 2035±11 Ma, is obtained from a rounded detrital zircon,indicating that a Paleoproterozoic thermal event took place in the South China. Geochemically, the Jingnan rhyolitic rocks are characterized by high K2O content, intermediate Al2O3 content, with the ACNK value 0.98-1.11, and belonging to high-K alkaline series. They are rich in ∑REE, Rb, Th and Ce,depleted in Ba, Sr, Eu, Ti, P and Nb-Ta, and with moderate negative Eu and Sr anomalies. These features
13. The age and tectonic environment of the rhyolitic rocks on the western side of Wuyi Mountain,South China
Institute of Scientific and Technical Information of China (English)
2008-01-01
During the geological survey of the metamorphic rocks in Xingning-Wuhua region on the western side of Wuyi Mountain, South China, we discovered the Neoproterozoic rhyolite and rhyolitic greywacke for the first time that outcrop in the Proterozoic metamorphic rocks near Jingnan Town of Xingning County, eastern Guangdong Province. A systematic research on petrology, geochemistry and geochronology of rhyolitic rocks was conducted to understand their tectonic setting and formation age. The Jingnan rhyolite is interbedded with a coeval greywacke, with a total thickness of 60 m; both rhyolite and greywacke display a similar folding and metamorphic pattern. Meta-rhyolite consists of groundmass and phenocrystals including sanidine, orthoclase, and quartz with distinct undulose extinction; the groundmass has been recrystallized into fine-grain feldspar, quartz and sericite aggregation. Meta-greywacke is composed of crystallinoclastic grains (sanidine, orthoclase, quartz and oligoclase) and clay groundmass. Zircon grains used for the SHRIMP U-Pb analysis are light brown-colored and euhedral or subeuhedral. Dating data suggest two age groups; eight grains of magmatype zircon with an idiomorphic form yield an age of 972±8 Ma, and the other seven weakly corroded grains of zircon with euhedral to subeuhedral shape construct an average age of 1097±11 Ma, which were captured from older rocks by an uplifting magma, implying that a late Mesoproterozoic basement exists in the Nanling region. In addition, one Paleoproterozoic age, 2035±11 Ma, is obtained from a rounded detrital zircon, indicating that a Paleoproterozoic thermal event took place in the South China. Geochemically, the Jingnan rhyolitic rocks are characterized by high K2O content, intermediate Al2O3 content, with the ACNK value 0.98―1.11, and belonging to high-K alkaline series. They are rich in ΣREE, Rb, Th and Ce, depleted in Ba, Sr, Eu, Ti, P and Nb-Ta, and with moderate negative Eu and Sr anomalies. These
14. Hydraulic properties and scale effects investigation in regional rock aquifers, south-western Quebec, Canada
Science.gov (United States)
Nastev, M.; Savard, M. M.; Lapcevic, P.; Lefebvre, R.; Martel, R.
This paper reports on the characterization of hydraulic properties of regional rock aquifers carried out within a groundwater resources assessment project in the St. Lawrence Lowlands of south-western Quebec. To understand the aquifer behavior at both the fracture level and at field scale, hydraulic investigations were carried out using various aquifer tests. The groundwater flow at the local scale is controlled mostly by the fracture system. Results of the constant-head injection tests show a weak decreasing trend of hydraulic conductivity with depth indicating that a major part of the groundwater flow occurs in the first meters of the rock sequence. At the regional scale, the equivalent porous media approach is applicable. The hydraulic conductivity measurements were correlated to the scale of the aquifer tests expressed with the investigated aquifer volume. A simple interpolation procedure for the hydraulic conductivity field was developed based on the distance between field measurements and the tested aquifer volumes. The regional distribution of the hydraulic conductivity for the major fractured aquifer units indicates that dolostone is the most permeable whereas sandstone and crystalline rocks are the least permeable units. Este artículo trata de la caracterización de las propiedades hidráulicas en acuíferos regionales rocosos, la cual se llevó a cabo dentro del proyecto de evaluación de los recursos de agua subterránea en St. Lawrence Lowlands al suroeste de Quebec. Para entender el comportamiento del acuífero tanto a nivel de fractura como a escala del campo, se ejecutaron investigaciones hidráulicas usando varias pruebas de acuífero. El flujo del agua subterránea a escala local está controlado principalmente por el sistema de fracturas. Los resultados de las pruebas de inyección con cabeza constante muestran una tendencia decreciente débil de la conductividad hidráulica con la profundidad, indicando que la mayor parte del flujo de agua
15. Rock strength measurements on Archaean basement granitoids recovered from scientific drilling in the active Koyna seismogenic zone, western India
Science.gov (United States)
Goswami, Deepjyoti; Akkiraju, Vyasulu V.; Misra, Surajit; Roy, Sukanta; Singh, Santosh K.; Sinha, Amalendu; Gupta, Harsh; Bansal, B. K.; Nayak, Shailesh
2017-08-01
Reservoir triggered earthquakes have been occurring in the Koyna area, western India for the past five decades. Triaxial tests carried out on 181 core samples of Archaean granitoids underlying the Deccan Traps provide valuable constraints on rock strength properties in the Koyna seismogenic zone for the first time. The data include measurements on granite gneiss, granite, migmatitic gneiss and mylonitised granite gneiss obtained from boreholes KBH-3, KBH-4A, KBH-5 and KBH-7 located in the western and eastern margins of the seismic zone. Salient results are as follows. (i) Increase of rock strength with increasing confining pressure allow determination of the linearized failure envelopes from which the cohesive strength and angle of internal friction are calculated. (ii) Variable differential stresses at different depths are the manifestations of deformation partitioning in close association of fault zone(s) or localized fracture zones. (iii) Fractures controlled by naturally developed weak planes such as cleavage and fabric directly affect the rock strength properties, but the majority of failure planes developed during triaxial tests is not consistent with the orientations of pre-existing weak planes. The failure planes may, therefore, represent other planes of weakness induced by ongoing seismic activity. (iv) Stress-strain curves confirm that axial deformation is controlled by the varying intensity of pre-existing shear in the granitoids, viz., mylonite, granite gneiss and migmatitic gneiss. (v) Frequent occurrences of low magnitude earthquakes may be attributed to low and variable rock strength of the granitoids, which, in turn, is modified by successive seismic events.
16. Origin and accumulation mechanisms of petroleum in the Carboniferous volcanic rocks of the Kebai Fault zone, Western Junggar Basin, China
Science.gov (United States)
Chen, Zhonghong; Zha, Ming; Liu, Keyu; Zhang, Yueqian; Yang, Disheng; Tang, Yong; Wu, Kongyou; Chen, Yong
2016-09-01
The Kebai Fault zone of the West Junggar Basin in northwestern China is a unique region to gain insights on the formation of large-scale petroleum reservoirs in volcanic rocks of the western Central Asian Orogenic Belt. Carboniferous volcanic rocks are widespread in the Kebai Fault zone and consist of basalt, basaltic andesite, andesite, tuff, volcanic breccia, sandy conglomerate and metamorphic rocks. The volcanic oil reservoirs are characterized by multiple sources and multi-stage charge and filling history, characteristic of a complex petroleum system. Geochemical analysis of the reservoir oil, hydrocarbon inclusions and source rocks associated with these volcanic rocks was conducted to better constrain the oil source, the petroleum filling history, and the dominant mechanisms controlling the petroleum accumulation. Reservoir oil geochemistry indicates that the oil contained in the Carboniferous volcanic rocks of the Kebai Fault zone is a mixture. The oil is primarily derived from the source rock of the Permian Fengcheng Formation (P1f), and secondarily from the Permian Lower Wuerhe Formation (P2w). Compared with the P2w source rock, P1f exhibits lower values of C19 TT/C23 TT, C19+20TT/ΣTT, Ts/(Ts + Tm) and ααα-20R sterane C27/C28 ratios but higher values of TT C23/C21, HHI, gammacerane/αβ C30 hopane, hopane (20S) C34/C33, C29ββ/(ββ + αα), and C29 20S/(20S + 20R) ratios. Three major stages of oil charge occurred in the Carboniferous, in the Middle Triassic, Late Triassic to Early Jurassic, and in the Middle Jurassic to Late Jurassic periods, respectively. Most of the oil charged during the first stage was lost, while moderately and highly mature oils were generated and accumulated during the second and third stages. Oil migration and accumulation in the large-scale stratigraphic reservoir was primarily controlled by the top Carboniferous unconformity with better porosity and high oil enrichment developed near the unconformity. Secondary dissolution
17. Speciation in fractured rock landforms: towards understanding the diversity of subterranean cockroaches (Dictyoptera: Nocticolidae: Nocticola) in Western Australia.
Science.gov (United States)
Trotter, Andrew J; McRAE, Jane M; Main, Dean C; Finston, Terrie L
2017-04-04
Three new species of subterranean cockroach of the genus Nocticola from the Pilbara region of Western Australia are described on morphological characters of males. Nocticola quartermainei n. sp., Nocticola cockingi n. sp. and Nocticola currani n. sp. occur in fractured rock landforms and have varying degrees of troglomorphies. Sequence divergence of mitochondrial cytochrome c oxidase subunit I (COXI) clearly demonstrated populations are reproductively isolated over very short distances for the highly troglomorphic Nocticola cockingi n. sp. and Nocticola currani n. sp. and conversely, there is less isolation within the same landforms for the less troglomorphic Nocticola quartermainei n. sp.
18. THE GEOCHEMISTRY AND AGES OF ROCKS IN THE FOOTWALL OF THE BUTULIYN-NUR AND ZAGAN METAMORPHIC CORE COMPLEXES (NORTH MONGOLIA – WESTERN TRANSBAIKALIA
Directory of Open Access Journals (Sweden)
T. V. Donskaya
2015-09-01
Full Text Available This article reviews data on ages of rocks in the footwall of the Butuliyn-Nur and Zagan metamorphic core complexes (MCC and provides new data on the geochemistry of the rock complexes. It is noted that the oldest rocks are mylonitized gneisses on rhyolites (554 Ma in the footwall of the Butuliyn-Nur MCC. The Late Permian – Triassic (249–211 Ma igneous rocks are ubiquitous in the footwall of the Butuliyn-Nur and Zagan MCC. The youngest rocks in the studied MCC are the Jurassic granitoids (178–152 Ma of the Naushki and Verhnemangirtui massifs. In the footwall of the Butuliyn-Nur and Zagan MCC, the most common are granitoids and felsic volcanic rocks (249–211 Ma with many similar geochemical characteristics, such as high alkalinity, high contents of Sr and Ba, moderate and low concentrations of Nb and Y. Considering the contents of trace elements and REE, the granitoids and the felsic volcanic rocks are similar to I-type granites. Specific compositions of these rocks suggest that they might have formed in conditions of the active continental margin of the Siberian continent over the subducting oceanic plate of the Mongol-Okhotsk Ocean. The granitoids of the Naushki and Verhnemangirtui massifs, which are the youngest of the studied rocks (178–152 Ma, also have similar geochemical characteristics. In both massif, granitoids are ferriferous, mostly alkaline rocks. By contents of both major and trace elements, they are comparable to A-type granites. Such granitoids formed in conditions of intracontinental extension while subduction was replaced by collision. Based on ages and geochemical characteristics of the rocks in the footwall of the Butuliyn-Nur and Zagan MCC, a good correlation is revealed between the studied rocks and the rock complexes of the Transbaikalian and North-Mongolian segments of the Central Asian fold belt (CAFB, and it can thus be suggested that the regions under study may have a common evolutionary history.
19. Petrogenesis of Cenozoic Volcanic Rocks in Tengchong Region of Western Yunnan Province,China
Institute of Scientific and Technical Information of China (English)
从柏林; 陈秋媛; 张儒瑷; 吴根耀; 徐平
1994-01-01
The Tengchong Cenozoic volcanic rocks belong to the high-K calc-alkaline rock series.They are strongly depleted in high field strength (HFS) elements and enriched in large-ion lithophile(LIL) elements and LREE.The generation of Tengchong volcanic rocks has been considered to be relatedto the evolution of the Neo-Tethys.The Indian Plate was subducted beneath the southeastern Asia conti-nent,which resulted in the formation of Indo-Burman Arc in the Late Cretaeeous-Palaeocene time.Thecollision between the Indian continent and Indo-Burman Arc started in Eocene and lasted to the present.The Andaman Sea and the Inner Burman Tertiary Basin are a back-arc basin that has been extended sincethe Late Miocene.A distinct characteristic of Tengchong volcanics is that they show a chemical affinityrelated to island arc but their generation postdated the subduetion of the ocean plate.
20. Palaeozoic and Mesozoic igneous activity in the Netherlands: a tectonomagmatic review
NARCIS (Netherlands)
Sissingh, W.
To date, igneous rocks, either intrusive or extrusive, have been encountered in the Palaeozoic-Mesozoic sedimentary series of the Netherlands in some 65 exploration and production wells. Following 17 new isotopic K/Ar age determinations of the recovered rock material (amounting to a total of 28
1. Palaeozoic and Mesozoic igneous activity in the Netherlands: a tectonomagmatic review
NARCIS (Netherlands)
Sissingh, W.
2004-01-01
To date, igneous rocks, either intrusive or extrusive, have been encountered in the Palaeozoic-Mesozoic sedimentary series of the Netherlands in some 65 exploration and production wells. Following 17 new isotopic K/Ar age determinations of the recovered rock material (amounting to a total of 28 isot
2. Palaeozoic and Mesozoic igneous activity in the Netherlands: a tectonomagmatic review
NARCIS (Netherlands)
Sissingh, W.
2004-01-01
To date, igneous rocks, either intrusive or extrusive, have been encountered in the Palaeozoic-Mesozoic sedimentary series of the Netherlands in some 65 exploration and production wells. Following 17 new isotopic K/Ar age determinations of the recovered rock material (amounting to a total of 28 isot
3. Map data and Unmanned Aircraft System imagery from the May 25, 2014 West Salt Creek rock avalanche in western Colorado
Science.gov (United States)
Coe, Jeffrey A.; Baum, Rex L.; Allstadt, Kate; Kochevar, Bernard; Schmitt, Robert G.; Morgan, Matthew L.; White, Jonathan L.; Stratton, Benjamin T.; Hayashi, Timothy A.; Kean, Jason W.
2016-01-01
On May 25, 2014, a rain-on-snow induced rock avalanche occurred in the West Salt Creek Valley on the northern flank of Grand Mesa in western Colorado. The avalanche traveled 4.6 km down the confined valley, killing 3 people. The avalanche was rare for the contiguous U.S. because of its large size (54.5 Mm3) and long travel distance. To understand the avalanche failure sequence, mechanisms, and mobility, we mapped landslide structures, geology, and ponds at 1:1000-scale. We used high-resolution, Unmanned Aircraft System (UAS) imagery from July 2014 as a base for our field mapping. Here we present the map data and UAS imagery. The data accompany an interpretive paper published in the journal Geosphere. The full citation for this interpretive journal paper is: Coe, J.A., Baum, R.L., Allstadt, K.E., Kochevar, B.F., Schmitt, R.G., Morgan, M.L., White, J.L., Stratton, B.T., Hayashi, T.A., and Kean, J.W., 2016, Rock avalanche dynamics revealed by large-scale field mapping and seismic signals at a highly mobile avalanche in the West Salt Creek Valley, western Colorado: Geosphere, v. 12, no. 2, p. 607-631, doi:10.1130/GES01265.1.
4. Complicated secondary textures in zircon record evolution of the host granitic rocks: Studies from Western Tauern Window and Ötztal-Stubai Crystalline Complex (Eastern Alps, Western Austria)
Science.gov (United States)
Kovaleva, Elizaveta; Harlov, Daniel; Klötzli, Urs
2017-07-01
Samples of metamorphosed and deformed granitic rocks were collected from two Alpine complexes with well-constrained metamorphic history: Western Tauern Window and Ötztal-Stubai Crystalline Complex. Zircon grains from these samples were investigated in situ by a combination of scanning electron microscope techniques, cathodoluminescence (CL) imaging and Raman spectroscopy. The aims were: to describe and interpret complicated secondary textures and microstructures in zircon; based on cross-cutting relationships between secondary microstructures, reconstruct the sequence of processes, affecting zircon crystals; link the evolution of zircon with the history of the host rocks. The results indicate that zircon in the sampled granitic rocks forms growth twins and multi-grain aggregates, which are unusual for this mineral. Moreover, various secondary textures have been found in the sampled zircon, often cross-cutting each other in a single crystal. These include: distorted oscillatory CL zoning with inner zones forming inward-penetrating, CL-bright embayments, which are the evidence of dry recrystallization via annealing/lattice recovery; CL mosaicism with no preservation of growth zoning, but abundant nano- and micro-scale pores and mineral inclusions, which are the evidence of recrystallization by coupled dissolution-reprecipitation and/or leaching; embayed zircon boundaries filled with apatite, monazite, epidote and mylonitic matrix, indicating mineral-fluid reactions resulting in zircon dissolution and fragmentation; overgrowth CL-dark rims, which contain nano-pores and point to transport and precipitation of dissolved zircon matter. We conclude that zircon in our meta-granites is sensitive to metamorphism/deformation events, and was reactive with metamorphic fluids. Additionally, we have found evidence of crystal-plastic deformation in the form of low angle boundaries and bent grain tips, which is a result of shearing and ductile deformation of the host rock. We
5. The Emeishan large igneous province:A synthesis
Institute of Scientific and Technical Information of China (English)
J.Gregory Shellnutt
2014-01-01
The late Permian Emeishan large igneous province (ELIP) covers w0.3 ? 106 km2 of the western margin of the Yangtze Block and Tibetan Plateau with displaced, correlative units in northern Vietnam (Song Da zone). The ELIP is of particular interest because it contains numerous world-class base metal deposits and is contemporaneous with the late Capitanian (w260 Ma) mass extinction. The flood basalts are the signature feature of the ELIP but there are also ultramafic and silicic volcanic rocks and layered mafic-ultramafic and silicic plutonic rocks exposed. The ELIP is divided into three nearly concentric zones (i.e. inner, middle and outer) which correspond to progressively thicker crust from the inner to the outer zone. The eruptive age of the ELIP is constrained by geological, paleomagnetic and geochronological evidence to an interval of ≤3 Ma. The presence of picritic rocks and thick piles of flood basalts testifies to high temperature thermal regime however there is uncertainty as to whether these magmas were derived from the subcontinental lithospheric mantle or sub-lithospheric mantle (i.e. asthenosphere or mantle plume) sources or both. The range of Sr (ISr≈0.7040e0.7132), Nd (3Nd(t)≈?14 to þ8), Pb (206Pb/204Pb1 ≈ 17.9e20.6) and Os (gOs ≈5 to þ11) isotope values of the ultramafic and mafic rocks does not permit a conclusive answer to ultimate source origin of the primitive rocks but it is clear that some rocks were affected by crustal contamination and the presence of near-depleted isotope compo-sitions suggests that there is a sub-lithospheric mantle component in the system. The silicic rocks are derived by basaltic magmas/rocks through fractional crystallization or partial melting, crustal melting or by interactions between mafic and crustal melts. The formation of the Fe-Ti-V oxide-ore deposits is probably due to a combination of fractional crystallization of Ti-rich basalt and fluxing of CO2-rich fluids whereas the Ni-Cu-(PGE) deposits are
6. Oxygen and hydrogen isotope compositions of eclogites and associated rocks from the Eastern Sesia zone (Western Alps, Italy)
Science.gov (United States)
Desmons, J.; O'Neil, J.R.
1978-01-01
Oxygen and hydrogen isotope analyses have been made of mineral separates from eclogites, glaucophanites and glaucophane schists from the eastern Sesia zone (Italian Western Alps). Regularities in (1) hydrogen isotope compositions, (2) order of 18O enrichment among coexisting minerals, and (3) ?? 18O (quartz-rutile) and ?? 18O (quartz-phengite) imply attainment of a high degree of isotopic equilibrium. However, some scattering of ??18O values of individual minerals indicates that the eclogitic assemblage did not form in the presence of a thoroughly pervasive fluid. Minerals from an eclogitic lens enclosed in marble have ??18O values distinctly different from those measured in the other rocks. The ??18O values are high in comparison with other type C eclogites of the world, and it is proposed that the fluid present during the high pressure metamorphism has to a large extent been inherited from the precursor rocks of amphibolite facies. An average formation temperature of 540 ?? C is inferred from the oxygen isotope fractionations between quartz and rutile and between quartz and white mica. This temperature is in accordance with petrologic considerations and implies subduction of the precursor rocks into the upper mantle to achieve the high pressures required. ?? 1978 Springer-Verlag.
7. Forensic Analysis of the May 2014 West Salt Creek Rock Avalanche in Western Colorado
Science.gov (United States)
Coe, J. A.; Baum, R. L.; Allstadt, K.; Kochevar, B. F.; Schmitt, R. G.; Morgan, M. L.; White, J. L.; Stratton, B. T.; Hayashi, T. A.; Kean, J. W.
2015-12-01
The rain-on-snow induced West Salt Creek rock avalanche occurred on May 25, 2014 on the northern flank of Grand Mesa. The avalanche was rare for the contiguous U.S. because of its large size (59 M m3) and high mobility (Length/Height=7.2). To understand the avalanche failure sequence, mechanisms, and mobility, we conducted a forensic analysis using large-scale (1:1000) structural mapping and seismic data. We used high-resolution, Unmanned Aircraft System (UAS) imagery as a base for our field mapping and analyzed seismic data from 22 broadband stations (distances avalanche exerted on the earth and tracked these forces using curves in the avalanche path. Our results revealed that the rock avalanche was a cascade of landslide events, rather than a single massive failure. The sequence began with a landslide/debris flow that started about 10 hours before the main avalanche. The main avalanche lasted just over 3 minutes and traveled at average velocities ranging from 15 to 36 m/s. For at least two hours after the avalanche ceased movement, a central, hummock-rich, strike-slip bound core continued to move slowly. Following movement of the core, numerous shallow landslides, rock slides, and rock falls created new structures and modified topography. Mobility of the main avalanche and central core were likely enhanced by valley floor material that liquefied from undrained loading by the overriding avalanche. Although the base was likely at least partially liquefied, our mapping indicates that the overriding avalanche internally deformed predominantly by sliding along discrete shear surfaces in material that was nearly dry and had substantial frictional strength. These results indicate that the West Salt Creek avalanche, and probably other long-traveled avalanches, could be modeled as two layers: a liquefied basal layer; and a thicker and stronger overriding layer.
8. Formation Conditions and Distribution Regularities of Oil—gas Pools in Tertiary Volcanic Rocks in Western Huimin Depression,Shandong Province
Institute of Scientific and Technical Information of China (English)
刘泽容; 王永杰; 等
1989-01-01
The formation conditions and distribution regularities of oil-gas pools in volcanic rocks in western Huimin Depression have been studied in terms of geolgic,sesmic and well logging information,This paper discusses the types and lithofacies,development and distribution of Tertiary volcanic rocks in the area.The results demonstrate that volcanic activity occurred mainly during the period from the Sha-4 stage to the Guantao episode,i.e.,before the oil-generating period(before the end of the Guantao episode and the Minghuazhen episode).The activity did not destroy oil and gas formation and accumulation,but was favourable for the concentration of organic matter and its conversion to hydrocarbons;besides,volcanic rocks can serve as reservoir rocks and cap rocks,playing a role very similar to that of a syndepositional anticline,The volcanic rocks are distributed near the margins of the oil-generating depression;there are many secondary interstices in the rocks,which are connected with each other.These are the leading conditions for the formation of oil-generating period and their self-sealing or good combination with other cap rocks are important factors for forming volcanic rock-hosted oil and gas pools.The oil-gas pools associated with volcanic rocks in western Huimin are mainly distributed around the deep oil-generating depression,in the central up lift or the high structural levels on the margins of the depression.In particular,the sites where several faults cross are usually locatons where hith-yielding oil-gas pools in volcanic rocks are concentrated.
9. Geochemistry and Sr, Nd isotopic composition of the Hronic Upper Paleozoic basic rocks (Western Carpathians, Slovakia
Directory of Open Access Journals (Sweden)
Vozár Jozef
2015-02-01
Full Text Available The paper presents new major and trace element and first Sr-Nd isotope data from selected lavas among the Permian basaltic andesite and basalts of the Hronicum Unit and the dolerite dykes cutting mainly the Pennsylvanian strata. The basic rocks are characterized by small to moderate mg# numbers (30 to 54 and high SiO2 contents (51-57 wt. %. Low values of TiO2 (1.07-1.76 wt. % span the low-Ti basalts. Ti/Y ratios in the dolerite dykes as well as the basaltic andesite and basalt of the 1st eruption phase are close to the recommended boundary 500 between high-Ti and low-Ti basalts. Ti/Y value from the 2nd eruption phase basalt is higher and inclined to the high-Ti basalts. In spite of this fact, in all studied Hronicum basic rocks Fe2O3* is lower than 12 wt. % and Nb/La ratios (0.3-0.6 are low, which is more characteristic of low-Ti basalts. The basic rocks are characterized by Nb/La ratios (0.56 to 0.33, and negative correlations between Nb/La and SiO2, which point to crustal assimilation and fraction crystallization. The intercept for Sr evolution lines of the 1st intrusive phase basalt is closest to the expected extrusions age (about 290 Ma with an initial 87Sr/86Sr ratio of about 0.7054. Small differences in calculated values ISr document a partial Sr isotopic heterogeneity source (0.70435-0.70566, or possible contamination of the original magma by crustal material. For Nd analyses of the three samples, the calculated values εCHUR (285 Ma are positive (from 1.75 to 3.97 for all samples with only subtle variation. Chemical and isotopic data permit us to assume that the parental magma for the Hronicum basic rocks was generated from an enriched heterogeneous source in the subcontinental lithospheric mantle.
10. Petrology and mineral chemistry of sedimentary rocks from the Western Solomon Sea
Science.gov (United States)
Crook, Keith A. W.
1986-12-01
Sedimentary rocks from the northern margin of the Trobriand Platform, the north wall of the New Britain Trench, and the floor of the Solomon Sea Basin are volcaniclastics, mudrocks, and neritic and bathyal limestones. Arc-volcanic debris from calc-alkaline or high-K magmatic sources is present at each locality. A minor metamorphic component occurs at one site on the Trobriand Platform which yielded Early Eocene to Middle Miocene material, and at the New Britain Trench site, which yielded Miocene or older and post-Miocene samples. Solomon Sea Basin samples are mudrocks which are apparently no older than Late Pliocene.
11. Geochemistry and Sr, Nd isotopic composition of the Hronic Upper Paleozoic basic rocks (Western Carpathians, Slovakia)
Science.gov (United States)
Vozár, Jozef; Spišiak, Ján; Vozárová, Anna; Bazarnik, Jakub; Krái, Ján
2015-02-01
The paper presents new major and trace element and first Sr-Nd isotope data from selected lavas among the Permian basaltic andesite and basalts of the Hronicum Unit and the dolerite dykes cutting mainly the Pennsylvanian strata. The basic rocks are characterized by small to moderate mg# numbers (30 to 54) and high SiO2 contents (51-57 wt. %). Low values of TiO2 (1.07-1.76 wt. %) span the low-Ti basalts. Ti/Y ratios in the dolerite dykes as well as the basaltic andesite and basalt of the 1st eruption phase are close to the recommended boundary 500 between high-Ti and low-Ti basalts. Ti/Y value from the 2nd eruption phase basalt is higher and inclined to the high-Ti basalts. In spite of this fact, in all studied Hronicum basic rocks Fe2O3* is lower than 12 wt. % and Nb/La ratios (0.3-0.6) are low, which is more characteristic of low-Ti basalts. The basic rocks are characterized by Nb/La ratios (0.56 to 0.33), and negative correlations between Nb/La and SiO2, which point to crustal assimilation and fraction crystallization. The intercept for Sr evolution lines of the 1st intrusive phase basalt is closest to the expected extrusions age (about 290 Ma) with an initial 87Sr/86Sr ratio of about 0.7054. Small differences in calculated values ISr document a partial Sr isotopic heterogeneity source (0.70435-0.70566), or possible contamination of the original magma by crustal material. For Nd analyses of the three samples, the calculated values ɛCHUR (285 Ma) are positive (from 1.75 to 3.97) for all samples with only subtle variation. Chemical and isotopic data permit us to assume that the parental magma for the Hronicum basic rocks was generated from an enriched heterogeneous source in the subcontinental lithospheric mantle.
12. The character and significance of basement rocks of the southern Molucca Sea region
Science.gov (United States)
Hall, Robert; Nichols, Gary; Ballantyne, Paul; Charlton, Tim; Ali, Jason
Pre-Neogene basement rocks in the southern Molucca Sea region include ophiolitic rocks, arc volcanic rocks and continental rocks. The ophiolitic complexes are associated with arc and forearc igneous and sedimentary rocks. They are interpreted as the oldest parts of the Philippine Sea Plate with equivalents in the ridges and plateaux of the northern Philippine Sea. In the Molucca Sea region igneous components include rocks with a "supra-subduction zone" character, bonintic volcanic rocks and basic volcanic rocks with a "within-plate" character; "MORB-type" rocks are rare or absent. The ophiolitic rocks are overlain by Upper Cretaceous and Eocene sedimentary and volcanic rocks. Plutonic rocks of island arc origin which intrude the ophiolites yield Late Cretaceous radiometric ages and amphibolites with ophiolitic protoliths yield Eocene ages. The "supra-subduction zone" ophiolites are speculated to have originated during a mid-Cretaceous plate reorganization event. For the Late Cretaceous and Eocene the present-day Marianas arc and forearc provides an attractive model. Volcanic rocks from the basement of Morotai, western Halmahera and much of Bacan. These also have an island arc character and are probably of Late Cretaceous-Paleogene age. Both the arc volcanic rocks and the ophiolitic complexes are overlain by shallow water Eocene limestones and an Oligocene rift sequence including basaltic pillow lavas and volcaniclastic turbidites. The distribution of the Eocene-Oligocene sequences indicate pre-Mid/Late Eocene amalgamation of the ophiolitic and arc terranes. Mid Eocene-Oligocene extension appears to be synchronous with opening of the central West Philippine Basin. Continental crust probably arrived in this region in the Late Paleogene-Early Neogene, either due to collision of the Australian margin with Pacific arc-ophiolite terranes or by terrane movement along the Sorong Fault Zone.
13. Identification methods of coal-bearing source rocks for Yacheng Formation in the western deepwater area of South China Sea
Institute of Scientific and Technical Information of China (English)
REN Jinfeng; ZHANG Yingzhao; WANG Hua; WANG Yahui; GAN Huajun; HE Weijun; SUN Ming; SONG Guangzeng
2015-01-01
would be sufficient organic matters to form abundant source rocks. The results show that the integrated methods can significantly improve prediction accuracy of coal-bearing source rocks, which is suitable for early exploration of western deepwater area of South China Sea.
14. Geochronology, geochemistry and tectonic evolution of the Western and Central cordilleras of Colombia
Science.gov (United States)
Villagómez, Diego; Spikings, Richard; Magna, Tomas; Kammer, Andreas; Winkler, Wilfried; Beltrán, Alejandro
2011-08-01
Autochthonous rocks of the pre-Cretaceous continental margin of NW South America (the Tahami Terrane) are juxtaposed against a series of para-autochthonous rock units that assembled during the Early Cretaceous. Allochthonous, oceanic crust of the Caribbean Large Igneous Province collided with and accreted onto the margin during the Late Cretaceous. We present the first regional-scale dataset of zircon U-Pb LA-ICP-MS ages for intrusive and metamorphic rocks of the autochthonous Tahami Terrane, Early Cretaceous igneous para-autochthonous rocks and accreted oceanic crust. The U-Pb zircon data are complemented by multiphase 40Ar/ 39Ar crystallization and cooling ages. The geochronological data are combined with whole rock major oxide, trace element and REE data acquired from the same units to constrain the tectonic origin of the rock units and terranes exposed in the Western Cordillera, Cauca-Patía Valley and the Central Cordillera of Colombia. The Tahami Terrane includes lower Paleozoic orthogneisses (~ 440 Ma) that may have erupted during the active margin stage of the Rheic Ocean. Basement gneisses were intruded by Permian, continental arc granites during the final assembly of Pangea. Triassic sedimentary rocks were subsequently deposited in rift basins and partially melted during high-T metamorphism associated with rifting of western Pangea during 240-220 Ma. Continental arc magmatism during 180-145 Ma is preserved along the whole length of the Central Cordillera and was followed by an Early Cretaceous out-board step of the arc axis and the inception of the Quebradagrande Arc that fringed the continental margin. Back-stepping of the arc axis may have been caused by the collision of buoyant seamounts, which were coeval with plateau rocks exposed in the Nicoya Peninsular of Costa Rica. Rapid westward drift of South America closed the Quebradagrande basin in the late Aptian and caused medium-high P-T metamorphic rocks of the Arquía Complex to exhume and obduct onto
15. Franciscan-type rocks off Monterey Bay, California: Implications for western boundary of Salinian Block
Science.gov (United States)
Mullins, Henry T.; Nagel, David K.
1981-07-01
Serpentinites and spilitic basalts recovered at depths of 1000 m from Ascension Submarine Canyon northwest of Monterey Bay, California indicate that Franciscan basement is present immediately to the west of the San Gregorio Fault. This new information, together with published geological/geophysical data, support previous suggestions that the offshore western boundary of the Salinian block (Sur-Nacimiento Fault) has been tectonically truncated by the San Gregorio Fault and has been displaced by as much as 90 km to the northwest since the mid-late Miocene.
16. U-Th-Pb zircon geochronology on igneous rocks in the Toija and Salittu Formations, Orijärvi area, southwestern Finland: constraints on the age of volcanism and metamorphism
Directory of Open Access Journals (Sweden)
Christopher L. Kirkland
2008-01-01
Full Text Available Zircons from a felsic volcanic rock in the Toija Formation and a synvolcanic gabbro intrusion in the Salittu Formation within the Orijärvi area were dated by U-Th-Pb SIMS in order to provide depositional constraints on these formations. Zircon crystals from the felsic rock preserve a two-stage crystallisation history with zoned core domains and homogeneous rim domains. Inner domains yield a 1878±4 Ma concordia age, interpreted to determine the crystallisation of this rock. Rims yield a 1815±3 Ma concordia age interpretedto determine the regional metamorphism. Small rounded zircon grains from the Salittu gabbro, located within the Jyly shear zone, yield a concordia age of 1792±5 Ma. We interpret the grain textures to suggest that they recrystallised from inherited zircon seeds during the heat and fluid flow into the shear zone. Although no direct ages for the Salittu Formation have been recovered, field relationships imply that it was deposited between 1878−1875 Ma.
17. On the Basic Principles of Igneous Petrology
Science.gov (United States)
Marsh, B. D.
2014-12-01
How and why Differentiation occurs has dominated Igneous Petrology since its beginning (~1880) even though many of the problems associated with it have been thoroughly solved. Rediscovery of the proverbial wheel with new techniques impedes progress. As soon as thin section petrography was combined with rock and mineral chemistry, rock diversity, compositional suites, and petrographic provinces all became obvious. The masterful 1902 CIPW norm in a real sense solved the chemical mystery of differentiation: rocks are related by the addition and subtraction of minerals in the anciently appreciated process of fractional crystallization. Yet few believed this, even after phase equilibria arrived. Assimilation, gas transfer, magma mixing, Soret diffusion, immiscibility, and other processes had strong adherents, even though by 1897 Becker conclusively showed the ineffectiveness of molecular diffusion in large-scale processes. The enormity of heat to molecular diffusion (today's Lewis no.) should have been convincing; but few paid attention. Bowen did, and he refined and restated the result; few still paid attention. And in spite of his truly masterful command of experiment and field relations in promoting fractional crystallization, Fenner and others fought him with odd arguments. The beauty of phase equilibria eventually dominated at the expense of knowing the physical side of differentiation. Bowen himself saw and struggled with the connection between physical and chemical processes. Progress has come from new concepts in heat transfer, kinetics, and slurry dynamics. The key approach is understanding the dynamic competition between spatial rates of solidification and all other processes. The lesson is clear: Scholarship and combined field, laboratory and technical expertise are critical to understanding magmatic processes. Magma is a limitlessly enchanting and challenging material wherein physical processes buttressed by chemistry govern.
18. Paleomagnetic and AMS study of Permian and Triassic rocks from the Hronic Nappe and Paleogene rocks from the Central Carpathian Paleogene Basin, Western Carpathians
Science.gov (United States)
Márton, Emö; Madzin, Jozef; Bučová, Jana; Grabowski, Jacek; Plašienka, Dušan; Aubrecht, Roman
2017-04-01
The Hronic (Choč) units form the highest cover nappe system of the Central Western Carpathians which was emplaced over the Fatric (Krížna) nappe system during the Late Cretaceous. The Permian (red beds and lava flows) and Triassic (sediments) rocks, the main targets of our study, were affected only by diagenetic or very low-grade, burial-related recrystallization and were tilted and transported together. The pre-late Cretaceous sequence is overlapped by Paleogene mainly flysch sequences. Three laboratories (Bratislava, Budapest and Warsaw) were involved in standard paleomagnetic processing and AMS measurements of the samples, while Curie-points were determined in Budapest. The site/locality mean paleomagnetic directions obtained were significantly different from the local direction of the present Earth magnetic field, indicating the long term stability of the paleomagnetic signal. The magnetic fabrics varied from un-oriented to dominantly schistose with well-defined lineations. The latter were normally subhorizontal, although subvertical maxima also occurred among the Triassic sediments. Shallow inclinations, after tilt corrections, suggest near-equatorial position for most of the Permian and Lower Triassic, while around 20°N for the Middle-Upper Triassic localities. The paleomagnetic declinations are interpreted in terms of CW tectonic rotations, which are normally larger for the Permian than for the Triassic samples, although there are some differences within the same age groups. This may be attributed to differential movements during nappe emplacement or subsequent tectonic disturbances. For two localities from the Paleogene cover sequence of the Hronic units, close to the main sampling area (Low Tatra Mts) of the present study documented fairly large CCW rotations, thus obtained additional evidence for the general CCW rotation of the Central Western Carpathians during the Cenozoic. Thus, we conclude that the Cenozoic CCW rotation was pre-dated by large CW
19. High-resolution mineralogical and rock magnetic study of ferromagnetic phases in metabasites from Oscar II Land, Western Spitsbergen—towards reliable model linking mineralogical and palaeomagnetic data
Science.gov (United States)
Burzyński, Mariusz; Michalski, Krzysztof; Nejbert, Krzysztof; Domańska-Siuda, Justyna; Manby, Geoffrey
2017-07-01
Typical 'whole rock' rock magnetic analyses are limited to the identification of the magnetic properties of the mixture of all ferromagnetic minerals within the samples. In this contribution standard 'whole rock' rock magnetic studies of two types of metabasites (metadolerites and metavolcanics) from the metamorphic Proterozoic-Lower Palaeozoic complex of Oscar II Land (Western Spitsbergen) are followed by separation of Fe-containing fractions and conducting magnetic analyses on Fe-containing separates. The main aim here is to determine if any ferromagnetic carriers of a palaeomagnetic signal preceding the Caledonian metamorphism persisted in the metabasites. A comprehensive set of applied methods has allowed for the precise identification of the ferromagnetic carriers and have revealed their textural context in the investigated rocks. The results of mineralogical and rock magnetic analyses of separates confirmed a dominance of low coercivity magnetite/maghemite and pyrrhotite in the metadolerites while in the metavolcanics the existence of magnetite/maghemite and hematite was highlighted. Our investigations support the hypothesis that Caledonian metamorphic remineralization has completely replaced the primary magmatic - Proterozoic/Lower Palaeozoic ferromagnetic minerals in the metadolerites. In the case of the metavolcanics, however, the existence of the ferromagnetic pre-Caledonian relicts cannot be excluded. Furthermore, this approach provided a unique opportunity for conducting rock magnetic experiments on natural mono-ferromagnetic fractions. The described methodologies and results of this study form a new approach that can be applied in further palaeomagnetic and petrographic studies of metamorphosed rock complexes of Svalbard.
20. Geochemical assessment of application effectiveness of the loess-like loamy stratum for shielding phytotoxic mining rock in the Western Donets Basin
Directory of Open Access Journals (Sweden)
M. M. Kharitonov
2006-03-01
Full Text Available Main environmental threats of the excavated rocks and gobs in theWestern Donbassare pollution of soils and subterranean waters by toxic salts and heavy metals. Use of the three-layered models with a stratum of protective shield of the loess-like loamy soil for the restoration considerably decreases this negative impact.
1. Origin of organic matter from tectonic zones in the Western Tatra Mountains Crystalline Basement, Poland: An example of bitumen-source rock correlation
Energy Technology Data Exchange (ETDEWEB)
Marynowski, Leszek; Gaweda, Aleksandra [Faculty of Earth Sciences, Department of Geochemistry, Mineralogy and Petrography, University of Silesia, ul. Bedzinska 60, 41-200 Sosnowiec (Poland); Poprawa, Pawel [Department of Regional and Petroleum Geology, Polish Geological Institute, ul. Rakowiecka 4, 00-975 Warszawa (Poland); Zywiecki, Michal M. [Institute of Geochemistry, Mineralogy and Petrology, Warsaw University, al. Zwirki i Wigury 93, 02-089 Warszawa (Poland); Kepinska, Beata [Mineral and Energy Economy Research Institute, Polish Academy of Sciences, ul. Wybickiego 7, 30-950 Cracow (Poland); Merta, Halina [Polish Oil and Gas Company, Geonafta Warsaw, 76 ul. Jagiellonska, 03-301 Warsaw (Poland)
2006-02-15
Solid bitumens of unknown origin, found in brittle tectonic shear zones cutting the crystalline basement of the Western Tatra Mts, show uniform geochemical characteristics that suggest a uniform source for the original hydrocarbons. On the basis of GC-MS data, a similarity between these solid bitumens and organic matter dispersed in the Mesozoic source rocks of Podhale Trough and sedimentary cover of the northern Tatra Mts is observed. The organic matter in the Mesozoic source rocks shows a higher maturation level than that in the solid bitumens. The molecular composition of the organic matter in both the solid bitumens and the basement rocks is significantly different from that in the Paleogene sedimentary rocks infilling the Podhale Trough. These immature to early mature Paleogene sedimentary rocks contain organic compounds typical of terrestrial plants, both conifers (simonellite and retene) and angiosperms (lupane, oleanane and taraxastene), which are absent in the solid bitumens and in the Mesozoic source rocks. Water-CO{sub 2} fluid inclusions in quartz sealing the shear zones have marine-like salinity, a dominance of CaCl{sub 2} and Mg{sup 2+} depletion, suggesting genetic affinity to dolomitised carbonate rocks such as potential Middle Triassic source rocks. The low maturity of the solid bitumen in the shear zones relative to its Mesozoic source can be explained by continued maturation of the Mesozoic source rocks after expulsion and migration into the shear zones. The results of hydrocarbon-generation modeling indicate that oil expulsion from the Mesozoic source rocks, its migration through the shear zones, and the subsequent maturation of the Mesozoic source rocks all occurred within a short Oligocene time interval. (author)
2. Petrographical Study of Ewekoro Carbonate Rocks, in Ibese, South Western Nigeria
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Osinowo O.O.
2010-12-01
Full Text Available
Limestone deposits can be found in every system of the geologic column since the Precambrian. In classifying this rock, various attempts have been made and notable among them is the classification scheme based on three components: allochems, cements and matrix. Another classification divided limestoneonthe basis of texture into grainstone, packstone, mudstone, wackestone and boundstone. Texturally, limestone ranges from fine to coarse grained with aragonite and calcite as the most common minerals. This work was aimed at identifying and describing both the allochemical and orthochemical components of the limestone deposits in order to classify and deduce their depositional environment.
Eight core samples of limestone deposits representing the Ewekoro Formation of the Dahomey Basin were studied petrographically.
The result of the analysis carried out on the samples showed that the Ibese limestone is composed of the following allochems: sponges, echinoids, bivalves, coralline algae, and pelecypod which represent the skeletal content and intraclasts, pellets and ooids which represent the non skeletal grains. The orthochemical constituents include the carbonate mud matrix and the sparry calcite cement.
These constituents observed from the slides indicate that the Ibese limestone belongs to the class of wackestone and could have been deposited in a quiet and low energy environment.
3. Natural and anthropogenic radionuclides in rocks and beach sands from Ezine region (Canakkale), Western Anatolia, Turkey.
Science.gov (United States)
Orgün, Y; Altinsoy, N; Sahin, S Y; Güngör, Y; Gültekin, A H; Karahan, G; Karacik, Z
2007-06-01
This paper represents the first reports on the natural and anthropogenic radionuclides in Kestanbol granitic pluton and surrounding rocks, and coastal region of the Ezine town. To assess the radiological hazard of the natural radioactivity, the radium equivalent activity, the absorbed dose rate and the external hazard index were calculated, and in situ gamma dose rates were measured. The high-activity concentrations were measured in the pluton and sands, which was originated mainly from the pluton, due to the presence of zircon, allanite, monazite, thorite, uranothorite and apatite. The average activity concentrations of (238)U, (232)Th and (40)K are 174.78, 204.69 and 1171.95 Bq kg(-1) for pluton, and 290.36, 532.04 and 1160.75 Bq kg(-1) for sands, respectively. (137)Cs in Ezine region ranged from 0-6.57 Bq kg(-1). The average absorbed dose rate for the granitic and sand samples were calculated to be 251.6 and 527.92 nGy h(-1), respectively. The maximum contribution to the total absorbed gamma dose rate in air was due to the (232)Th (52.3% for pluton and 67.1% for sands). The Raeq activities of the pluton and sands are higher than the recommended maximum value of 370 Bq kg(-1) criterion limit of Raeq activity for building materials.
4. Plume-proximal mid-ocean ridge origin of Zhongba mafic rocks in the western Yarlung Zangbo Suture Zone, Southern Tibet
Science.gov (United States)
He, Juan; Li, Yalin; Wang, Chengshan; Dilek, Yildirim; Wei, Yushuai; Chen, Xi; Hou, Yunling; Zhou, Aorigele
2016-05-01
The >2000 km-long Yarlung Zangbo Suture Zone (YZSZ) in southern Tibet includes the remnants of the Mesozoic Neotethyan oceanic lithosphere, and is divided by the Zhada-Zhongba microcontinent into northern and southern branches in its western segment. Zircon U-Pb dating of a doleritic rock from the northern branch has revealed a concordant age of 160.5 ± 1.3 Ma. All of the doleritic samples from the northern branch and the pillow basalt and gabbro samples from the southern branch display consistent REE and trace element patterns similar to those of modern OIB-type rocks. The geochemical and Sr-Nd-Pb isotopic signatures of these OIB-type rocks from the western segment are identical with those of OIB-type and alkaline rocks from other ophiolite massifs along the central and eastern segments of the YZSZ, suggesting a common mantle plume source for their melt evolution. The enriched Sr-Nd-Pb isotopic character of the gabbroic dike rocks from the southern branch points to a mantle plume source, contaminated by subducted oceanic crust or pelagic sediments. We infer that the mafic rock associations exposed along the YZSZ represent the remnants of a Neotethyan oceanic lithosphere, which was developed as part of a plume-proximal seafloor-spreading system, reminiscent of the seamount chains along-across the modern mid-ocean ridges in the Pacific Ocean.
5. The Amazon-Laurentian connection as viewed from the Middle Proterozoic rocks in the central Andes, western Bolivia and northern Chile
Science.gov (United States)
Tosdal, R.M.
1996-01-01
Middle Proterozoic rocks underlying the Andes in western Bolivia, western Argentina, and northern Chile and Early Proterozoic rocks of the Arequipa massif in southern Peru?? from the Arequipa-Antofalla craton. These rocks are discontinuously exposed beneath Mesozoic and Cenozoic rocks, but abundant crystalline clasts in Tertiary sedimentary rocks in the western altiplano allow indirect samples of the craton. Near Berenguela, western Bolivia, the Oligocene and Miocene Mauri Formation contains boulders of granodiorite augen gneiss (1171??20 Ma and 1158??12 Ma; U-Pb zircon), quartzose gneiss and granofels that are inferred to have arkosic protoliths (1100 Ma source region; U-Pb zircon), quartzofeldspathic and mafic orthogneisses that have amphibolite- and granulite-facies metamorphic mineral assemblages (???1080 Ma metamorphism; U-Pb zircon), and undeformed granitic rocks of Phanerozoic(?) age. The Middle Proterozoic crystalline rocks from Berenguela and elsewhere in western Bolivia and from the Middle Proterozoic Bele??n Schist in northern Chile generally have present-day low 206Pb/204Pb ( 15.57), and elevated 208Pb/204Pb (37.2 to 50.7) indicative of high time-averaged Th/U values. The Middle Proterozoic rocks in general have higher presentday 206Pb/204Pb values than those of the Early Proterozoic rocks of the Arequipa massif (206Pb/204Pb between 16.1 and 17.1) but lower than rocks of the southern Arequipa-Antofalla craton (206Pb/204Pb> 18.5), a difference inferred to reflect Grenvillian granulite metamorphism. The Pb isotopic compositions for the various Proterozoic rocks lie on common Pb isotopic growth curves, implying that Pb incorporated in rocks composing the Arequipa-Antofalla craton was extracted from a similar evolving Pb isotopic reservoir. Evidently, the craton has been a coherent terrane since the Middle Proterozoic. Moreover, the Pb isotopic compositions for the Arequipa-Antofalla craton overlap those of the Amazon craton, thereby supporting a link
6. Genetic relationships between skarn ore deposits and magmatic activity in the Ahar region, Western Alborz, NW Iran
Directory of Open Access Journals (Sweden)
Mollai Habib
2014-06-01
Full Text Available Paleocene to Oligocene tectonic processes in northwest Iran resulted in extensive I-type calc-alkaline and alkaline magmatic activity in the Ahar region. Numerous skarn deposits formed in the contact between Upper Cretaceous impure carbonate rocks and Oligocene-Miocene plutonic rocks. This study presents new field observations of skarns in the western Alborz range and is based on geochemistry of igneous rocks, mineralogy of the important skarn deposits, and electron microprobe analyses of skarn minerals. These data are used to interpret the metasomatism during sequential skarn formation and the geotectonic setting of the skarn ore deposit related igneous rocks. The skarns were classified into exoskarn, endoskarn and ore skarn. Andraditic garnet is the main skarn mineral; the pyroxene belongs to the diopside-hedenbergite series. The skarnification started with pluton emplacement and metamorphism of carbonate rocks followed by prograde metasomatism and the formation of anhydrous minerals like garnet and pyroxene. The next stage resulted in retro gradation of anhydrous minerals along with the formation of oxide minerals (magnetite and hematite followed by the formation of hydrosilicate minerals like epidote, actinolite, chlorite, quartz, sericite and sulfide mineralization. In addition to Fe, Si and Mg, substantial amounts of Cu, along with volatile components such as H2S and CO2 were added to the skarn system. Skarn mineralogy and geochemistry of the igneous rocks indicate an island arc or subduction-related origin of the Fe-Cu skarn deposit.
7. Geochemistry of metamorphosed basaltic and sedimentary rocks from the Smolník Cu-pyrite deposit (Gemeric Superunit, Western Carpathians: a reappraisal of older geochemical data
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Peter Ivan
2016-12-01
Full Text Available Stratiform chalcopyrite-pyrite deposit of Smolník is located in the low-grade metamorphosed Early Palaeozoic volcano-sedimentary Gelnica Group. Various types of phyllites, mostly sericite and graphite-sericite phyllites with metadolerite bodies build up proximate vicinity of the deposit. The imminent host rocks of sulphide pods are chlorite phyllites with subordinate chlorite-sericite phyllites intercallations. Metadolerites previously interpreted as effusive rocks are probably subvolcanic in origin. Original igneous mineral association of clinopyroxene, plagioclase, ilmenite and probably also olivine were transformed to association of amphiboles, albite, clinozoisite/epidote, titanite ± calcite by metamorphic alteration. Composition of metadolerites is close to basaltic liquids although indices of some fractionation of plagioclase, olivine/chromspinelide or clinopyroxene exist. Trace element distribution points to their similarity to within-plate continental tholeiites (CT and probable relation to the beginning of rifting in the Lower Devonian time. Three possible sources of sedimentary material have been identified in the sedimentary host rocks of the Smolník deposit: (i basalts generated from enriched mantle reservoir; (ii less fractionated calc-alkaline volcanic rocks and (iii fractionated calc-alkaline rhyolites. An additional hydrothermal source for silica and iron is supposed for chlorite phyllites and allows classified them as metaexhalites. The sulphide ores were directly precipitated in the exhalite environment due to reaction hydrothermal solution with hydrogen sulphide produced by thermochemical reduction of the marine sulphate. Geochemical data on metamorphosed dolerites and sediments in combination to other geological characteristics of the Smolník deposit support its classification as the Besshi-type deposit.
8. Variations of Ni, Cr and Mn Concentration in Soils Formed Along a Toposequence of Ultrabasic Rocks in Western Mashhad
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S. Akbari
2016-02-01
Full Text Available Introduction: Parent materials as one of the main soil formation factors have a great impact on the concentration of heavy metals in the soil. Heavy metals are released to the soil during weathering and pedogenic processes. Ultrabasic rocks are known as the potential natural source of heavy metals, especially Ni, Cr and Mn in the soil. Average concentrations of Ni and Cr in the soils are 84 and 34 mg kg-1, respectively; while, in soil derived from ultrabasic parent material, the concentration of these elements may reach up to 100000 mg kg-1. Binaloud zone in northeastern composed of different geological materials. There is a narrow band of ophiolitic rocks in this zone that located along Mashhad city. The geochemical behavior of ultrabsic rocks and the associated soil have been frequently studied mostly in humid regions. But, there are a few research works done in arid environments. The objective of this study was to investigate the physical and chemical properties and concentrations of Ni, Cr and Mn in soils formed along a toposequence of ultrabasic rocks in western Mashhad. Materials and Methods: The study area is located in the hilly land landscape of Binaloud zone in the Western part of Mashhad. Mean annual precipitation and temperature is 260 mm and 13.7 oC, respectively. Soil temperature and moisture regimes are thermic and aridic boarder on mesic, respectively. Studied soils developed on hornblendite rocks that are ultrabasic rocks with SiO2 less than 45% and contain ferromagnesian minerals. A toposequence was selected and, three soil profiles on shoulder, backslope and footslope geomorphic positions were described acoording to key to soil taxonmy 2014 and the soil horizons were sampled. Air-dried samples were passed through 2 mm sieve and were used for laboratory analysis. Pseudo-total concentrations of Ni, Cr and Mn were extracted by aqua regia digestion procedure. Free iron oxides (Fed and amorphous iron oxides (Feo were extracted by
9. Constraints of REE and trace elements of high-pressure-veins and host rocks in western Tianshan on origin of deep fluids in paleosubduction zones
Institute of Scientific and Technical Information of China (English)
HUANG De-zhi; GAO Jun; DAI Ta-gen
2005-01-01
The western Tianshan high-pressure(HP) metamorphic belt represents the paleosubduction mélange of paleozoic south Tianshan ocean between the Yili-central Tianshan and Tarim plates. High-pressure veins are extensively developed in this HP belt. Compared with normal mid-ocean ridge basalt(N-MORB), the high-pressure veins and host rocks are enriched in light rare earth elements(LREE) and incompatible elements. But high-pressure veins show a larger variation than host rocks in total REE abundance. On the trace element spidergram, all the samples are enriched in incompatible elements and show strong positive Pb anomaly relative to N-MORB. The array tendency lines of plots of the HP rocks have apparent slopes on diagram of m(Sr) vs m(Sr)/m(Zr), m(Li) vs m(Li)/m(Y) and m(Ce) vs m(Ce)/m(Pb), which indicates that the enrichment in LREE and incompatible elements relative to N-MORB of the HP-metamorphic rocks from western Tianshan is not attributed to magma evolution process of the protolith. High field strength elements, such as Nb, Ta, Ti, Zr and Hf, do not show negative anomaly relative to N-MORB, which is dissimilar to that of island arc basalts. Therefore, the enrichment in LREE and incompatible elements of the HP rocks is not attributed to the enrichment of the source of the protolith. The mass ratios of Rb to Ba, Ce to Pb, Nb to U and Ta to U of high-pressure veins and host rocks are intermediate of mid-ocean ridge basalt or oceanic island basalt and continental crust. The fluids in western Tianshan paleosubduction zones are mixtures of two sources, dehydration or devolatilization of host rocks and of subducted sediments.
10. The first deep heat flow determination in crystalline basement rocks beneath the Western Canadian Sedimentary Basin
Science.gov (United States)
Majorowicz, Jacek; Chan, Judith; Crowell, James; Gosnold, Will; Heaman, Larry M.; Kück, Jochem; Nieuwenhuis, Greg; Schmitt, Douglas R.; Unsworth, Martyn; Walsh, Nathaniel; Weides, Simon
2014-05-01
Heat flow (Q) determined from bottom-hole temperatures measured in oil and gas wells in Alberta show a large scatter with values ranging from 40 to 90 mW m-2. Only two precise measurements of heat flow were previously reported in Alberta, and were made more than half a century ago. These were made in wells located near Edmonton, Alberta, and penetrated the upper kilometre of clastic sedimentary rocks yielding heat flows values of 61 and 67 mW m-2 (Garland & Lennox). Here, we report a new precise heat flow determination from a 2363-m deep well drilled into basement granite rocks just west of Fort McMurray, Alberta (the Hunt Well). Temperature logs acquired in 2010-2011 show a significant increase in the thermal gradient in the granite due to palaeoclimatic effects. In the case of the Hunt Well, heat flow at depths >2200 m is beyond the influence of the glacial-interglacial surface temperatures. Thermal conductivity and temperature measurements in the Hunt Well have shown that the heat flow below 2.2 km is 51 mW m-2 (±3 mW m-2), thermal conductivity measured by the divided bar method under bottom of the well in situ like condition is 2.5 W m-1 K-1, and 2.7 W m-1 K-1 in ambient conditions), and the geothermal gradient was measured as 20.4 mK m-1. The palaeoclimatic effect causes an underestimate of heat flow derived from measurements collected at depths shallower than 2200 m, meaning other heat flow estimates calculated from basin measurements have likely been underestimated. Heat production (A) was calculated from spectral gamma recorded in the Hunt Well granites to a depth of 1880 m and give an average A of 3.4 and 2.9 μW m-3 for the whole depth range of granites down to 2263 m, based on both gamma and spectral logs. This high A explains the relatively high heat flow measured within the Precambrian basement intersected by the Hunt Well; the Taltson Magmatic Zone. Heat flow and related heat generation from the Hunt Well fits the heat flow-heat generation
11. Possible Biosphere-Lithosphere Interactions Preserved in Igneous Zircon and Implications for Hadean Earth.
Science.gov (United States)
Trail, Dustin; Tailby, Nicholas D; Sochko, Maggie; Ackerson, Michael R
2015-07-01
Granitoids are silicic rocks that make up the majority of the continental crust, but different models arise for the origins of these rocks. One classification scheme defines different granitoid types on the basis of materials involved in the melting/crystallization process. In this end-member case, granitoids may be derived from melting of a preexisting igneous rock, while other granitoids, by contrast, are formed or influenced by melting of buried sedimentary material. In the latter case, assimilated sedimentary material altered by chemical processes occurring at the near surface of Earth-including biological activity-could influence magma chemical properties. Here, we apply a redox-sensitive calibration based on the incorporation of Ce into zircon crystals found in these two rock types, termed sedimentary-type (S-type) and igneous-type (I-type) granitoids. The ∼400 Ma Lachlan Fold Belt rocks of southeastern Australia were chosen for investigation here; these rocks have been a key target used to describe and explore granitoid genesis for close to 50 years. We observe that zircons found in S-type granitoids formed under more reducing conditions than those formed from I-type granitoids from the same terrain. This observation, while reflecting 9 granitoids and 289 analyses of zircons from a region where over 400 different plutons have been identified, is consistent with the incorporation of (reduced) organic matter in the former and highlights one possible manner in which life may modify the composition of igneous minerals. The chemical properties of rocks or igneous minerals may extend the search for ancient biological activity to the earliest period of known igneous activity, which dates back to ∼4.4 billion years ago. If organic matter was incorporated into Hadean sediments that were buried and melted, then these biological remnants could imprint a chemical signature within the subsequent melt and the resulting crystal assemblage, including zircon.
12. Lithic technology and behavioural modernity: new results from the Still Bay site, Hollow Rock Shelter, Western Cape Province, South Africa.
Science.gov (United States)
2011-08-01
The Hollow Rock Shelter site in Western Cape Province, South Africa, was excavated in 1993 and 2008. This study presents new results from a technological analysis of Still Bay points and bifacial flakes from the site. The results show that Still Bay points from the site are standardized tools. The points in the assemblage consist of a complex mixture of whole and fragmented points in all phases of production. The fragmentation degree is high; approximately 80% of the points are broken. A high proportion of bending fractures shows that several of the points were discarded due to production failures, and points with impact damage or hafting traces show that used points were left in the cave. This illustrates that the production of points as well as replacement of used points took place at the site. The result also shows that worked but not finished preforms and points were left at the site, suggestive of future preparation. The points were produced within the framework of three different chaînes opératoires, all ending up in a typologically uniform tool. This shows that the manufacture of Still Bay points should be regarded as a special bifacial technology, only partly comparable with other bifacial technologies. A raw material analysis shows that locally available quartz and quartzite were used in the production, and that points made of silcrete were brought to the site. Based on the technological analysis, a discussion of behavioural modernity, focusing on hypotheses about social interaction, experimentation, different strategies for learning to knap, and landscape memories, results in an interpretation that behavioural modernity was established at Hollow Rock Shelter in the Still Bay phase of the southern African Middle Stone Age. Copyright © 2011 Elsevier Ltd. All rights reserved.
13. Study of the optimization of shooting lithology and the technology of static correction in the area developed with igneous rock in near surface in XW%XW 表层火成岩发育区激发岩性优选及静校正技术研究
Institute of Scientific and Technical Information of China (English)
马永乐; 朱峰; 谢纯华; 石一青; 晋为真; 张寒松
2016-01-01
The distribution of near surface igneous rock in XW area is so complicated that there always exists the static correction problems.In the field operation,lithology and conformity of shooting were taken into consideration to get better data.Further,the optimized static correction and usage of uphole time are so helpful to improve the onsite processing sec-tion.Through the integrated data acquiring and data procession,such static correction problem has been resolved and the fi-nal data has been comparatively improved.%XW 地区近地表岩性复杂多变，地震资料中存在一定的静校正问题。在地震勘探中，通过优选激发岩性和改善激发的一致性，获得了较好的原始资料，并结合井口时间的应用和静校正方法的优选，改善了现场处理剖面的质量。通过这种采集、处理一体化的方式，在解决该地区静校正问题上，取得了较好的效果。
14. Heat-pulse flowmeter test to characterize the seawater intrusion in fractured rock, western coast of Korea
Science.gov (United States)
Oh, H.; Hwang, S.; Shin, J.; Park, K.
2007-12-01
Seawater intrusion occurs commonly along the western and southern coasts of Korea. Almost coastal area consists of a reclaimed land, and is affected by seawater intrusion through the fractured rocks connected the seaside within several kilometers of coasts. A combination of drilling, conventional geophysical well logging including caliper log, natural gamma log, fluid temperature/conductivity log etc., acoustic televiewer, flowmeter, hydrophysical logging, packer test, and freshwater injection test was performed to evaluate seawater intrusion through the fractured rock in Baeksu-eup, Youngkwang-gun, Korea. The geological structure of the survey area comprises mud, sand, and granite and andesite bedrock (below an approximate depth of 22 m). The test boreholes are located with the brackish area interpreted with surface geophysical survey and hydrogeochemcial survey. The depth of two test boreholes is 50m, and the diameter is 3 inch, the distance between boreholes is 10m. Although the core log showed the several fractures, we didn't identify the minor fractures using 3-arm caliper logs because of small aperture size of fractures. The electrical conductivity of the borehole fluid is seen to be more than 1000 μS/cm at depth of about 35 m, and the highest conductivity is about 5000 μS/cm. Several intervals shown the change of conductivity logs doesn't relate with fractures identified by 3-arm caliper logs. In order to verify the permeable fractures, heat-pulse flowmeter test was conducted within single hole and interpreted with Paillet inversion method. Five permeable fractures are detected and hydraulic properties are estimated. These results are compared with hydrophysical logging performed one borehole. After the replacement of borehole fluid with freshwater, the change of fluid conductivity shows at least seven fractures with different salinity. Main fractures with highest salinity detected acoustic televiewer show low dip angles. To define subsurface connection
15. The Paleozoic tectonic evolution and metallogenesis of the northern margin of East Junggar, Central Asia Orogenic Belt: Geochronological and geochemical constraints from igneous rocks of the Qiaoxiahala Fe-Cu deposit
Science.gov (United States)
Liang, Pei; Chen, Huayong; Hollings, Pete; Xiao, Bing; Wu, Chao; Bao, Zhiwei; Cai, Keda
2016-11-01
The East Junggar terrane (NW China) is an important constituent of the Central Asian Orogenic Belt (CAOB). From the Devonian to Permian, regional magmatism evolved from mainly calc-alkaline (I-type) to alkaline (A-type). The Qiaoxiahala Fe-Cu deposit, located in the Late Paleozoic Dulate island arc (northern margin of the East Junggar), is hosted in the volcanic rocks of the Middle Devonian Beitashan Formation. Two magmatic stages were identified in the deposit, the Qiaoxiahala diorite porphyry (380 ± 4.0 Ma) and a younger aplite (331 ± 3.1 Ma). The (high-K) calc-alkaline Beitashan Formation basaltic rocks are characterized by LILE and LREE enrichments and HFSE depletions, pointing to a subduction-related affinity. The high Mg# (42-75), elevated Ce/Th and Ba/Th, depleted Nb, positive εNd(t) (6.6), low (87Sr/86Sr)i (0.7037) and MORB-like Pb isotope characters all suggest an origin involving partial melting of a MORB-like depleted mantle wedge (metasomatized by slab-derived fluids) with little evidence of crustal contamination. The calc-alkaline (I-type) diorite porphyry, characterized by LILE and LREE enrichments and HFSE depletions, may have formed from fractional crystallization of the basaltic rocks, with its parental magma derived from the same depleted mantle wedge. The negative εHf(t) (-8.26), Hf model age (TDMC) of 1406 Ma and the presence of inherited zircons (ca. 470 and 506 Ma) indicate that the diorite has assimilated older crustal material. The alkaline, metaluminous (A-type) aplite is characterized by HFSE enrichment and depletions in Sr, P and Ti, distinct from the basaltic rocks and diorite porphyry at Qiaoxiahala. The low Mg# (35-38), positive Zr and Hf, positive εHf(t) (4.77-9.75) and εNd(t) (6.85-6.86) and low T2DM (538-520 Ma) suggest a juvenile lower crustal source due to partial melting of basaltic lower crust as a result of underplating of mantle-derived melts and accompanied by magma mixing. The tectonic evolution of the Paleozoic East
16. Igneous history of the aubrite parent asteroid - Evidence from the Norton County enstatite achondrite
Science.gov (United States)
Okada, Akihiko; Keil, Klaus; Taylor, G. Jeffrey; Newsom, Horton
1988-01-01
Numerous specimens of the Norton County enstatite achondrite (aubrite) were studied by optical microscopy, electron microprobe, and neutron-activation analysis. Norton County is found to be a fragmental impact breccia, consisting of a clastic matrix made mostly of crushed enstatite, into which are embedded a variety of mineral and lithic clasts of both igneous and impact melt origin. The Norton County precursor materials were igneous rocks, mostly plutonic orthopyroxenites, not grains formed by condensation from the solar nebula. The Mg-silicate-rich aubrite parent body experienced extensive melting and igneous differentiation, causing formation of diverse lithologies including dunites, plutonic orthopyroxenites, plutonic pyroxenites, and plagioclase-silica rocks. The presence of impact melt breccias (the microporphyritic clasts and the diopside-plagioclase-silica clast) of still different compositions further attests to the lithologic diversity of the aubrite parent body.
17. Domains and enrichment mechanism of the lithospheric mantle in western Yunnan: A comparative study on two types of Cenozoic ultrapotassic rocks
Institute of Scientific and Technical Information of China (English)
XIA; Ping; XU; Yigang
2005-01-01
Geochemical comparison of two suites of Cenozoic potassic volcanic rocks in western Yunnan reveals the existence of two mantle domains beneath this region, which correspond to their respective tectonic affinity. The Erhai ultrapotassic rocks (42-24Ma) in western Yangtze Craton are characterized by LILE enrichment, HFSE depletion, low TiO2 content (＜1%),high initial 87Sr/86Sr (0.7064-0.7094) and negative εNd (-3.84--4.64). Geochemically similar to K-rich volcanism in subduction setting, they were probably originated from a refractory spinel harzburgitic source metasomatized by subduction-related fluids. In contrast, the Maguan potassic magmas (＜16Ma) in the South China Block show an OIB-type trace elemental signature, high TiO2 content (＞2%), low initial 87Sr/86Sr (0.7041-0.7060) and positive εNd (5.46-7.03). These features resemble the typical intraplate potassic rocks around the world. These rocks are thus interpreted as melting products of a fertile garnet Iherzolitic source which has been infiltrated by small-volume, asthenosphere-derived silicate melts. The temporal and spatial distribution of these two types of K-rich rocks cannot be explained by any unified tectonic model. It is proposed that the Oligocene magmatism in the Erhai area may have resulted from convective thinning of the thickened lithosphere, whereas the post-Miocene volcanism in the Maguan area was related to the opening of South China Sea.
18. Geothermal resources of the western arm of the Black Rock Desert, northwestern Nevada. Part I. Geology and geophysics
Energy Technology Data Exchange (ETDEWEB)
Schaefer, D.H.; Welch, A.H.; Maurer, D.K.
1983-01-01
Studies of the geothermal potential of the western arm of the Black Rock Desert in northwestern Nevada included a compilation of existing geologic data on a detailed map, a temperature survey at 1-meter depth, a thermal-scanner survey, and gravity and seismic surveys to determine basin geometry. The temperature survey showed the effects of heating at shallow depths due to rising geothermal fluids near the known hot spring areas. Lower temperatures were noted in areas of probable near-surface ground-water movement. The thermal-scanner survey verified the known geothermal areas and showed relatively high-temperature areas of standing water and ground-water discharge. The upland areas of the desert were found to be distinctly warmer than the playa area, probably due to the low thermal diffusivity of upland areas caused by low moisture content. Surface geophysical surveys indicated that the maximum thickness of valley-fill deposits in the desert is about 3200 meters. Gravity data further showed that changes in the trend of the desert axis occurred near thermal areas. 53 refs., 8 figs., 3 tabs.
19. DSC modelling for predicting resilient modulus of crushed rock base as a road base material for Western Australia roads
Institute of Scientific and Technical Information of China (English)
KHOBKLANG Pakdee; VIMONSATIT Vanissorn; JITSANGIAM Peerapong; NIKRAZ Hamid
2013-01-01
In order to increase the applied efficiency of crushed rock base (CRB) in pavement structure design for Western Australia roads,the material modelling based on the experimental results was investigated,and the disturbed state concept (DSC) was used to predict the resilient modulus of CRB because of its simplicity and strong ability in capturing the elastic and inelastic responses of materials to loads.The actual deformation of DSC,at any loading state,was determined from its assumed relative intact (RI) state.The DSC equation of CRB was constructed by using a set of experimental results of resilient modulus tests,and an idealized material model,namely the linear elastic model,of relative intact (RI) part was considered.Analysis results reveal that the resilient modulus-applied stress relationships back-predicted by using the DSC modelling are consistent with the experimental results,so,the DSC equation is suited for predicting the resilient modulus of CRB specimen.However,the model and the equation coming from the test results are conducted in accordance with the Austroads standard,so further investigation and validation with respect to the field behaviours of pavement structure should be performed.7 figs,11 refs.
20. Modelling deep water habitats to develop a spatially explicit, fine scale understanding of the distribution of the western rock lobster, Panulirus cygnus.
Directory of Open Access Journals (Sweden)
Renae K Hovey
Full Text Available BACKGROUND: The western rock lobster, Panulirus cygnus, is endemic to Western Australia and supports substantial commercial and recreational fisheries. Due to and its wide distribution and the commercial and recreational importance of the species a key component of managing western rock lobster is understanding the ecological processes and interactions that may influence lobster abundance and distribution. Using terrain analyses and distribution models of substrate and benthic biota, we assess the physical drivers that influence the distribution of lobsters at a key fishery site. METHODS AND FINDINGS: Using data collected from hydroacoustic and towed video surveys, 20 variables (including geophysical, substrate and biota variables were developed to predict the distributions of substrate type (three classes of reef, rhodoliths and sand and dominant biota (kelp, sessile invertebrates and macroalgae within a 40 km(2 area about 30 km off the west Australian coast. Lobster presence/absence data were collected within this area using georeferenced pots. These datasets were used to develop a classification tree model for predicting the distribution of the western rock lobster. Interestingly, kelp and reef were not selected as predictors. Instead, the model selected geophysical and geomorphic scalar variables, which emphasise a mix of terrain within limited distances. The model of lobster presence had an adjusted D(2 of 64 and an 80% correct classification. CONCLUSIONS: Species distribution models indicate that juxtaposition in fine scale terrain is most important to the western rock lobster. While key features like kelp and reef may be important to lobster distribution at a broad scale, it is the fine scale features in terrain that are likely to define its ecological niche. Determining the most appropriate landscape configuration and scale will be essential to refining niche habitats and will aid in selecting appropriate sites for protecting critical
1. Isotopic data for Late Cretaceous intrusions and associated altered and mineralized rocks in the Big Belt Mountains, Montana
Science.gov (United States)
du Bray, Edward A.; Unruh, Daniel M.; Hofstra, Albert H.
2017-03-07
The quartz monzodiorite of Mount Edith and the concentrically zoned intrusive suite of Boulder Baldy constitute the principal Late Cretaceous igneous intrusions hosted by Mesoproterozoic sedimentary rocks of the Newland Formation in the Big Belt Mountains, Montana. These calc-alkaline plutonic masses are manifestations of subduction-related magmatism that prevailed along the western edge of North America during the Cretaceous. Radiogenic isotope data for neodymium, strontium, and lead indicate that the petrogenesis of the associated magmas involved a combination of (1) sources that were compositionally heterogeneous at the scale of the geographically restricted intrusive rocks in the Big Belt Mountains and (2) variable contamination by crustal assimilants also having diverse isotopic compositions. Altered and mineralized rocks temporally, spatially, and genetically related to these intrusions manifest at least two isotopically distinct mineralizing events, both of which involve major inputs from spatially associated Late Cretaceous igneous rocks. Alteration and mineralization of rock associated with the intrusive suite of Boulder Baldy requires a component characterized by significantly more radiogenic strontium than that characteristic of the associated igneous rocks. However, the source of such a component was not identified in the Big Belt Mountains. Similarly, altered and mineralized rocks associated with the quartz monzodiorite of Mount Edith include a component characterized by significantly more radiogenic strontium and lead, particularly as defined by 207Pb/204Pb values. The source of this component appears to be fluids that equilibrated with proximal Newland Formation rocks. Oxygen isotope data for rocks of the intrusive suite of Boulder Baldy are similar to those of subduction-related magmatism that include mantle-derived components; oxygen isotope data for altered and mineralized equivalents are slightly lighter.
2. Rock-degrading endophytic bacteria in cacti
Science.gov (United States)
M. Esther Puente; Ching Y. Li; Yoav Bashan
2009-01-01
A plant-bacterium association of the cardon cactus (Pachycereus pringlei) and endophytic bacteria promotes establishment of seedlings and growth on igneous rocks without soil. These bacteria weather several rock types and minerals, unbind significant amounts of useful minerals for plants from the rocks, fix in vitro N2. produce...
3. Petrogenesis of Volcanic Rocks in the Khabr-Marvast Tectonized Ophiolite: Evidence for Subduction Processes in the South-Western Margin of Central Iranian Microcontinent
Institute of Scientific and Technical Information of China (English)
2009-01-01
The Late Cretaceous Khabr-Marvast tectonized ophiolite is located in the middle part of the Nain-Baft ophiolite belt, at the south-western edge of the central Iranian microcontinent. Although all the volcanic rocks in the study area indicate subduction-related magmatism (e.g. high LILE (large ion lithophile elements)/ HFSE (high field strenght elements) ratios and negative anomalies in Nb and Ta), geological and geochemical data clearly distinguish two distinct groups of volcanic rocks in the tectonized association: (1) group 1 is comprised of hyaloclustic breccias, basaltic pillow iavas, and andesite sheet flows. These rocks represent the Nain-Baft oceanic crust; and (2) group 2 is alkaline iavas from the top section of the ophiolite suite. These lavas show shoshonite affinity, but do not support the propensity of ophiolite.
4. A study of radioactive elements of various rocks in Pattani Province with gamma ray spectrometer
Directory of Open Access Journals (Sweden)
Kaewtubtim, P.
2002-01-01
Full Text Available The radioactivity of the three elements, potassium, uranium and thorium, in rocks of various types in Pattani Province was investigated by using a gamma ray spectrometer. It was found that potassium contents in igneous rocks, sedimentary rocks and metamorphic rocks were 6.29 %, 2.21% and 1.54 % respectively. Uranium equivalent contents in igneous rock, sedimentary rocks and metamorphic rocks were found to be 22.51 ppm, 11.25 ppm and 14.13 ppm, while thorium contents in these rocks were 21.78 ppm, 18.88 ppm and 18.15 ppm respectively. The results obtained were similar to those reported by Pungtip Ranglek (1995 for igneous rock at Liwong Pluton site in Thepha, Na Thawi, Chana and Saba Yoi Districts, Songkhla Province, and were about six times higher than those reported by Kittichai Wattananikorn (1994 for igneous rock in the northern part of Thailand.
5. Determining the diet of larvae of western rock lobster (Panulirus cygnus using high-throughput DNA sequencing techniques.
Directory of Open Access Journals (Sweden)
Richard O'Rorke
Full Text Available The Western Australian rock lobster fishery has been both a highly productive and sustainable fishery. However, a recent dramatic and unexplained decline in post-larval recruitment threatens this sustainability. Our lack of knowledge of key processes in lobster larval ecology, such as their position in the food web, limits our ability to determine what underpins this decline. The present study uses a high-throughput amplicon sequencing approach on DNA obtained from the hepatopancreas of larvae to discover significant prey items. Two short regions of the 18S rRNA gene were amplified under the presence of lobster specific PNA to prevent lobster amplification and to improve prey amplification. In the resulting sequences either little prey was recovered, indicating that the larval gut was empty, or there was a high number of reads originating from multiple zooplankton taxa. The most abundant reads included colonial Radiolaria, Thaliacea, Actinopterygii, Hydrozoa and Sagittoidea, which supports the hypothesis that the larvae feed on multiple groups of mostly transparent gelatinous zooplankton. This hypothesis has prevailed as it has been tentatively inferred from the physiology of larvae, captive feeding trials and co-occurrence in situ. However, these prey have not been observed in the larval gut as traditional microscopic techniques cannot discern between transparent and gelatinous prey items in the gut. High-throughput amplicon sequencing of gut DNA has enabled us to classify these otherwise undetectable prey. The dominance of the colonial radiolarians among the gut contents is intriguing in that this group has been historically difficult to quantify in the water column, which may explain why they have not been connected to larval diet previously. Our results indicate that a PCR based technique is a very successful approach to identify the most abundant taxa in the natural diet of lobster larvae.
6. Determining the diet of larvae of western rock lobster (Panulirus cygnus) using high-throughput DNA sequencing techniques.
Science.gov (United States)
O'Rorke, Richard; Lavery, Shane; Chow, Seinen; Takeyama, Haruko; Tsai, Peter; Beckley, Lynnath E; Thompson, Peter A; Waite, Anya M; Jeffs, Andrew G
2012-01-01
The Western Australian rock lobster fishery has been both a highly productive and sustainable fishery. However, a recent dramatic and unexplained decline in post-larval recruitment threatens this sustainability. Our lack of knowledge of key processes in lobster larval ecology, such as their position in the food web, limits our ability to determine what underpins this decline. The present study uses a high-throughput amplicon sequencing approach on DNA obtained from the hepatopancreas of larvae to discover significant prey items. Two short regions of the 18S rRNA gene were amplified under the presence of lobster specific PNA to prevent lobster amplification and to improve prey amplification. In the resulting sequences either little prey was recovered, indicating that the larval gut was empty, or there was a high number of reads originating from multiple zooplankton taxa. The most abundant reads included colonial Radiolaria, Thaliacea, Actinopterygii, Hydrozoa and Sagittoidea, which supports the hypothesis that the larvae feed on multiple groups of mostly transparent gelatinous zooplankton. This hypothesis has prevailed as it has been tentatively inferred from the physiology of larvae, captive feeding trials and co-occurrence in situ. However, these prey have not been observed in the larval gut as traditional microscopic techniques cannot discern between transparent and gelatinous prey items in the gut. High-throughput amplicon sequencing of gut DNA has enabled us to classify these otherwise undetectable prey. The dominance of the colonial radiolarians among the gut contents is intriguing in that this group has been historically difficult to quantify in the water column, which may explain why they have not been connected to larval diet previously. Our results indicate that a PCR based technique is a very successful approach to identify the most abundant taxa in the natural diet of lobster larvae.
7. The High Arctic Large Igneous Province Mantle Plume caused uplift of Arctic Canada
Science.gov (United States)
Galloway, Jennifer; Ernst, Richard; Hadlari, Thomas
2016-04-01
The Sverdrup Basin is an east-west-trending extensional sedimentary basin underlying the northern Canadian Arctic Archipelago. The tectonic history of the basin began with Carboniferous-Early Permian rifting followed by thermal subsidence with minor tectonism. Tectonic activity rejuvenated in the Hauterivian-Aptian by renewed rifting and extension. Strata were deformed by diapiric structures that developed during episodic flow of Carboniferous evaporites during the Mesozoic and the basin contains igneous components associated with the High Arctic Large Igneous Province (HALIP). HALIP was a widespread event emplaced in multiple pulses spanning ca. 180 to 80 Ma, with igneous rocks on Svalbard, Franz Josef Island, New Siberian Islands, and also in the Sverdrup Basin on Ellef Ringnes, Axel Heiberg, and Ellesmere islands. Broadly contemporaneous igneous activity across this broad Arctic region along with a reconstructed giant radiating dyke swarm suggests that HALIP is a manifestation of large mantle plume activity probably centred near the Alpha Ridge. Significant surface uplift associated with the rise of a mantle plume is predicted to start ~10-20 my prior to the generation of flood basalt magmatism and to vary in shape and size subsequently throughout the LIP event (1,2,3) Initial uplift is due to dynamical support associated with the top of the ascending plume reaching a depth of about 1000 km, and with continued ascent the uplift topography broadens. Additional effects (erosion of the ductile lithosphere and thermal expansion caused by longer-term heating of the mechanical lithosphere) also affect the shape of the uplift. Topographic uplift can be between 1 to 4 km depending on various factors and may be followed by subsidence as the plume head decays or become permanent due to magmatic underplating. In the High Arctic, field and geochronological data from HALIP relevant to the timing of uplift, deformation, and volcanism are few. Here we present new evidence
8. Sedimentary connection between rock glaciers and torrential channels: definition, inventory and quantification from a test area in the south-western Swiss Alps
Science.gov (United States)
Kummert, Mario; Barboux, Chloé; Delaloye, Reynald
2017-04-01
order to validate these estimations, the resulting sediment transfer rates are compared to transfer rates calculated from repeated terrestrial LiDAR surveys on selected study cases. This contribution presents results from the application of this methodology in a test study area in the south-western Swiss Alps. The methodology reveals itself suitable to identify rock glaciers connected to the torrential network. For each of the detected rock glaciers, an estimation of the sediment yield is proposed. The transfer rates range from tens of cubic meters per year for some slow moving and/or partially connected landforms, to several thousands of cubic meters per year. References: Delaloye R. (2004). Contribution à l'étude du pergélisol de montagne en zone marginale. GeoFocus vol. 10, Thèse, Département de Géosciences/Géographie, Université de Fribourg. Delaloye, R., Lambiel, C., Gärtner-Roer, I. (2010). Overview of rock glacier kinematics research in the Swiss Alps. Seasonal rhythm, interannual variations and trends over several decades. Geogr. Helv., 65: 2, 135-145. Delaloye, R., Morard, S., Barboux, C., Abbet, D., Gruber, V., Riedo, M. & Gachet, S. (2013). Rapidly moving rock glaciers in Mattertal. In: Graf, C. (Eds). Mattertal - ein Tal in Bewegung. Publikation zur Jahrestagung der Schweizerischen Geomorphologischen Gesellschaft 29. Juni - 1. Juli 2011, St. Niklaus, Birmensdorf, Eidg. Forschungsanstalt WSL, 113 - 124. Gärtner-Roer, I. (2012). Sediment transfer rates of two active rockglaciers in the Swiss Alps. Geomorphology, 167-168, 45-50. Lugon, R. & Stoffel, M. (2010). Rock glacier dynamics and magnitude-frequency relations of debris flows in a high-elevation watershed : Ritigraben, Swiss Alps. Global and Planetary Change, 73, 202-210.
9. Timing and duration of volcanism in the North Atlantic Igneous Province
DEFF Research Database (Denmark)
Storey, Michael; Duncan, Robert A.; Tegner, Christian
2007-01-01
We combine new and published 40Ar/39Ar age determinations from incremental heating experiments on whole rocks and mineral separates to assess the timing, duration and distribution of volcanic activity during construction of the North Atlantic Igneous Province. We use these ages together with volume...... estimates of erupted magmas and their cumulates to calculate melt production rates for the early Tertiary flood basalts of East Greenland and the Faeroes Islands. The lavas lie at opposite ends of the Greenland-Iceland-Faeroes Ridge, the postulated Iceland hotspot track, and record volcanic activity leading......, to the Faeroe Islands and the western British Isles, a roughly circular area 2000 km in diameter. Volcanic activity was increasingly intermittent by 57-56 Ma, but at 56.1 ± 0.5 Ma the average melt production rate increased by more than an order of magnitude over previous levels (from 3000 km3/km...
10. Hydrothermal modification of host rock geochemistry within Mo-Cu porphyry deposits in the Galway Granite, western Ireland
Science.gov (United States)
Tolometti, Gavin; McCarthy, Will
2016-04-01
Hydrothermal alteration of host rock is a process inherent to the formation of porphyry deposits and the required geochemical modification of these rocks is regularly used to indicate proximity to an economic target. The study involves examining the changes in major, minor and trace elements to understand how the quartz vein structures have influenced the chemistry within the Murvey Granite that forms part of the 380-425Ma Galway Granite Complex in western Ireland. Molybdenite mineralisation within the Galway Granite Complex occurred in close association with protracted magmatism at 423Ma, 410Ma, 407Ma, 397Ma and 383Ma and this continues to be of interest to active exploration. The aim of the project is to characterize hydrothermal alteration associated with Mo-Cu mineralisation and identify geochemical indicators that can guide future exploration work. The Murvey Granite intrudes metagabbros and gneiss that form part of the Connemara Metamorphic complex. The intrusion is composed of albite-rich pink granite, garnetiferous granite and phenocrytic orthoclase granite. Minor doleritic dykes post-date the Murvey Granite, found commonly along its margins. Field mapping shows that the granite is truncated to the east by a regional NW-SE fault and that several small subparallel structures host Mo-Cu bearing quartz veins. Petrographic observations show heavily sericitized feldspars and plagioclase and biotite which have undergone kaolinization and chloritisation. Chalcopyrite minerals are fine grained, heavily fractured found crystallized along the margins of the feldspars and 2mm pyrite crystals. Molybdenite are also seen along the margins of the feldspars, crystallized whilst the Murvey Granite cooled. Field and petrographic observations indicate that mineralisation is structurally controlled by NW-SE faults from the selected mineralization zones and conjugate NE-SW cross cutting the Murvey Granite. Both fault orientations exhibit quartz and disseminated molybdenite
11. The Central European, Tarim and Siberian Large Igneous Provinces, Late Palaeozoic orogeny and coeval metallogeny
NARCIS (Netherlands)
de Boorder, H.
2014-01-01
The formation of the Central European and Tarim Large Igneous Provinces (LIPs) in the Early Permian coincided with the demise of the Variscan and the Southern Tianshan orogens, respectively. The Early Triassic Siberian LIP was formed in the wake of the Western Altaid orogeny in the Late Permian. The
12. Volcanic stratigraphy and geochemical variations in Miocene-age rocks in western and southeastern Fort Irwin, California
Science.gov (United States)
Buesch, D.
2015-12-01
Lava flows and tuffaceous deposits ranging in composition from basalt to rhyolite, including basaltic trachyandesite to trachyte, are exposed in 800 km2 of western Fort Irwin area, California, and form the eastern edge of the Eagle Crags volcanic field (ECVF). The main ECVF has 40Ar/39Ar ages from ~18.7-12.4 Ma (mostly 18.7-18.5 Ma; Sabin et al. 1994), and on Fort Irwin, the ages are from 21.0-15.8 Ma (mostly 18.6-15.8 Ma; Schermer et al. 1996). 68 samples (56 lava flow, 4 dome-collapse breccia, 3 ignimbrite, and 5 fallout tephra) were analyzed for major, minor, and trace elements. Typically, stratigraphic sequences dip cinder cones. A general upward felsic to mafic compositional sequence occurs throughout the area, but is not continuous as B is locally in a R-D sequence and B is at the base of and interstratified with a BA-A sequence. Also, there are compositional variations at different locations along the edges of the field. In the Goldstone Mesa, Pink Canyon, and Stone Ridge areas (~70 km2), B-BA forms the youngest lava flows, but ~21 km to the north in the Garry Owen area (~25 km2), BTA forms the youngest lava flows. Compared to the Stone Ridge area with a D-A-TA-BA trend, ~6 km west in the Pioneer Plateau area is R-TA-D, ~3 km south in the Pink Canyon area is R-B-BA-A, and ~8 km east at Dacite Dome is D only (all areas have slightly different Na2O+K2O in each rock type). A non-ECVF, 5.6 Ma BA flow in SE Fort Irwin also has distinct compositions. Chemical variations indicate the region had similar general evolution of magma sources, but (1) there were numerous small, isolated chambers that fed flows along the edges of the field, (2) several tuffs are similar to local lavas but some differ and might have distant sources, and (3) basalt flows locally encroached into adjacent areas.
13. Rock relationships in the Mogok metamorphic belt, Tatkon to Mandalay, central Myanmar
Science.gov (United States)
Mitchell, A. H. G.; Htay, Myint Thein; Htun, Kyaw Min; Win, Myint Naing; Oo, Thura; Hlaing, Tin
2007-03-01
The Mogok metamorphic belt (MMB), over 1450 km long and up to 40 km wide, consists of regionally metamorphosed rocks including kyanite and sillimanite schists and granites lying along the Western margin of the Shan Plateau in central Myanmar and continuing northwards to the eastern Himalayan syntaxis. Exposures in quarries allow correlation of Palaeozoic meta-sedimentary, early Mesozoic meta-igneous and late Mesozoic intrusive rocks within a 230 km long northerly-trending segment of the MMB, from Tatkon to Kyanigan north of Mandalay, and with the Mogok gemstone district 100 km to the northeast. Relationships among the metamorphic and intrusive rocks, with sparse published radiometric age controls, indicate at least two metamorphic events, one before and one after the intrusion of Late Jurassic to early Cretaceous calc-alkaline rocks. These relationships can be explained by either of two possible tectonic histories. One, constrained by correlation of mid-Permian limestones across Myanmar, requires early Permian and early Jurassic regional metamorphic events, prior to an early Tertiary metamorphism, in the western part of but within a Shan-Thai - western Myanmar block. The second, not compatible with a single laterally continuous Permian limestone, requires pre-Upper Jurassic regional metamorphism and orogenic gold mineralization in the Mergui Group and western Myanmar, early Cretaceous collision of an east-facing Mergui-western Myanmar island arc with the Shan Plateau, and early Tertiary metamorphism in the MMB related to reversal in tectonic polarity following the arc-Plateau collision.
14. Petrogenesis of Igneous-Textured Clasts in Martian Meteorite Northwest Africa 7034
Science.gov (United States)
Santos, A. R.; Agee, C. B.; Humayun, M.; McCubbin, F. M.; Shearer, C. K.
2016-01-01
The martian meteorite Northwest Africa 7034 (and pairings) is a breccia that samples a variety of materials from the martian crust. Several previous studies have identified multiple types of igneous-textured clasts within the breccia [1-3], and these clasts have the potential to provide insight into the igneous evolution of Mars. One challenge presented by studying these small rock fragments is the lack of field context for this breccia (i.e., where on Mars it formed), so we do not know how many sources these small rock fragments are derived from or the exact formation his-tory of these sources (i.e., are the sources mantle de-rived melt or melts contaminated by a meteorite impactor on Mars). Our goal in this study is to examine specific igneous-textured clast groups to determine if they are petrogenetically related (i.e., from the same igneous source) and determine more information about their formation history, then use them to derive new insights about the igneous history of Mars. We will focus on the basalt clasts, FTP clasts (named due to their high concentration of iron, titanium, and phosphorous), and mineral fragments described by [1] (Fig. 1). We will examine these materials for evidence of impactor contamination (as proposed for some materials by [2]) or mantle melt derivation. We will also test the petrogenetic models proposed in [1], which are igneous processes that could have occurred regardless of where the melt parental to the clasts was formed. These models include 1) derivation of the FTP clasts from a basalt clast melt through silicate liquid immiscibility (SLI), 2) derivation of the FTP clasts from a basalt clast melt through fractional crystallization, and 3) a lack of petrogenetic relationship between these clast groups. The relationship between the clast groups and the mineral fragments will also be explored.
15. Lead immobilization in thermally remediated soils and igneous rocks
Energy Technology Data Exchange (ETDEWEB)
Hickmott, D.D.; Carey, J.W. [Los Alamos National Lab., NM (United States). Earth and Environmental Science Div.; Stimac, J.; Larocque, A. [Univ. of Manitoba, Winnipeg, Manitoba (Canada). Dept. of Geological Sciences; Abell, R. [Virginia Polytechnic Inst. and State Univ., Blacksburg, VA (United States). Dept. of Geological Sciences; Gauerke, E. [Univ. of New Mexico, Albuquerque, NM (United States). Dept. of Geological Sciences; Eppler, A. [Univ. of California, Berkeley, CA (United States). Dept. of Chemistry
1997-06-01
This is the final report for a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The principal goal of this project was to investigate the speciation of lead in the environment at LANL and to determine the feasibility of using thermal remediation methods to immobilize lead in the environment. Lead occurs as pyromorphite [Pb(PO{sub 4}){sub 3}(Cl, OH)], cerussite (PbCO{sub 3}) and galena (PbS) in vapor-phase-altered Bandelier Tuff samples. LANL soils primarily contain cerussite and PbO. Thermal remediation experiments at high temperatures (up to 400 C) suggest that thermal immobilization of highly-reactive Pb compounds in the environment may be feasible, but that this technique is not optimal for more refractory lead phases such as cerussite and PbO.
16. Pristine Igneous Rocks and the Genesis of Early Planetary Crusts
Science.gov (United States)
Warren, Paul H.; Lindstrom, David (Technical Monitor)
2002-01-01
Our studies are highly interdisciplinary, but are focused on the processes and products of early planetary and asteroidal differentiation, especially the genesis of the ancient lunar crust. The compositional diversity that we explore is the residue of process diversity, which has strong relevance for comparative planetology.
17. Paleozoic sedimentary rocks in the Red Dog Zn-Pb-Ag district and vicinity, western Brooks Range, Alaska: provenance, deposition, and metallogenic significance
Science.gov (United States)
Slack, John F.; Dumoulin, Julie A.; Schmidt, J.M.; Young, L.E.; Rombach, Cameron
2004-01-01
Geochemical analyses of Paleozoic sedimentary rocks in the western Brooks Range reveal a complex evolutionary history for strata surrounding the large Zn-Pb-Ag deposits of the Red Dog district. Data for major elements, trace elements, and rare earth elements (REE) were obtained on 220 samples of unaltered and unmineralized siliciclastic rocks from the Upper Devonian-Lower Mississippian Endicott Group (Hunt Fork Shale, Noatak Sandstone, Kanayut Conglomerate, Kayak Shale), the overlying Carboniferous Lisburne Group (Kuna Formation, unnamed drowned shelf facies), and the Pennsylvanian-Permian Siksikpuk Formation. Major base metal sulfide deposits of the region are present only in the Kuna Formation, which in the Red Dog district comprises siliceous black shale and black chert, minor limestone (calcareous radiolarite), and sparse lithic turbidite and bedded siliceous rock. Gray and rare black shales of the Kayak Shale and common black shales of the Kuna Formation are anomalously low in iron (avg Fe/Ti = 6.25 and 6.34, respectively) relative to other Paleozoic shales in the region (9.58-10.6) and to average shales worldwide (10.1-10.5). In contrast, the bedded siliceous rocks contain appreciable hematite (avg Fe/Ti = 35.0) and high U/Ti and REE/Ti ratios that are interpreted to reflect low amounts of detrital material and a major Fe-rich eolian component.
18. Surface-groundwater interactions in hard rocks in Sardon Catchment of western Spain: an integrated modeling approach
NARCIS (Netherlands)
Tanvir Hassan, S.M.; Lubczynski, M.; Niswonger, R.G.; Su, Zhongbo
2014-01-01
The structural and hydrological complexity of hard rock systems (HRSs) affects dynamics of surface–groundwater interactions. These complexities are not well described or understood by hydrogeologists because simplified analyses typically are used to study HRSs. A transient, integrated hydrologic
19. Review of the Basinal Igneous Tectonics%沉积盆地火成构造研究综述
Institute of Scientific and Technical Information of China (English)
刘晓峰; 齐荣
2011-01-01
Magmatic activity is widespread in sedimentary basins world-wide. As hydrocarbon exploration spreads to igneous rocks, the understanding of the role of igneous complexes in the basin is becomes increasingly important. Basinal igneous tectonics is defined here as the deformations involving igneous complexes, host rocks and overburden resulted from magma intrusion and extrusion. Recently, the study of geometry and emplacement mechanisms of igneous sills by using 3D seismic reflection data has made great achievements, which has started a new ear of igneous tectonic analysis. Interpretation of 3 D reflection seismic data offers a novel approach to the understanding of the fundamental aspects and hydrocarbon implications of basinal igneous tectonics. The research of igneous tectonics is one of the key fundamental problems of structural analysis in sedimentary basins, and is of broad practice prospecting in the petroleum exploration. A better understanding of the igneous rocks will improve our understanding of basinal structures and hydrocarbon traps related igneous rocks, and bring a number of new ideas of hydrocarbon exploration.%岩浆活动在沉积盆地中是非常广泛的.随着油气勘探领域的扩展,对沉积盆地火成岩及相关构造的研究愈加重要.沉积盆地火成构造是指在沉积盆地中由岩浆侵入或喷发作用形成的岩浆和围岩及上覆层变形构造的总和.当前,利用三维地震数据研究岩席的几何学与侵位机制取得了重要进展,开启了沉积盆地火成构造研究的新时代.三维地震分析是沉积盆地火成构造研究强有力的手段.加强火成构造的研究不仅可以深化对沉积盆地构造的认识,也可以深化对火成构造圈闭的认识,为寻找与火成岩相关的油气藏提供了新思路.
20. Igneous and metamorphic petrology in the field: a problem-based, writing-intensive alternative to traditional classroom petrology
Science.gov (United States)
DeBari, S. M.
2011-12-01
The Geology Department at Western Washington University (~100 geology majors) offers field and classroom versions of its undergraduate petrology course. This is a one-quarter course (igneous and metamorphic petrology) with mineralogy as a prerequisite. The field version of the course is offered during the three weeks prior to fall quarter and the classroom version is offered in spring quarter. We take 15-20 students around the state of Washington, camping at different outcrop sites where students integrate observational skills, petrologic knowledge, and writing. Petrogenetic associations in various tectonic settings provide the theme of the course. We compare ophiolites vs. arc sequences (volcanic, plutonic, and metamorphic rocks), S- vs. I-type granitoids (plutonic rocks and associated metamorphic rocks), Barrovian vs. Buchan vs. subduction zone metamorphism of different protoliths, and flood-basalt vs. active-arc volcanism. Some basics are covered in the first day at WWU, followed by 17 days of field instruction. Lecture is integrated with outcrop study in the field. For example, students will listen to a lecture about magma differentiation processes as they examine cumulate rocks in the Mt. Stuart batholith, and a lecture about metamorphic facies as they study blueschist facies rocks in the San Juan Islands. Students study multiple outcrops around a site for 1-4 days. They then use their observations (sketches and written descriptions of mineral assemblages, rock types, rock textures, etc.) and analysis techniques (e.g. geochemical data plotting, metamorphic protolith analysis) to write papers in which the data are interpreted in terms of a larger tectonic problem. In advance of the writing process, students use group discussion techniques such as whiteboarding to share their observational evidence and explore interpretations. Student evaluations indicate that despite the intense pace of the course, they enjoy it more. Students also feel that they retain more
1. Magnetic Susceptibility as a Tool for Investigating Igneous Rocks—Experience from IODP Expedition 304
Directory of Open Access Journals (Sweden)
Roger C. Searle
2008-07-01
Full Text Available Continuous measurements of magnetic susceptibility have been commonly used on Ocean Drilling Program (ODP and Integrated Ocean Drilling Program (IODPexpeditions to study minor lithological variations (forexample, those related to climatic cycles in sedimentary rocks, but they have been less frequently used on igneous rocks, although important post-cruise studies have utilized them (e.g., Ildefonse and Pezard, 2001. Here I report its use (and that of the closely related electrical conductivity on IODP Expedition 304 to examine igneous crustal rocks. Expedition 304/305 targeted the Atlantis Massif, an oceanic core complex on the Mid-Atlantic Ridge, and recovered a suite of igneous rocks comprising mainly gabbros, troctolites, and some diabases (Blackman et al., 2006; Ildefonse et al., 2006, 2007; IODP Expeditions 304 and 305 Scientists, 2005. Shipboard measurements (on D/V JOIDES Resolution of physical properties were made to characterize lithological units and alteration products, to correlate cored material with down-hole logging data, and to interpret broader-scale geophysical data.
2. The role of igneous sills in shaping the Martian uplands
Science.gov (United States)
Wilhelms, D. E.; Baldwin, R. J.
Relations among geologic units and landforms suggest that igneous sills lie beneath much of the intercrater and intracrater terrain of the Martian uplands. The igneous rocks crop out along the upland-lowland front and in crater floors and other depressions that are low enough to intersect the sill's intrusion horizons. It is suggested that heat from the cooling sills melted some of the ice contained in overlying fragmental deposits, creating valley networks by subsurface flow of the meltwater. Terrains with undulatory, smooth surfaces and softened traces of valleys were created by more direct contact with the sills. Widespread subsidence following emplacement of the sills deformed both them and the nonvolcanic deposits that overlie them, accounting for the many structures that continue from ridged plains into the hilly uplands. Crater counts show that the deposit that became valleyed, softened, and ridged probably began to form (and to acquire interstitial ice) during or shortly after the Middle Noachian Epoch, and continued to form as late as the Early Hesperian Epoch. The upper layers of this deposit, many of the visible valleys, and the ridged plains and postulated sills all have similar Early Hesperian ages. Continued formation of valleys is indicated by their incision of fresh-appearing crater ejecta. The dependence of valley formation on internal processes implies that Mars did not necessarily have a dense early atmosphere or warm climate.
3. Magmatic systems of large continental igneous provinces
Directory of Open Access Journals (Sweden)
E. Sharkov
2017-07-01
Full Text Available Large igneous provinces (LIPs formed by mantle superplume events have irreversibly changed their composition in the geological evolution of the Earth from high-Mg melts (during Archean and early Paleoproterozoic to Phanerozoic-type geochemically enriched Fe-Ti basalts and picrites at 2.3 Ga. We propose that this upheaval could be related to the change in the source and nature of the mantle superplumes of different generations. The first generation plumes were derived from the depleted mantle, whereas the second generation (thermochemical originated from the core-mantle boundary (CMB. This study mainly focuses on the second (Phanerozoic type of LIPs, as exemplified by the mid-Paleoproterozoic Jatulian–Ludicovian LIP in the Fennoscandian Shield, the Permian–Triassic Siberian LIP, and the late Cenozoic flood basalts of Syria. The latter LIP contains mantle xenoliths represented by green and black series. These xenoliths are fragments of cooled upper margins of the mantle plume heads, above zones of adiabatic melting, and provide information about composition of the plume material and processes in the plume head. Based on the previous studies on the composition of the mantle xenoliths in within-plate basalts around the world, it is inferred that the heads of the mantle (thermochemical plumes are made up of moderately depleted spinel peridotites (mainly lherzolites and geochemically-enriched intergranular fluid/melt. Further, it is presumed that the plume heads intrude the mafic lower crust and reach up to the bottom of the upper crust at depths ∼20 km. The generation of two major types of mantle-derived magmas (alkali and tholeiitic basalts was previously attributed to the processes related to different PT-parameters in the adiabatic melting zone whereas this study relates to the fluid regime in the plume heads. It is also suggested that a newly-formed melt can occur on different sides of a critical plane of silica undersaturation and can
4. Metamorphic Rocks in West Irian
NARCIS (Netherlands)
Wegen, van der G.
1971-01-01
Low-grade metamorphics of West Irian occur to the east of Geelvink Bay associated with two narrow belts of basic and ultrabasic igneous rocks which represent ophiolitic suites of an eugeosynclinical development beginning in Early Mesozoic time. In both of these belts there are indications of regiona
5. From incipient slope instability through slope deformation to catastrophic failure - Different stages of failure development on the Ivasnasen and Vollan rock slopes (western Norway)
Science.gov (United States)
Oppikofer, T.; Saintot, A.; Hermanns, R. L.; Böhme, M.; Scheiber, T.; Gosse, J.; Dreiås, G. M.
2017-07-01
The long-term evolution of rock slope failures involves different stages, from incipience of slope instability to catastrophic failure, through a more or less long-lasting slope deformation phase that also involves creeping or sliding. Topography, lithology, and structural inheritance are the main intrinsic factors that influence this evolution. Here, we investigate the role of these intrinsic factors on the rock slope failure development of the Ivasnasen and Vollan rock slopes (Sunndal Valley, western Norway) using a multitechnique approach that includes geomorphologic and structural field mapping, kinematic analysis, terrestrial cosmogenic nuclide exposure dating, topographic reconstruction, and deformation quantification. Ivasnasen is a rock slope failure complex with several past rock slope failures and a present unstable rock slope, located on a cataclinal NW-facing slope and developed in augen gneiss. Vollan on the opposite valley side is a deep-seated gravitational slope deformation (DSGSD) affecting the whole mountainside, developed in quartzite in the upper part and micaschist in the lower part. These different lithologies belong to different nappe complexes that were emplaced and folded into a series of syn- and anticlines during the Caledonian orogeny. These folds lead to different lithologies being exposed in different structural orientations on the opposite valley flanks, which in turn leads to different types and evolution of rock slope failures. At Ivasnasen the 45°-55° NW-dipping ductile foliation allowed for a fairly simple planar sliding mechanism for the 1.2 million m3 post-glacial rock slope failure. Failure occurred ca. 3.3 ka ago after a short period of prefailure deformation. For the present 2.2 million m3 unstable rock slope at Ivasnasen, a steepening of the foliation at the toe impedes such a mechanism and up to 10 m of displacement has not lead to a catastrophic failure yet. The Vollan DSGSD is characterized by a steep major back scarp
6. Silurian and Devonian source rocks and crude oils from the western part of Libya: Organic geochemistry, palynology and carbon stratigraphy
NARCIS (Netherlands)
Elkelani, Mohamed M.A.
2015-01-01
The Early Silurian “hot” shales and Late Devonian black shales are major regional oil and gas source rocks in North Africa. Their deposition probably played a major role in global carbon cycling in general because of the large areas of the ocean affected. Comparing the Libyan δ13C record with record
7. Discovery of the boninite series volcanic rocks in the Bangong Lake ophiolite mélange,western Tibet,and its tectonic implications
Institute of Scientific and Technical Information of China (English)
SHI Rendeng; YANG Jingsui; XU Zhiqin; QI Xuexiang
2004-01-01
The boninite series volcanic rocks, mainly composed of basaltic andesite, andesitic lava breccia and andesite porphyrite, were recognized for the first time in the Bangong Lake ophiolite mé1ange, western Tibet. These rocks have a strong boninitic affinity, with high SiO2 (55.61％-59.23％,weight percent), MgO (6.63％-13.08％, 9.13％ on average (weight percent)), A1203/1iO2 ratios (36-54), Mg# (0.61-0.74), Ni (116 ppm on average) and Cr (354 ppm on average)low TiO2 (0.23％-0.39％, weight percent), and strong LILEs enrichment relative to the depleted HFSEs. C1-chondrite normalized (La/Gd)N and (Gd/Yb)N ratios of about 1.70 and 0.83, respectively, produce prominent“U-shaped” normalized REE (rare earth element) patterns. Such a close compositional affinity to boninite indicates that these volcanic rocks were formed in a forearc setting produced by the intra-oceanic subduction.
8. Origin of the deep fluids in the paleosubduction zones in western Tianshan: Evidence from Pb- and Sr-isotope compositions of high-pressure veins and host rocks
Institute of Scientific and Technical Information of China (English)
HUANG; Dezhi; GAO; Jun; DAI; Tageng; ZOU; Haiyang; XIONG; X
2005-01-01
Fluids in the deep subduction zones play an important role in crust-mantle exchange related to the subduction process. Identification of fluids origin, internal or external, can help us to evaluate the contribution of crust materials to mantle during this process. High-pressure veins, which developed in the western Tianshan HP-metamorphic belt extensively, are the direct products of the fluids in subduction zones. In western Tianshan, high-pressure veins and host rocks have overall Pb- and Sr-isotope compositions. At t = 340 Ma, the high-pressure metamorphic time, the ratios of 206Pb/204Pb, 207Pb/204Pb, 208Pb/204Pb and 87Sr/86Sr of high pressure veins are 17.122―18.431, 15.477―15.611, 37.432―38.689 and 0.70529―0.70705, and are 17.605―17.834, 15.508―15.564, 37.080―38.145 and 0.70522―0.70685 for host rocks. However, high-pressure veins show a much larger variation in Pb-isotope compositions than host rocks. Plots of samples are distributed roughly along a line parallel to and far away from the Northern Hemisphere reference line (NHRL) on the plot of 206Pb/204Pb vs 207Pb/204Pb. On the plot of 206Pb/204Pb vs 208Pb/204Pb, plots of data are distributed nearby mid-ocean-ridge basalts (MORB) area or along a line parallel to and not far away from NHRL, which shows that the data plots are farther away from MORB and ocean island basalts (OIB) areas on the plot of 206Pb/204Pb vs 207Pb/204Pb than on the plot of 206Pb/204Pb vs 208Pb/204Pb. The compositions of Pb- and Sr-isotopes of these high-pressure metamorphic rocks are between that of enriched mantle 1(EMI) and of sediments or upper crust. A notable characteristic can be seen from plots of Pb-isotope ratio vs Pb-isotope ratio and 206Pb/204Pb vs 87Sr/86Sr that array of plots shows an evident tendency of mixture of two end members. Ratios of Rb/Ba, Ce/Pb, Nb/U and Ta/U of high-pressure veins and host rocks are between that of OIB or MORB and that of continental crust, which indicates that continental crust
9. Latest Cretaceous and Cenozoic magmatic rocks of Alaska: polygon data
Data.gov (United States)
U.S. Geological Survey, Department of the Interior — This map is a statewide summary of magmatic (igneous) rocks grouped into geologic units that can be portrayed cartographically at 1:2,500,000. This dataset consists...
10. Geochemical characteristics and zircon U-Pb isotopic ages of island-arc basic igneous complexes from the Tianshui area in West Qinling
Institute of Scientific and Technical Information of China (English)
PEI Xianzhi; LI Zuochen; LIU Huibin; LI Gaoyang; DING Saping; LI Yong; HU Bo; GUO Junfeng
2007-01-01
The Liushuigou intermediate-basic meta-igneous complex at Guanzizhen, Tianshui area, is mainly composed of metagabbro, metagabbro diorite and metadiorite, while the Baihua basic meta-igneous complex consists mainly of pyroxenite, gabbro (gabbro diorite), diorite and quartz diorite.They form a relatively complete comagmatic evolutionary series. The geochemical characteristics of intermediate-basic igneous rocks indicate that they belong to a tholeiite suite.Their chondrite-normalized REE patterns are nearly flat and are LREE-slightly enriched type, and their primitive mantle-normalized and MORB-normalized trace element spider-grams are generally similar; the LILEs Cs, Ba, Sr, Th and U are enriched, while Rb and K and the HFSEs Nb, P, Zr,Sm, Ti and Y are depleted. All these show comagmatic evolu-tionary and genetic characteristics. The tectonic environment discrimination by trace element reveals that these igneous complexes formed in an island-arc setting. The Thermal Ionization Mass Spectrometry (TIMS) single-grain zircon U-Pb age for the Liushuigou intermediate-basic meta-igneous rocks in the Guanzizhen area is (507.5 ± 3.0) Ma, represent-ing the age of these igneous complexes, which indicates that island-arc-type magmatite rocks in the northern zone of West Qinling are Late Cambrian and also reveals that the timing of subduction of the paleo-ocean basin represented by the Guanzizhen ophiolite and resulting island-arc-type magrnaticactivity are probably Late Cambrian to Early Ordovician.
11. Fatty acid profiles of phyllosoma larvae of western rock lobster (Panulirus cygnus) in cyclonic and anticyclonic eddies of the Leeuwin Current off Western Australia
Science.gov (United States)
Wang, M.; O'Rorke, R.; Waite, A. M.; Beckley, L. E.; Thompson, P.; Jeffs, A. G.
2014-03-01
The recent dramatic decline in settlement in the population of the spiny lobster, Panulirus cygnus, may be due to changes in the oceanographic processes that operate offshore of Western Australia. It has been suggested that this decline could be related to poor nutritional condition of the post-larvae, especially lipid which is accumulated in large quantities during the preceding extensive pelagic larval stage. The current study focused on investigations into the lipid content and fatty acid (FA) profiles of lobster phyllosoma larvae from three mid to late stages of larval development (stages VI, VII, VIII) sampled from two cyclonic and two anticyclonic eddies of the Leeuwin Current off Western Australia. The results showed significant accumulation of lipid and energy storage FAs with larval development regardless of location of capture, however, larvae from cyclonic eddies had more lipid and FAs associated with energy storage than larvae from anticyclonic eddies. FA food chain markers from the larvae indicated significant differences in the food webs operating in the two types of eddy, with a higher level of FA markers for production from flagellates and a lower level from copepod grazing in cyclonic versus anticyclonic eddies. The results indicate that the microbial food web operating in cyclonic eddies provides better feeding conditions for lobster larvae despite anticyclonic eddies being generally more productive and containing greater abundances of zooplankton as potential prey for lobster larvae. Gelatinous zooplankton, such as siphonophores, may play an important role in cyclonic eddies by accumulating dispersed microbial nutrients and making them available as larger prey for phyllosoma. The markedly superior nutritional condition of lobster larvae feeding in the microbial food web found in cyclonic eddies, could greatly influence their subsequent settlement and recruitment to the coastal fishery.
12. Molecular marker and stable carbon isotope analyses of carbonaceous Ambassador uranium ores of Mulga Rock in Western Australia
Science.gov (United States)
Jaraula, C.; Schwark, L.; Moreau, X.; Grice, K.; Bagas, L.
2013-12-01
Mulga Rock is a multi-element deposit containing uranium hosted by Eocene peats and lignites deposited in inset valleys incised into Permian rocks of the Gunbarrel Basin and Precambrian rocks of the Yilgarn Craton and Albany-Fraser Orogen. Uranium readily adsorbs onto minerals or phytoclasts to form organo-uranyl complexes. This is important in pre-concentrating uranium in this relatively young ore deposit with rare uraninite [UO2] and coffinite [U(SiO4)1-x(OH)4x], more commonly amorphous and sub-micron uranium-bearing particulates. Organic geochemical and compound-specific stable carbon isotope analyses were conducted to identify possible associations of molecular markers with uranium accumulation and to recognize effect(s) of ionizing radiation on molecular markers. Samples were collected from the Ambassador deposit containing low (2000 ppm) uranium concentrations. The bulk rock C/N ratios of 82 to 153, Rock-Eval pyrolysis yields of 316 to 577 mg hydrocarbon/g TOC (Hydrogen Index, HI) and 70 to 102 mg CO2/g TOC (Oxygen Index, OI) are consistent with a terrigenous and predominantly vascular plant OM source deposited in a complex shallow water system, ranging from lacustrine to deltaic, swampy wetland and even shallow lake settings as proposed by previous workers. Organic solvent extracts were separated into saturated hydrocarbon, aromatic hydrocarbon, ketone, and a combined free fatty acid and alcohol fraction. The molecular profiles appear to vary with uranium concentration. In samples with relatively low uranium concentrations, long-chain n-alkanes, alcohols and fatty acids derived from epicuticular plant waxes dominate. The n-alkane distributions (C27 to C31) reveal an odd/even preference (Carbon Preference Index, CPI=1.5) indicative of extant lipids. Average δ13C of -27 to -29 ‰ for long-chain n-alkanes is consistent with a predominant C3 plant source. Samples with relatively higher uranium concentrations contain mostly intermediate-length n
13. Rock Testing Handbook (Test Standards 1993)
Science.gov (United States)
1993-01-01
and Earth (50) International Glossary of H.tlrology, Geneva, Switzerland, World Structures, McGraw-Hill Book Co., Inc., New York, (1951...reactive with alkalies in concrete. igneous rocks of lower silica content such as diorite, gabbro , 5.2 opal-a hydrous form of silica (SiO 2 -nH 2O...in European many rocks, such as ferruginous sandstones, shales. clay- usage dolerite) is a rock of similar composition to gabbro and ironstones, and
14. Sr and O isotopes in western Aleutian seafloor lavas: Implications for the source of fluids and trace element character of arc volcanic rocks
Science.gov (United States)
Yogodzinski, Gene M.; Kelemen, Peter B.; Hoernle, Kaj; Brown, Shaun T.; Bindeman, Ilya; Vervoort, Jeffrey D.; Sims, Kenneth W. W.; Portnyagin, Maxim; Werner, Reinhard
2017-10-01
High Mg# andesites and dacites (Mg# = molar Mg/Mg + Fe) from western Aleutian seafloor volcanoes carry high concentrations of Sr (>1000 ppm) that is unradiogenic (87Sr/86Sr 0.7030). Data patterns in plots of 87Sr/86Sr vs Y/Sr and Nd/Sr imply the existence of an eclogite-melt source component - formed by partial melting of MORB eclogite in the subducting Pacific Plate - which is most clearly expressed in the compositions of western Aleutian andesites and dacites (Nd/Sr and Y/Sr viewed in combination with inversely correlated εNd and 87Sr/86Sr, these patterns rule out aqueous fluids as an important source of Sr because mixtures of fluids from altered oceanic crust with depleted mantle and sediment produce compositions with 87Sr/86Sr higher than in common Aleutian rocks. The unradiogenic nature of Sr in the western Aleutian andesite-dacite end-member may be understood if H2O required to drive melting of the subducting oceanic crust is transported in fluids containing little Sr. Mass balance demonstrates that such fluids may be produced by dewatering of serpentinite in the mantle section of the subducting plate. If the eclogite-melt source component is present throughout the Aleutian arc, melting of the subducting plate must extend into minimally altered parts of the sheeted dike section or upper gabbros, at depths >2 km below the paleo-seafloor. Oxygen isotopes in western Aleutian seafloor lavas, which fall within a narrow range of MORB-like values (δ18 O = 5.1- 5.7), are also consistent with this model. These results indicate that the subducting Pacific lithosphere beneath the Aleutian arc is significantly hotter than indicated my most thermal models.
15. Rock-avalanche dynamics revealed by large-scale field mapping and seismic signals at a highly mobile avalanche in the West Salt Creek valley, western Colorado
Science.gov (United States)
Coe, Jeffrey A.; Baum, Rex L.; Allstadt, Kate; Kochevar, Bernard; Schmitt, Robert G.; Morgan, Matthew L.; White, Jonathan L.; Stratton, Benjamin T.; Hayashi, Timothy A.; Kean, Jason W.
2016-01-01
On 25 May 2014, a rain-on-snow–induced rock avalanche occurred in the West Salt Creek valley on the northern flank of Grand Mesa in western Colorado (United States). The avalanche mobilized from a preexisting rock slide in the Green River Formation and traveled 4.6 km down the confined valley, killing three people. The avalanche was rare for the contiguous United States because of its large size (54.5 Mm3) and high mobility (height/length = 0.14). To understand the avalanche failure sequence, mechanisms, and mobility, we conducted a forensic analysis using large-scale (1:1000) structural mapping and seismic data. We used high-resolution, unmanned aircraft system imagery as a base for field mapping, and analyzed seismic data from 22 broadband stations (distances avalanche exerted on the earth and tracked these forces using curves in the avalanche path. Our results revealed that the rock avalanche was a cascade of landslide events, rather than a single massive failure. The sequence began with an early morning landslide/debris flow that started ∼10 h before the main avalanche. The main avalanche lasted ∼3.5 min and traveled at average velocities ranging from 15 to 36 m/s. For at least two hours after the avalanche ceased movement, a central, hummock-rich core continued to move slowly. Since 25 May 2014, numerous shallow landslides, rock slides, and rock falls have created new structures and modified avalanche topography. Mobility of the main avalanche and central core was likely enhanced by valley floor material that liquefied from undrained loading by the overriding avalanche. Although the base was likely at least partially liquefied, our mapping indicates that the overriding avalanche internally deformed predominantly by sliding along discrete shear surfaces in material that was nearly dry and had substantial frictional strength. These results indicate that the West Salt Creek avalanche, and probably other long-traveled avalanches, could be modeled as two
16. Source rock
OpenAIRE
Abubakr F. Makky; Mohamed I. El Sayed; Ahmed S. Abu El-Ata; Ibrahim M. Abd El-Gaied; Mohamed I. Abdel-Fattah; Zakaria M. Abd-Allah
2014-01-01
West Beni Suef Concession is located at the western part of Beni Suef Basin which is a relatively under-explored basin and lies about 150 km south of Cairo. The major goal of this study is to evaluate the source rock by using different techniques as Rock-Eval pyrolysis, Vitrinite reflectance (%Ro), and well log data of some Cretaceous sequences including Abu Roash (E, F and G members), Kharita and Betty formations. The BasinMod 1D program is used in this study to construct the burial history ...
17. Electrical Resistivity Imaging of a Thin Clayey Aquitard Developed on Basement Rocks in Parts of Adekunle Ajasin University Campus, Akungba-Akoko, South-western Nigeria
Directory of Open Access Journals (Sweden)
Muslim B Aminu
2015-05-01
Full Text Available In this study, 2-dimensional electrical resistivity surveying has been used to reveal the nature and development of a thin clayey aquitard on basement complex rocks of the Adekunle Ajasin University campus, Akungba-Akoko south-western Nigeria. The aim was to evaluate the occurrence, geometry and groundwater viability of this clayey aquitard as an alternative source of water supply on the Campus. Prior, a hand-dug well, which supplied moderate volumes of water all year round, had been abstracting water from this aquitard. Three east-west geo-electric traverses were surveyed using the dipole-dipole array configuration with an electrode separation of 5 m and a maximum dipole length of 45 m. Each of the three traverses was 60 m long. The observed field data were inverted for subsurface 2D resistivity structure using a commercially available 2.5D finite element modelling inversion software. The clayey aquitard is imaged to exist as low resistivity response patterns which have developed in elongated trough-like depressions created as a result of deep weathering of the feldspar and amphibolite-rich sections of the basement rocks of the area. This clayey layer reaches a thickness of 10 m at the southern end of the survey and in some sections is compartmentalised into segments by basement rocks which have better resisted weathering. Where the topographic slope of the ground surface is low enough as to allow the accumulation of run-off, the clayey aquitard develops into visible marshy swamps. Although, clayey aquitards of this nature supply water at low rates, their capacity to store high volumes and to be available all-year-round could prove essential to ameliorating acute water shortages experienced in the area during the dry season.DOI: http://dx.doi.org/10.5755/j01.erem.71.1.9016
18. Environmental Suitability and Distribution of the Caucasian Rock Agama, Paralaudakia caucasia (Sauria:Agamidae) in Western and Central Asia
Institute of Scientific and Technical Information of China (English)
Seyyed Saeed HOSSEINIAN YOUSEFKHANI; Gentile Francesco FICETOLA; Nasrullah RASTEGAR-POUYANI; Natalia B ANANJEVA; Eskandar RASTEGAR-POUYANI; Rafaqat MASROOR
2013-01-01
Predictive potential distribution modeling is crucial in outlining habitat usage and establishing conservation management priorities. In this paper we provide detailed data on the distribution of the Caucasian rock agama Para-laudakia caucasia, and use species distribution models (MAXENT) to evaluate environmental suitability and potential distribution at a broad spatial scale. Locality data on the distribution of P. caucasia have been gathered over nearly its entire range by various authors from ifeld surveys. The distribution model of P. caucasia showed good performance (AUC=0.887), and predicted high suitability in regions mainly located in Tajikistan, north Pakistan, Afghanistan, southeast Turkmenistan, northeast Iran along the Elburz mountains, Transcaucasus (Azerbajan, Armenia, Georgia), northeastern Turkey and northward along the Caspian Sea coast in Daghestan, Russia. The identiifcation of suitable areas for this species will help to assess conservation status of the species, and to set up management programs.
19. Microseismic activity analysis for the study of the rupture mechanisms in unstable rock masses (Matterhorn, North-western Alps)
Science.gov (United States)
Amitrano, D.; Arattano, M.; Chiarle, M.; Mortara, G.; Occhiena, C.; Pirulli, M.; Scavia, C.
2009-04-01
Rockfalls are very frequent events in alpine areas and can endanger human lifes and activities. Since high mountains have been affected by an increasing number of these phenomena in the last years, a possible correlation with the effects of climate changes can be hypothesized. The permafrost degradation, causing the thaw of the ice that fills the rock discontinuities, is then investigated among possible causes of rockfalls. Therefore the monitoring of potential rock instabilities in high mountain in relation with permafrost degradation has been carried out in the frame of the Interreg IIIA ALCOTRA "PERMAdataROC" project. Within the project, a monitoring network has been installed in 2007 on the Italian side of the Matterhorn peak, close to the J. A. Carrel refuge (3829 m a.s.l.). This site is an important destination for climbers going to the Matterhorn peak and is frequently affected by rockfall events. The monitoring network consists of a set of 5 triaxial geophones, to record the existing microseismic activity, and one thermometer, to analyze the temperature trend. A preliminary data processing has concerned the classification of the recorded signals, the identification of the most important microseismic events and the analysis of their distribution in time. As far as this last aspect is concerned, first interpretations have evidenced a possible correlation between the temperature trend and the event concentrations, during particular thermal sequences. The research is still in progress and it is expected that a longer recording period of seismic events and temperatures will help to understand if the microseismic activity is mainly concentrated in some periods of the year, in some parts of the slope and if it is produced by superficial or deep events. A concentration of superficial events in some parts of the slope, together with a structural analysis of those portions, could help to focus on the areas that can be more unstable. While, their correlation with
20. Petrogenesis of gold-mineralized magmatic rocks of the Taerbieke area, northwestern Tianshan (western China): Constraints from geochronology, geochemistry and Sr-Nd-Pb-Hf isotopic compositions
Science.gov (United States)
Tang, Gong-Jian; Wang, Qiang; Wyman, Derek A.; Sun, Min; Zhao, Zhen-Hua; Jiang, Zi-Qi
2013-09-01
Many Late Paleozoic Cu-Au-Mo deposits occur in the Central Asian Orogenic Belt (CAOB). However, their tectonic settings and associated geodynamic processes have been disputed. This study provides age, petrologic and geochemical data for andesites and granitic porphyries of the Taerbieke gold deposit from the Tulasu Basin, in the northwestern Tianshan Orogenic Belt (western China). LA-ICP-MS zircon U-Pb dating indicates that the granitic porphyries have an Early Carboniferous crystallization age (349 ± 2 Ma) that is broadly contemporaneous with the eruption age (347 ± 2 Ma) of the andesites. The andesites have a restricted range of SiO2 (58.94-63.85 wt.%) contents, but relatively high Al2O3 (15.39-16.65 wt.%) and MgO (2.51-6.59 wt.%) contents, coupled with high Mg# (57-69) values. Geochemically, they are comparable to Cenozoic sanukites in the Setouchi Volcanic Belt, SW Japan. Compared with the andesites, the granitic porphyries have relatively high SiO2 (72.68-75.32 wt.%) contents, but lower Al2O3 (12.94-13.84 wt.%) and MgO (0.10-0.33 wt.%) contents, coupled with lower Mg# (9-21) values. The andesites and granitic porphyries are enriched in both large ion lithophile and light rare earth elements, but depleted in high field strength elements, similar to those of typical arc magmatic rocks. They also have similar Nd-Hf-Pb isotope compositions: ɛNd(t) (+0.48 to +4.06 and -0.27 to +2.97) and zircons ɛHf(t) (+3.4 to +8.0 and -1.7 to +8.2) values and high (206Pb/204Pb)i (18.066-18.158 and 17.998-18.055). We suggest that the Taerbieke high-Mg andesitic magmas were generated by the interaction between mantle wedge peridotites and subducted oceanic sediment-derived melts with minor basaltic oceanic crust-derived melts, and that the magmas then fractionated to produce the more felsic members (i.e., the Taerbieke granitic porphyries) during late-stage evolution. Taking into account the Carboniferous magmatic record from the western Tianshan Orogenic Belt, we suggest that
1. Igpet software for modeling igneous processes: examples of application using the open educational version
Science.gov (United States)
Carr, Michael J.; Gazel, Esteban
2016-09-01
We provide here an open version of Igpet software, called t-Igpet to emphasize its application for teaching and research in forward modeling of igneous geochemistry. There are three programs, a norm utility, a petrologic mixing program using least squares and Igpet, a graphics program that includes many forms of numerical modeling. Igpet is a multifaceted tool that provides the following basic capabilities: igneous rock identification using the IUGS (International Union of Geological Sciences) classification and several supplementary diagrams; tectonic discrimination diagrams; pseudo-quaternary projections; least squares fitting of lines, polynomials and hyperbolae; magma mixing using two endmembers, histograms, x-y plots, ternary plots and spider-diagrams. The advanced capabilities of Igpet are multi-element mixing and magma evolution modeling. Mixing models are particularly useful for understanding the isotopic variations in rock suites that evolved by mixing different sources. The important melting models include, batch melting, fractional melting and aggregated fractional melting. Crystallization models include equilibrium and fractional crystallization and AFC (assimilation and fractional crystallization). Theses, reports and proposals concerning igneous petrology are improved by numerical modeling. For reviewed publications some elements of modeling are practically a requirement. Our intention in providing this software is to facilitate improved communication and lower entry barriers to research, especially for students.
2. Igpet software for modeling igneous processes: examples of application using the open educational version
Science.gov (United States)
Carr, Michael J.; Gazel, Esteban
2017-04-01
We provide here an open version of Igpet software, called t-Igpet to emphasize its application for teaching and research in forward modeling of igneous geochemistry. There are three programs, a norm utility, a petrologic mixing program using least squares and Igpet, a graphics program that includes many forms of numerical modeling. Igpet is a multifaceted tool that provides the following basic capabilities: igneous rock identification using the IUGS (International Union of Geological Sciences) classification and several supplementary diagrams; tectonic discrimination diagrams; pseudo-quaternary projections; least squares fitting of lines, polynomials and hyperbolae; magma mixing using two endmembers, histograms, x-y plots, ternary plots and spider-diagrams. The advanced capabilities of Igpet are multi-element mixing and magma evolution modeling. Mixing models are particularly useful for understanding the isotopic variations in rock suites that evolved by mixing different sources. The important melting models include, batch melting, fractional melting and aggregated fractional melting. Crystallization models include equilibrium and fractional crystallization and AFC (assimilation and fractional crystallization). Theses, reports and proposals concerning igneous petrology are improved by numerical modeling. For reviewed publications some elements of modeling are practically a requirement. Our intention in providing this software is to facilitate improved communication and lower entry barriers to research, especially for students.
3. The oldest rock of Ivory Coast
Science.gov (United States)
Kouamelan, Alain Nicaise; Djro, Sagbrou Chérubin; Allialy, Marc Ephrem; Paquette, Jean-Louis; Peucat, Jean-Jacques
2015-03-01
The tonalitic gneiss of Balmer (TGB), in the SASCA area of south-western Ivory Coast, previously dated at 3141 ± 2 Ma using the single zircon evaporation method, is regarded as a relic of Archean rock within the Paleoproterozoic (Birimian) formation of the West African Craton (WAC). We present new geochronological data for the TGB using the laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) method. We obtain a U-Pb age of 3207 ± 7 Ma for abundant zircons extracted from the tonalitic gneiss, and interpret this age as that of the magmatic protolith because of the igneous-type homogeneous zircon population. Certain magmatic zircon edges and some round zircons define an upper intercept age of 3155 ± 17 Ma which could represent overgrowths during gneissification. It appears that the TGB was not affected by the events posterior to its genesis, i.e. the Liberian (2.9-2.7 Ga) and Eburnean (2.4-2.0 Ga) events. Additionally, the TGB proves to be a juvenile Leonian rock, as indicated by the Nd model age of 3456 Ma, and could also constitute the protolith of the granulitic grey gneisses and charnockites of the Man area, which are 150-400 Ma younger.
4. Precise U-Pb Zircon Dating of the Syenite Phase from the Ditrau Alkaline Igneous Complex
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Pană Dinu
2000-04-01
Full Text Available The Ditrău igneous complex represents the largest alkaline intrusion in the Carpathian-Pannonian region consisting of a plethora of rock types formed by complicated magmatic and metasomatic processes. A detailed U-Pb zircon age study is currently underway and the results for the syenite intrusion phase is reported herein. The U-Pb zircon emplacement age of the syenite of 229.6 +1.7/-1.2 Ma documents the quasi-contemporaneous production and emplacement of the gabbro and syenite magmas. We suggest that the syenite and associated granite formed by crustal melting during the emplacement of the mantle derived gabbroic magma around 230 Ma. The thermal contact aureole produced by the Ditrău alkaline igneous complex constrains the main tectonism recorded by surrounding metamorphic lithotectonic assemblages to be pre-Ladinian.
5. Surface-groundwater interactions in hard rocks in Sardon Catchment of western Spain: an integrated modeling approach
Science.gov (United States)
Hassan, S.M. Tanvir; Lubczynski, Maciek W.; Niswonger, Richard G.; Zhongbo, Su
2014-01-01
The structural and hydrological complexity of hard rock systems (HRSs) affects dynamics of surface–groundwater interactions. These complexities are not well described or understood by hydrogeologists because simplified analyses typically are used to study HRSs. A transient, integrated hydrologic model (IHM) GSFLOW (Groundwater and Surface water FLOW) was calibrated and post-audited using 18 years of daily groundwater head and stream discharge data to evaluate the surface–groundwater interactions in semi-arid, ∼80 km2 granitic Sardon hilly catchment in Spain characterized by shallow water table conditions, relatively low storage, dense drainage networks and frequent, high intensity rainfall. The following hydrological observations for the Sardon Catchment, and more generally for HRSs were made: (i) significant bi-directional vertical flows occur between surface water and groundwater throughout the HRSs; (ii) relatively large groundwater recharge represents 16% of precipitation (P, 562 mm.y−1) and large groundwater exfiltration (∼11% of P) results in short groundwater flow paths due to a dense network of streams, low permeability and hilly topographic relief; deep, long groundwater flow paths constitute a smaller component of the water budget (∼1% of P); quite high groundwater evapotranspiration (∼5% of P and ∼7% of total evapotranspiration); low permeability and shallow soils are the main reasons for relatively large components of Hortonian flow and interflow (15% and 11% of P, respectively); (iii) the majority of drainage from the catchment leaves as surface water; (iv) declining 18 years trend (4.44 mm.y−1) of groundwater storage; and (v) large spatio-temporal variability of water fluxes. This IHM study of HRSs provides greater understanding of these relatively unknown hydrologic systems that are widespread throughout the world and are important for water resources in many regions.
6. Geochemical characterization of surface water and spring water in SE Kashmir Valley, western Himalaya: Implications to water–rock interaction
Gh Jeelani; Nadeem A Bhat; K Shivanna; M Y Bhat
2011-10-01
Water samples from precipitation, glacier melt, snow melt, glacial lake, streams and karst springs were collected across SE of Kashmir Valley, to understand the hydrogeochemical processes governing the evolution of the water in a natural and non-industrial area of western Himalayas. The time series data on solute chemistry suggest that the hydrochemical processes controlling the chemistry of spring waters is more complex than the surface water. This is attributed to more time available for infiltrating water to interact with the diverse host lithology. Total dissolved solids (TDS), in general, increases with decrease in altitude. However, high TDS of some streams at higher altitudes and low TDS of some springs at lower altitudes indicated contribution of high TDS waters from glacial lakes and low TDS waters from streams, respectively. The results show that some karst springs are recharged by surface water; Achabalnag by the Bringi stream and Andernag and Martandnag by the Liddar stream. Calcite dissolution, dedolomitization and silicate weathering were found to be the main processes controlling the chemistry of the spring waters and calcite dissolution as the dominant process in controlling the chemistry of the surface waters. The spring waters were undersaturated with respect to calcite and dolomite in most of the seasons except in November, which is attributed to the replenishment of the CO2 by recharging waters during most of the seasons.
7. Correlation of metabasic rocks from metamorphic soles of the Dinaridic and the Western Vardar zone ophiolites (Serbia: Three contrasting pressure-temperature-time paths
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Srećković-Batoćanin Danica
2012-01-01
Full Text Available The field, petrological-mineralogical, geochemical and geochronological data of the metamorphic sole rocks recorded beneath the Fruška Gora, Povlen (Tejići, Stolovi and Banjska ophiolites in the Western Vardar Zone (WVZ and beneath the Zlatibor, Bistrica, Sjenički Ozren and Brezovica ophiolites in the Dinaridic ophiolite belt (DOB in Serbia are compared. The focus has been made on metabasic rocks formed in contact with the oceanic crust members: cumulate gabbro and basalts of SSZ-type with E-MORB and OIB-signature and more evolved tholeiitic basalts of MOR-affinity. Amphibole, the major phase formed from the mafic sole components, depending on pressure-temperature conditions exhibits compositional variations. According to mineral assemblages, estimated P-T conditions and ages, the potential P-T paths are given: high pressure - low temperature blueschist facies assemblage (7-9 kbar and ~400°C and <300-350°C and 4-8 kbar, recorded only in the metamorphic sole at the Fruška Gora (WVZ; high pressure - high temperature amphibolite to granulite facies (8-10 kbar and >700-850°C, recorded in both domains, the WVZ (Banjska and the DOB (Bistrica, Sjenički Ozren, Brezovica and medium pressure - medium temperature amphibolite facies assemblages (~3.5-7 kbar and >350-650°C recognized in the WZV (Tejići, Devovići and the DOB (Zlatibor. The peak metamorphic conditions point to depths of the oceanic lithosphere detachment and its initial cooling at 10-30 km, but the ages and tectonic setting of ophiolites remain poorly constrained. The summarized data may be used as an important key in geodynamic evolution of the Mesozoic Tethyan ophiolites. [Projekat Ministarstva nauke Republike Srbije, br. 176019 and br. 176016
8. Climate change and human disturbance can lead to local extinction of Alpine rock ptarmigan: new insight from the western Italian Alps.
Science.gov (United States)
Imperio, Simona; Bionda, Radames; Viterbi, Ramona; Provenzale, Antonello
2013-01-01
Alpine grouses are particularly vulnerable to climate change due to their adaptation to extreme conditions and to their relict distributions in the Alps where global warming has been particularly marked in the last half century. Grouses are also currently threatened by habitat modification and human disturbance, and an assessment of the impact of multiple stressors is needed to predict the fate of Alpine populations of these birds in the next decades. We estimated the effect of climate change and human disturbance on a rock ptarmigan population living in the western Italian Alps by combining an empirical population modelling approach and stochastic simulations of the population dynamics under the a1B climate scenario and two different disturbance scenarios, represented by the development of a ski resort, through 2050.The early appearance of snow-free ground in the previous spring had a favorable effect on the rock ptarmigan population, probably through a higher reproductive success. On the contrary, delayed snowfall in autumn had a negative effect possibly due to a mismatch in time to molt to white winter plumage which increases predation risk. The regional climate model PROTHEUS does not foresee any significant change in snowmelt date in the study area, while the start date of continuous snow cover is expected to be significantly delayed. The net effect in the stochastic projections is a more or less pronounced (depending on the model used) decline in the studied population. The addition of extra-mortality due to collision with ski-lift wires led the population to fatal consequences in most projections. Should these results be confirmed by larger studies the conservation of Alpine populations would deserve more attention. To counterbalance the effects of climate change, the reduction of all causes of death should be pursued, through a strict preservation of the habitats in the present area of occurrence.
9. Climate change and human disturbance can lead to local extinction of Alpine rock ptarmigan: new insight from the western Italian Alps.
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Simona Imperio
Full Text Available Alpine grouses are particularly vulnerable to climate change due to their adaptation to extreme conditions and to their relict distributions in the Alps where global warming has been particularly marked in the last half century. Grouses are also currently threatened by habitat modification and human disturbance, and an assessment of the impact of multiple stressors is needed to predict the fate of Alpine populations of these birds in the next decades. We estimated the effect of climate change and human disturbance on a rock ptarmigan population living in the western Italian Alps by combining an empirical population modelling approach and stochastic simulations of the population dynamics under the a1B climate scenario and two different disturbance scenarios, represented by the development of a ski resort, through 2050.The early appearance of snow-free ground in the previous spring had a favorable effect on the rock ptarmigan population, probably through a higher reproductive success. On the contrary, delayed snowfall in autumn had a negative effect possibly due to a mismatch in time to molt to white winter plumage which increases predation risk. The regional climate model PROTHEUS does not foresee any significant change in snowmelt date in the study area, while the start date of continuous snow cover is expected to be significantly delayed. The net effect in the stochastic projections is a more or less pronounced (depending on the model used decline in the studied population. The addition of extra-mortality due to collision with ski-lift wires led the population to fatal consequences in most projections. Should these results be confirmed by larger studies the conservation of Alpine populations would deserve more attention. To counterbalance the effects of climate change, the reduction of all causes of death should be pursued, through a strict preservation of the habitats in the present area of occurrence.
10. Organic-rich shales from internal Betic basins (SE Spain): potential source rocks analogs for the pre-Messinian Salt play in the western Mediterranean
Energy Technology Data Exchange (ETDEWEB)
Permanyer, A.; Jorge, R.; Baudino, R.; Gilbert, L.
2016-07-01
Southeastern Spain has a large number of Late Neogene basins with substantial evaporitic deposits that developed under an overall NNW-SSE compressional regime related to the African-European tectonic plates collision. Located in the Betic Cordillera, they can be considered as marginal Mediterranean basins that became gradually isolated during the Tortonian and Early Messinian due to tectonic uplift. Different evaporitic units accumulated in these basins during isolation and, in several cases, evaporitic conditions were associated to episodes of important organic matter accumulation. Results obtained from Late Tortonian to Early Messinian shales collected from boreholes, mines and outcrops in the internal Betic basins of Las Minas de Hellín, Cenajo and Socovos are presented. The organic matter was studied under fluorescence and scanning electron microscopy (SEM), and the main geochemical characteristics defined. They show a relation between organic-rich intervals with high potential of hydrocarbon generation, native sulfur, bio-induced dolomite and evaporitic deposits. These organicrich shales can be found before, during and after the evaporitic episodes. Results from the present study are compared with those previously obtained in the pre-evaporitic deposits of the Lorca Basin that showed high oil generation potential, a restricted-marine origin of the organic matter and a low degree of maturity. The occurrence of such potential source rocks in several basins points to a broad regional distribution. At a larger scale, in the Mediterranean Basin, organic-rich sediments were deposited before and during the Messinian Salinity Crisis. The studied examples could represent analogs for potential source rocks of the pre-Messinian salt play in the Western Mediterranean. (Author)
11. Inception and demise of a Neoproterozoic ocean basin: evidence from the Ougda complex, western Hoggar (Algeria)
Science.gov (United States)
Dostal, J.; Caby, R.; Dupuy, C.; Mevel, C.; Owen, J. V.
1996-12-01
The Neoproterozoic Ougda magmatic complex occurs within platformal carbonate rocks in the western part of the Pan-African fold belt of the Tuareg shield (NW Africa). It is composed of - 800 Ma old, relatively high P-T (i.e., Grt + Cpx-bearing: P > 5 kbar; T≈900'Q, tholeiitic mafic/ultramafic cumulates and related rocks intruded by intermediate to mafic calcalkali plutons (e.g., Cpx+Hbl-bearing gabbro) and dikes. Apparent contrasts in structural level of crystallization indicate that the calc-alkali rocks are significantly younger than the tholeiites, which temporally correlate with a period of regional extension in this part of Africa. Intrusion of the calc-alkali rocks may have occurred during the formation of an arc after the tholeiitic rocks had been (diapirically?) emplaced within the shelf carbonates, and prior to (> 630 Ma) the Pan-African orogeny. Data reported herein indicate that the Ougda complex records the inception and demise of a Neoproterozoic ocean basin. Similar crustal sections have been described from collisional (e.g., Aleutian islands) and extensional (e.g., Ivreä-Verbano zone) settings, indicating that processes operating in both environments can generate nearly indistinguishable igneous suites; the prevalence of shallow-level calc-alkali rocks in both settings may mask the presence of more mafic, tholeiitic rocks at depth.
12. Variscan thrusting in I- and S-type granitic rocks of the Tribeč Mountains, Western Carpathians (Slovakia: evidence from mineral compositions and monazite dating
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Broska Igor
2015-12-01
Full Text Available The Tribeč granitic core (Tatric Superunit, Western Carpathians, Slovakia is formed by Devonian/Lower Carboniferous, calc-alkaline I- and S-type granitic rocks and their altered equivalents, which provide a rare opportunity to study the Variscan magmatic, post-magmatic and tectonic evolution. The calculated P-T-X path of I-type granitic rocks, based on Fe-Ti oxides, hornblende, titanite and mica-bearing equilibria, illustrates changes in redox evolution. There is a transition from magmatic stage at T ca. 800–850 °C and moderate oxygen fugacity (FMQ buffer to an oxidation event at 600 °C between HM and NNO up to the oxidation peak at 480 °C and HM buffer, to the final reduction at ca. 470 °C at ΔNN= 3.3. Thus, the post-magmatic Variscan history recorded in I-type tonalites shows at early stage pronounced oxidation and low temperature shift back to reduction. The S-type granites originated at temperature 700–750 °C at lower water activity and temperature. The P-T conditions of mineral reactions in altered granitoids at Variscan time (both I and S-types correspond to greenschist facies involving formation of secondary biotite. The Tribeč granite pluton recently shows horizontal and vertical zoning: from the west side toward the east S-type granodiorites replace I-type tonalites and these medium/coarse-grained granitoids are vertically overlain by their altered equivalents in greenschist facies. Along the Tribeč mountain ridge, younger undeformed leucocratic granite dykes in age 342±4.4 Ma cut these metasomatically altered granitic rocks and thus post-date the alteration process. The overlaying sheet of the altered granites is in a low-angle superposition on undeformed granitoids and forms “a granite duplex” within Alpine Tatric Superunit, which resulted from a syn-collisional Variscan thrusting event and melt formation ~340 Ma. The process of alteration may have been responsible for shifting the oxidation trend to the observed
13. Variscan thrusting in I- and S-type granitic rocks of the Tribeč Mountains, Western Carpathians (Slovakia): evidence from mineral compositions and monazite dating
Science.gov (United States)
Broska, Igor; Petrík, Igor
2015-12-01
The Tribeč granitic core (Tatric Superunit, Western Carpathians, Slovakia) is formed by Devonian/Lower Carboniferous, calc-alkaline I- and S-type granitic rocks and their altered equivalents, which provide a rare opportunity to study the Variscan magmatic, post-magmatic and tectonic evolution. The calculated P-T-X path of I-type granitic rocks, based on Fe-Ti oxides, hornblende, titanite and mica-bearing equilibria, illustrates changes in redox evolution. There is a transition from magmatic stage at T ca. 800-850 °C and moderate oxygen fugacity (FMQ buffer) to an oxidation event at 600 °C between HM and NNO up to the oxidation peak at 480 °C and HM buffer, to the final reduction at ca. 470 °C at ΔNN= 3.3. Thus, the post-magmatic Variscan history recorded in I-type tonalites shows at early stage pronounced oxidation and low temperature shift back to reduction. The S-type granites originated at temperature 700-750 °C at lower water activity and temperature. The P-T conditions of mineral reactions in altered granitoids at Variscan time (both I and S-types) correspond to greenschist facies involving formation of secondary biotite. The Tribeč granite pluton recently shows horizontal and vertical zoning: from the west side toward the east S-type granodiorites replace I-type tonalites and these medium/coarse-grained granitoids are vertically overlain by their altered equivalents in greenschist facies. Along the Tribeč mountain ridge, younger undeformed leucocratic granite dykes in age 342±4.4 Ma cut these metasomatically altered granitic rocks and thus post-date the alteration process. The overlaying sheet of the altered granites is in a low-angle superposition on undeformed granitoids and forms "a granite duplex" within Alpine Tatric Superunit, which resulted from a syn-collisional Variscan thrusting event and melt formation ~340 Ma. The process of alteration may have been responsible for shifting the oxidation trend to the observed partial reduction.
14. Faunal associations, paleoecology and paleoenvironment of marine Jurassic rocks in the Mae Sot, Phop Phra, and Umphang areas, western Thailand
Institute of Scientific and Technical Information of China (English)
MEESOOK; Assanee; YAMEE; Chotima; SAENGSRICHAN; Wirote
2009-01-01
We here report a paleoecological analysis and depositional history of the marine Jurassic (Toarcian–early Bajocian) strata cropping out in the western part of Thailand, based on bivalve assemblages with additional data from ammonites, brachiopods, and microfossils. Generally, the benthic bivalve facies in most outcrops is rich in infaunal, semi-infaunal and epifaunal suspension-feeders. Of these, infaunal forms dominate. The diversity of this benthic assemblage was influenced by energy level, substrate, sedimentation rate, and salinity. Low to intermediate energy levels and rather soft fine-grained siliciclastic substrate are proposed as factors governing faunal distribution and explaining the greater abundance and diversity of infaunal than epifaunal suspension-feeders. There were paleoenvironmental changes both in space and time, i.e., from south to north (Umphang to Mae Sot) and from Early Bajocian to Toarcian. In the Toarcian, most outcrops in Umphang are dominated by benthic bivalve facies (infaunal, semi-infaunal, and epifaunal associations). This implies warm, shallow water (inner neritic, 50―100 m) and oxygenated conditions except for the Mae Sot area where a deeper setting (outer neritic to possibly upper continental slope, 50―200 m) with restricted basinal anoxic conditions is favored as indicated by the presence of Bositra. After higher energy conditions in the Toarcian, lower energy conditions with low sediment supplies prevail in the Alenian, and the Mae Sot area was still a restricted basin. As a result of higher sea levels, the oxygen content in the basin is increased, resulting in the presence of the ammonites. By the end of the Alenian-early Bajocian, an ammonite-bivalve association (mixed facies A) and the presence of corals and microfauna (mixed facies B) are dominant but pass upwards to near-shore higher energy conditions in most areas except for restricted basin in Mae Sot. By the middle Bajocian the environment in all areas had changed
15. Contrasting environmental memories by ancient soils on different parent rocks in the South-western Italian Alps
Science.gov (United States)
D'Amico, Michele; Catoni, Marcella; Bonifacio, Eleonora; Zanini, Ermanno
2014-05-01
Ancient soils (pre-Holocenic paleosols and vetusols) are uncommon on the Alps, because of the extensive Pleistocenic glaciations which erased most of the previously existing soils, the slope steepness and climatic conditions favoring soil erosion. However, in few sites, particularly in the outermost sections of the Alpine range, Pleistocene glaciers covered only small and scattered surfaces because of the low altitude reached in the basins, and ancient soils could be preserved for long periods of time on particularly stable surfaces. We described and sampled soils on 11 stable surfaces in the Upper Tanaro valley, Ligurian Alps (Southwestern Piemonte, Italy). The sampling sites were characterized by low steepness and elevation between 600 to 1600 m, under present day lower montane Castanea sativa/Ostrya carpinifolia forests, montane Fagus sylvatica and Pinus uncinata forests or montane heath/grazed grassland, on different substrata. In particular, we sampled soils developed on dolomite, limestone, quartzite, gneiss and shales. The soils were always well representative of the pedogenic trends active on the respective parent materials, i.e. the skeletal fraction in each soil was always composed of just one rock type, despite the proximity of lithological boundaries and the small dimensions of the different outcrops, often coexisting on the same stable surface. All the considered profiles showed signs of extremely long pedogenesis and/or different phases of intense pedogenesis interrupted by the deposition of periglacial cover beds in the steepest sites. Up to four phases of intense pedogenesis were recognized where cover beds were developed, presumably during cold Pleistocene phases, as present-day climate is not cold enough to create such periglacial morphologies. In such cases, each cover bed underwent similar pedogenesis, strongly dependent on the parent material: on quartzite, podzols with thick E horizons and well developed placic ones were formed in all phases
16. Rock History and Culture
OpenAIRE
Gonzalez, Éric
2013-01-01
Two ambitious works written by French-speaking scholars tackle rock music as a research object, from different but complementary perspectives. Both are a definite must-read for anyone interested in the contextualisation of rock music in western popular culture. In Une histoire musicale du rock (i.e. A Musical History of Rock), rock music is approached from the point of view of the people – musicians and industry – behind the music. Christophe Pirenne endeavours to examine that field from a m...
17. 40Ar/39Ar hornblende and biotite geochronology of the Bulfat Igneous Complex, Zagros Suture Zone, NE Iraq: New insights on complexities of Paleogene arc magmatism during closure of the Neotethys Ocean
Science.gov (United States)
Aswad, Khalid J.; Ali, Sarmad A.; Al. Sheraefy, Ruaa M.; Nutman, Allen P.; Buckman, Solomon; Jones, Brian G.; Jourdan, F.
2016-12-01
In NE Iraq, the eastern edge of the Arabian plate is overlain by arc rock allochthons whose genesis and tectonic emplacement were related to the consumption and closure of the Neotethys Ocean. This paper demonstrates the occurrence of unrelated Paleogene arc rocks in two adjacent allochthons. The Bulfat Igneous Complex at Wadi Rashid (NE Iraq) is an intrusion within the Upper Allochthon Albian-Cenomanian Gimo-Qandil sequence suprasubduction zone assemblage. A thrust separates this allochthon from the underlying Lower Allochthon of the Eocene-Oligocene Walash-Naopurdan volcanic-sedimentary arc rocks. The Bulfat Igneous Complex at Wadi Rashid consists of gabbro and granitic composite intrusions in which components mingle down to a small scale. Textural relationships in the Bulfat Igneous Complex rocks indicate emplacement at high crustal levels with rapid cooling, which is consistent with amphibole geobarometry indicating crystallisation pressures between 250 and 300 Mpa. Ti-rich igneous pargasite and Ti-rich igneous Fe-biotite from gabbroic and granitic components yielded 40Ar/39Ar ages of 39.23 ± 0.21 and 38.87 ± 0.24 Ma respectively. These ages agree within analytical error and suggest coeval emplacement and rapid cooling of mafic and felsic magmas in the Eocene, in an event that was distinct and much younger than the host Albian-Cenomanian rocks. This igneous event was unrelated to formation of Cenozoic rocks in the underlying, tectonically separate, lower allochthon. The trace element signatures of the Wadi Rashi volcanic rocks show volcanic-arc characteristics for the granites and the gabbroic rocks resemble E type MORB. The presence of Eocene arc-related rocks in two allochthons suggests complexity in Paleogene subduction systems, with possibly two subduction zones operating at that time.
18. Rocks Are Boring--Aren't They?
Science.gov (United States)
Lievesley, Tara
2014-01-01
The new English Curriculum requiring not only the study of sedimentary and igneous rocks but also understanding of fossil formation, is a great opportunity to make this one of the most exciting units any science teacher can present. When an animal or plant dies, it "disappears" completely as it is degraded by a range of organisms. It may…
19. 柴达木盆地西部第三系盐湖相有效生油岩的识别%Identification of Effective Source Rocks in the Tertiary Evaporate Facies in the Western Qaidam Basin
Institute of Scientific and Technical Information of China (English)
金强; 查明; 赵磊
2001-01-01
柴达木盆地西部第三系发现了储量可观的油气资源，但是总体上讲这里的生油层钙质含量高、有机质丰度低；如何识别有效生油岩，正确评价油气资源潜量，成为这里油气勘探和地球化学的首要问题。通过上、下干柴沟组生油岩的沉积特征和地球化学分析，可发现盐湖相存在许多有机质丰度较高的生油岩；利用热解和模拟实验等方法确定出有效生油岩的有机碳含量下限为0.4%。这样既为该区生油岩提供了评价标准，又找到大量有效生油岩，解决了研究区油气资源预测的基本问题。%Although there have been large volumes of oil and gas discovered from the Tertiary reservoirs in the western Qaidam basin, the source rocks have been believed as the mudstones and shales with high calcite contents and low organic carbon contents (TOC as low as 0.2%) which were deposited in the Tertiary evapo rate facies. The mudstones and shales are in great thick and distributed widely in the western Qaidam basin. In general sense, an effective source rock is ref erred to the rock with enough TOC， which expels oil when its generating oil is over a saturation in the porosity of the rock at proper buried depths or subsurf ace temperatures. If a rock with very low TOC, its generating oil could not be over the saturation for oil to be expelled out, the rock was called as ineffective source rock. Most samples analyzed by previous studies belong to the ineffec tive source rocks as their original TOC too low. Therefore, how to identify the effective source rocks is one of key aspects in petroleum resource assess ment on the Tertiary of the Qaidam basin. By sedimentology study on the potential source rocks (dark colored mudstones and shales in the evaporate facies), the authors of this article discovered that th ere were significantly vertical changes in lithologies and TOC contents in the m udstones and shales, even in a single rhythmic
20. Petrology of the Betulia Igneous Complex, Cauca, Colombia
Science.gov (United States)
Gil-Rodriguez, Javier
2014-12-01
The Betulia Igneous Complex (BIC) is a group of Late-Miocene (11.8 ± 0.2 Ma) hypabyssal intrusions of intermediate to felsic composition located in the SW of the Colombian Andes. These bodies have a calc-alkaline tendency and are related to the subduction of the Nazca plate under the South American plate. Diorites, quartz diorites and tonalities have porphyritic and phaneritic textures and are composed of plagioclase, amphibole, quartz, biotite, and orthoclase. Plagioclase is mainly of andesine-type and the amphiboles were classified mainly as magnesiohornblendes, actinolites, and tschermakites. BIC rocks have a narrow range of SiO2 content (59-67wt%) and exhibit an enrichment of LILE and LREE relative to HFSE and HREE, respectively. These features are attributed to enrichment of LILE from the source and retention of HFSE (mainly Nb, Ta, and Ti) by refractory phases within the same source. The depletion of HREE is explained by fractionation of mineral phases that have a high partition coefficients for these elements, especially amphiboles, the major mafic phase in the rocks. Nevertheless, the fractionation of garnet in early stages of crystallization is not unlikely. Probably all BIC units were generated by the same magma chamber or at least by the same petrologic mechanism as shown by the similar patterns in spider and REE diagrams; fractional crystallization and differentiation processes controlled the final composition of the rocks, and crystallization stages determined the texture. Isotopic compositions of BIC rocks (87Sr/86Sr: 0.70435-0.70511; 143Nd/144Nd: 0.51258-0.51280; 206Pb/204Pb: 19.13-19.31; 207Pb/204Pb: 15.67-15.76; 208Pb/204Pb: 38.93-39.20) indicate a source derived from the mantle with crustal contamination. The model proposed for the BIC consists of fluids from the dehydration of the subducted slab (Nazca plate) and subducted sediments that generated partial melting of the mantle wedge. These basaltic melts ascended to the mantle-crust boundary
1. Hydrothermal reequilibration of igneous magnetite in altered granitic plutons and its implications for magnetite classification schemes: Insights from the Handan-Xingtai iron district, North China Craton
Science.gov (United States)
Wen, Guang; Li, Jian-Wei; Hofstra, Albert H.; Koenig, Alan E.; Lowers, Heather A.; Adams, David
2017-09-01
Magnetite is a common mineral in igneous rocks and has been used as an important petrogenetic indicator as its compositions and textures reflect changing physiochemical parameters such as temperature, oxygen fugacity and melt compositions. In upper crustal settings, igneous rocks are often altered by hydrothermal fluids such that the original textures and compositions of igneous magnetite may be partly or completely obliterated, posing interpretive problems in petrological and geochemical studies. In this paper, we present textural and compositional data of magnetite from variably albitized granitoid rocks in the Handan-Xingtai district, North China Craton to characterize the hydrothermal reequilibration of igneous magnetite. Four types of magnetite have been identified in the samples studied: pristine igneous magnetite (type 1), reequilibrated porous magnetite (type 2), reequilibrated nonporous magnetite (type 3), and hydrothermal magnetite (type 4). Pristine igneous magnetite contains abundant well-developed ilmenite exsolution lamellae that are largely replaced by titanite during subsequent hydrothermal alteration. The titanite has a larger molar volume than its precursor ilmenite and thus causes micro-fractures in the host magnetite grains, facilitating dissolution and reprecipitation of magnetite. During sodic alteration, the igneous magnetite is extensively replaced by type 2 and type 3 magnetite via fluid-induced dissolution and reprecipitation. Porous type 2 magnetite is the initial replacement product of igneous magnetite and is subsequently replaced by the nonoporous type 3 variety as its surface area is reduced and compositional equilibrium with the altering fluid is achieved. Hydrothermal type 4 magnetite is generally euhedral and lacks exsolution lamellae and porosity, and is interpreted to precipitate directly from the ore-forming fluids. Hydrothermal reequilibration of igneous magnetite has led to progressive chemical purification, during which trace
2. Synmagmatic deformation in the underplated igneous complex of the Ivrea-Verbano zone
Science.gov (United States)
Quick, J.E.; Sinigoi, S.; Negrini, L.; Demarchi, G.; Mayer, A.
1992-01-01
The Ivrea-Verbano zone, northern Italy, contains an igneous complex up to 10km thick that is thought to have been intruded near the interface between the continental crust and mantle during the late Paleozoic. New data indicate that this complex is pervasively deformed and concentrically foliated. The presence of analogous features in ophiolitic gabbros suggests that emplacement of the Ivrea-Verbano zone plutonic rocks involved large-scale flow of crystal mush in a dynamic, and possibly extensional, tectonic environment. -from Authors
3. The Potential Role of Igneous Intrusions on Hydrocarbon Migration, West of Shetlands, UK
Science.gov (United States)
Rateau, R.; Schofield, N.; Smith, M.
2014-12-01
Numerous challenges for petroleum exploration exist within basins containing sequences of intrusive and extrusive rocks, ranging from seismic imaging to drilling. One poorly understood element in dealing with volcanic-affected basins is assessing the impact magmatism has on the elements of the petroleum system. Within this study we attempt to evaluate the potential impact that the extensive sequence of igneous intrusions of the Faroe-Shetland Basin may have on hydrocarbon migration. Using available well data combined with regional 3D seismic surveys, we show that geometrical relationships between sills location and overlying hydrocarbons shows, together with several cases of gas-charged open fractures in the sills, point toward the recognition of igneous intrusions as a factor in hydrocarbon migration through sill intrusions acting as both barriers or conduits to hydrocarbon migration. We also provide a series of general conceptual models dealing with hydrocarbon migration and igneous compartmentalization within sedimentary basins, which can be applied not just to the Faroe-Shetland Basin, but to other sedimentary basins worldwide if it is found (via well data or other methods) that the intrusions are interacting with a petroleum system.
4. Geochemistry and origin of metamorphosed mafic rocks from the Lower Paleozoic Moretown and Cram Hill Formations of North-Central Vermont: Delamination magmatism in the western New England appalachians
Science.gov (United States)
Coish, Raymond; Kim, Jonathan; Twelker, Evan; Zolkos, Scott P.; Walsh, Gregory J.
2015-01-01
The Moretown Formation, exposed as a north-trending unit that extends from northern Vermont to Connecticut, is located along a critical Appalachian litho-tectonic zone between the paleomargin of Laurentia and accreted oceanic terranes. Remnants of magmatic activity, in part preserved as metamorphosed mafic rocks in the Moretown Formation and the overlying Cram Hill Formation, are a key to further understanding the tectonic history of the northern Appalachians. Field relationships suggest that the metamorphosed mafic rocks might have formed during and after Taconian deformation, which occurred at ca. 470 to 460 Ma. Geochemistry indicates that the sampled metamorphosed mafic rocks were mostly basalts or basaltic andesites. The rocks have moderate TiO2 contents (1–2.5 wt %), are slightly enriched in the light-rare earth elements relative to the heavy rare earths, and have negative Nb-Ta anomalies in MORB-normalized extended rare earth element diagrams. Their chemistry is similar to compositions of basalts from western Pacific extensional basins near volcanic arcs. The metamorphosed mafic rocks of this study are similar in chemistry to both the pre-Silurian Mount Norris Intrusive Suite of northern Vermont, and also to some of Late Silurian rocks within the Lake Memphremagog Intrusive Suite, particularly the Comerford Intrusive Complex of Vermont and New Hampshire. Both suites may be represented among the samples of this study. The geochemistry of all samples indicates that parental magmas were generated in supra-subduction extensional environments during lithospheric delamination.
5. Different stages of chemical alteration on metabasaltic rocks in the subduction channel: Evidence from the Western Tianshan metamorphic belt, NW China
Science.gov (United States)
Xiao, Yuanyuan; Niu, Yaoling; Wang, Kuo-Lung; Iizuka, Yoshiyuki; Lin, Jinyan; Wang, Dong; Tan, Yulong; Wang, Guodong
2017-09-01
To understand the geochemistry of subduction zone metamorphism, especially the large-scale mass transfer at forearc to subarc depths, we carried out a detailed study of a ∼1.5 m size metabasaltic block with well-preserved pillow structures from the Chinese Western Tianshan high- to ultrahigh-pressure metamorphic belt. This metabasaltic block is characterized by omphacite-rich interiors gradually surrounded by abundant channelized (veins) glaucophane-rich patches toward the rims. The glaucophane-rich rims share the same peak metamorphic conditions with omphacite-rich interiors, but have experienced stronger blueschist-facies overprinting during exhumation. Representative samples from the glaucophane-rich rims and omphacite-rich interiors yield a well-defined Rb-Sr isochron age of 307 ± 23 Ma, likely representing this overprinting event. Both glaucophane-rich rims and omphacite-rich interiors show elevated K-Rb-Cs-Ba-Pb-Sr contents relative to their protolith, reflecting a large-scale enrichment of these elements and formation of abundant phengite during subduction. Compared with the omphacite-rich interiors, the glaucophane-rich rims have gained rare earth elements (REEs, >25%), U-Th (∼75%), Pb-Sr (>100%) and some transition metals like Co and Ni (25-50%), but lost P (∼75%), Na (>25%), Li and Be (∼50%); K-Rb-Cs-Ba show only 10% loss. These chemical changes would be caused by serpentinite-derived fluids during the exhumation in the subduction channel. Therefore, there are two stages of fluid action in the subduction channel. As the formation of phengite stabilizes K-Rb-Cs-Ba at the first stage, the residual fluids released from the phengite-rich metabasaltic rocks would be depleted in these elements, which are unlikely to contribute to elevated contents of these elements in arc magmas if phengite remains stable at subarc depths. In addition, the decrease of U/Pb ratios as the preferred enrichment of Pb over U in the eclogitic rocks during the first stage
6. Taos Plateau Volcanic Project: A Vehicle for Integration of Concepts in Igneous Petrology
Science.gov (United States)
Henry, D.; Dutrow, B.
2003-12-01
Integrating concepts of igneous petrology is generally a challenge, but can be effective in the context of a project based on actual field, geochemical and geochronological data. The final lab project in the igneous portion of petrology involves a series of volcanic and associated rock samples that were collected from the Taos Plateau Volcanic Field, New Mexico, USA. Samples were collected over an area of several tens of km2 throughout the Plateau and represent a spatially and temporally correlated rock suite related to continental rifting. Rift-related magmatism encompasses much of the diversity of terrestrial magma types. Compositions of mafic magmas range from tholeiite to some of the most silica-undersaturated magmas found on the continents. Large effusive eruptions from fissures are typical of some rifts, whereas others may be dominated by central vent cones or even silicic caldera complexes. The injection of mantle-derived magma in extending crust may have a profound effect on the rheology of the crust and, therefore, the style of deformation associated with extension. Most of these aspects of rift volcanism and a wide range of mafic to silicic magma compositions are represented in the Rio Grande rift and the volcanic rocks of the Taos Plateau. In addition, much published data exists for whole rock and trace element geochemistry as well as geochronology. Rock samples and associated information are presented so that the student must integrate multiple lines of evidence, petrographic, petrologic, geochemical and geochronological data in a geospatial framework, to establish a geologic history of the region. The student must also draw on skills learned in mineralogy and structural geology furthering core geoscience education. Subsequent to the petrology course, the students visit the Taos Plateau Volcanic Field during their required field camp, thus reinforcing the linkage between the classroom setting and geologic reality.
7. Uranium in alkaline rocks
Energy Technology Data Exchange (ETDEWEB)
Murphy, M.; Wollenberg, H.; Strisower, B.; Bowman, H.; Flexser, S.; Carmichael, I.
1978-04-01
Geologic and geochemical criteria were developed for the occurrence of economic uranium deposits in alkaline igneous rocks. A literature search, a limited chemical analytical program, and visits to three prominent alkaline-rock localities (Ilimaussaq, Greenland; Pocos de Caldas, Brazil; and Powderhorn, Colorado) were made to establish criteria to determine if a site had some uranium resource potential. From the literature, four alkaline-intrusive occurrences of differing character were identified as type-localities for uranium mineralization, and the important aspects of these localities were described. These characteristics were used to categorize and evaluate U.S. occurrences. The literature search disclosed 69 U.S. sites, encompassing nepheline syenite, alkaline granite, and carbonatite. It was possible to compare two-thirds of these sites to the type localities. A ranking system identified ten of the sites as most likely to have uranium resource potential.
8. From Rocks to Cement. What We Make. Science and Technology Education in Philippine Society.
Science.gov (United States)
Philippines Univ., Quezon City. Science Education Center.
This module deals with the materials used in making concrete hollow blocks. Topics discussed include: (1) igneous, metamorphic, and sedimentary rocks; (2) weathering (the process of breaking down rocks) and its effects on rocks; (3) cement; (4) stages in the manufacturing of Portland cement; and (5) the transformation of cement into concrete…
9. Evidence for metasomatic mantle carbonatitic magma extrusion in Mesoproterozoic ore-hosting dolomite rocks in the middle Kunyang rift, central Yunnan, China
Institute of Scientific and Technical Information of China (English)
2008-01-01
The Kunyang rift lying on the western margin of the Yangtze platform is a rare Precambrian Fe-Cu mineralization zone. Wuding- Lufeng basin that is an important part of the zone is located on the west edge in the middle of the rift. The most important ore-hosting rocks are Mesoproterozoic dolomite rocks in the basin controlled by a ring fracture system, which is a fundamental structure of the basin. Plenty of silicate minerals and acicular apatite, feldspar phenocrysts and small vesicular, flown line and flown plane structures, melt inclusion and high temperature fluid inclusion found in most ore-hosting dolomites suggest that this kind of rocks could not be sedimentary dolomite, marble or hydrothermal carbonate rocks. The Zr/Hf and Nb/Ta values of the rocks are identical with those of associated mantle-derived rocks, and vary widely. For the monomineral dolomite, δ18OSMOW‰=+5.99 to +18.4 and δ13CPDB‰=-3.01to+0.94, which fall within the range for all carbonatitic volcanic rocks of the world. As for the accessory minerals, the values of δ18OSMOW‰ of magnetite (=+3.47 to +5.99%0) are close to that of the mantle (<5.7%), and the δ34S‰ values of sulfides (-5.09 to+5.78, averaging+1.50) are close to that of meteorite. For all the ore-bearing dolomite rocks, εNd = +0.19 to +2.27, and the calculated Isr = 0.699143, while for the associated mantle-derived rocks, εNd = +3.18 to +3.72. All the data suggest that the mineral assemblage is not only igneous but also of metasomatic mantle origin. And the presence of acicular apatite indicates that the rocks were formed by magma rapidly cooling. And the phenocryst texture and vesicular, flown and ropy and pyroclastic structures suggest that the igneous rocks were extrusive. Therefore, the ore-bearing dolomite rocks are carbonatitic volcanic rocks. This conclusion implies that most iron and copper ore deposits hosted in the dolomite rocks should be of the carbonatitc type.
10. Trace-element fingerprints of chromite, magnetite and sulfides from the 3.1 Ga ultramafic-mafic rocks of the Nuggihalli greenstone belt, Western Dharwar craton (India)
Science.gov (United States)
Mukherjee, Ria; Mondal, Sisir K.; González-Jiménez, José M.; Griffin, William L.; Pearson, Norman J.; O'Reilly, Suzanne Y.
2015-06-01
The 3.1 Ga Nuggihalli greenstone belt in the Western Dharwar craton is comprised of chromitite-bearing sill-like ultramafic-mafic rocks that are surrounded by metavolcanic schists (compositionally komatiitic to komatiitic basalts) and a suite of tonalite-trondhjemite-granodiorite gneissic rocks. The sill-like plutonic unit consists of a succession of serpentinite (after dunite)-peridotite-pyroxenite and gabbro with bands of titaniferous magnetite ore. The chromitite ore-bodies (length ≈30-500 m; width ≈2-15 m) are hosted by the serpentinite-peridotite unit. Unaltered chromites from massive chromitites (>80 % modal chromite) of the Byrapur and Bhaktarhalli chromite mines in the greenstone belt are characterized by high Cr# (100Cr/(Cr + Al)) of 78-86 and moderate Mg# (100 Mg/(Mg + Fe2+)) of 45-55. In situ trace-element analysis (LA-ICPMS) of unaltered chromites indicates that the parental magma of the chromitite ore-bodies was a komatiite lacking nickel-sulfide mineralization. In the Ga/Fe3+# versus Ti/Fe3+# diagram, the Byrapur chromites plot in the field of suprasubduction zone (SSZ) chromites while those from Bhaktarhalli lie in the MOR field. The above results corroborate our previous results based on major-element characteristics of the chromites, where the calculated parental melt of the Byrapur chromites was komatiitic to komatiitic basalt, and the Bhaktarhalli chromite was derived from Archean high-Mg basalt. The major-element chromite data hinted at the possibility of a SSZ environment existing in the Archean. Altered and compositionally zoned chromite grains in our study show a decrease in Ga, V, Co, Zn, Mn and enrichments of Ni and Ti in the ferritchromit rims. Trace-element heterogeneity in the altered chromites is attributed to serpentinization. The trace-element patterns of magnetite from the massive magnetite bands in the greenstone belt are similar to those from magmatic Fe-Ti-V-rich magnetite bands in layered intrusions, and magnetites from
11. Study on Petrological Characteristics and Cycle of Volcano Rocks in Qingshuigou Area of Western Qilian Mountain%西祁连清水沟地区火山岩岩石学特征及旋回研究
Institute of Scientific and Technical Information of China (English)
李国涛; 孙丽莎; 翟孝志; 孙晓亮; 吴洪彬
2016-01-01
Cambrian volcano rocks in Dangjinshan Qingshuigou area in western Qilian mountain developed in vol⁃cano rock group in Cambrian Lapeiquan group. Distribution characteristics of the volcano rock and petrological char⁃acteristics have been studied and divided into 3 types of volcano rock facies, such as eruption facies, sedimentary facies and effusive facies. Volcano eruption cycles have been studied as well. The formation evolution characteristics in Dangjinshan area has been revealed. It has a certain guiding significance for the comparison of volcanic rock are⁃as and the recovery of volcanic mechanism.%西祁连当金山清水沟一带的寒武纪火山岩发育在寒武纪拉配泉岩群火山岩组。对该火山岩分布特征和岩石学特征进行了研究，划分了3类火山岩岩相：爆发相、沉积相、喷溢相，并对火山岩喷发旋回进行了研究，揭示了当金山地区地层演化特征，对火山岩区域对比及火山机构恢复具有一定的指导意义。
12. Igneous mineralogy at Bradbury Rise: The first ChemCam campaign at Gale crater
Science.gov (United States)
Sautter, V.; Fabre, C.; Forni, O.; Toplis, M. J.; Cousin, A.; Ollila, A. M.; Meslin, P. Y.; Maurice, S.; Wiens, R. C.; Baratoux, D.; Mangold, N.; Le Mouélic, S.; Gasnault, O.; Berger, G.; Lasue, J.; Anderson, R. A.; Lewin, E.; Schmidt, M.; Dyar, D.; Ehlmann, B. L.; Bridges, J.; Clark, B.; Pinet, P.
2014-01-01
and compositional analyses using Chemistry Camera (ChemCam) remote microimager and laser-induced breakdown spectroscopy (LIBS) have been performed on five float rocks and coarse gravels along the first 100 m of the Curiosity traverse at Bradbury Rise. ChemCam, the first LIBS instrument sent to another planet, offers the opportunity to assess mineralogic diversity at grain-size scales (~ 100 µm) and, from this, lithologic diversity. Depth profiling indicates that targets are relatively free of surface coatings. One type of igneous rock is volcanic and includes both aphanitic (Coronation) and porphyritic (Mara) samples. The porphyritic sample shows dark grains that are likely pyroxene megacrysts in a fine-grained mesostasis containing andesine needles. Both types have magnesium-poor basaltic compositions and in this respect are similar to the evolved Jake Matijevic rock analyzed further along the Curiosity traverse both with Alpha-Particle X-ray Spectrometer and ChemCam instruments. The second rock type encountered is a coarse-grained intrusive rock (Thor Lake) showing equigranular texture with millimeter size crystals of feldspars and Fe-Ti oxides. Such a rock is not unique at Gale as the surrounding coarse gravels (such as Beaulieu) and the conglomerate Link are dominated by feldspathic (andesine-bytownite) clasts. Finally, alkali feldspar compositions associated with a silica polymorph have been analyzed in fractured filling material of Preble rock and in Stark, a putative pumice or an impact melt. These observations document magmatic diversity at Gale and describe the first fragments of feldspar-rich lithologies (possibly an anorthosite) that may be ancient crust transported from the crater rim and now forming float rocks, coarse gravel, or conglomerate clasts.
13. Estimation of radiation hazard indices from natural radioactivity of some rocks
Institute of Scientific and Technical Information of China (English)
2006-01-01
Different samples of igneous and metamorphic rocks from Egypt and Germany have been considered to measure γ-ray activity concentrations due to naturally occurring, potentially hazardous radonuclides 2266Ra, 232Th and 40K. The radiation hazard parameters including radiation equivalent activity, gamma-absorbed dose rate, and external and internal hazard indices have been estimated. The gamma-absorbed dose rates in air of rocks in Egypt range found that the radiation hazard indices in common igneous rocks are distinctly higher in acidic than in ultrabasic rocks. The results are discussed and compared with the corresponding published data.
14. Transition element distribution in stony meteorites and in terrestrial and lunar rocks.
Science.gov (United States)
Mason, B.; Jarosewich, E.; Nelen, J.
1971-01-01
Discussion of the distribution of the transition elements (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) among the individual minerals of stony meteorites, and comparison with data on comparable lunar and terrestrial minerals. As an example of meteorite distribution patterns, data on the Modoc meteorite are presented. For the lunar rocks, microprobe data are used, along with published information from other investigators. For comparison with terrestrial igneous rocks, Skaergaard intrusion rocks are used. They present some striking analogies in mineralogy and petrology with the lunar igneous rocks and are thus peculiarly suitable for this cross comparison.
15. 新疆西天山古生代侵入岩的地质特征及构造意义%Geological characteristics and tectonic significance of Paleozoic intrusive rocks in Western Tianshan of Xinjiang Province.
Institute of Scientific and Technical Information of China (English)
朱志新; 李锦轶; 董连慧; 王克卓; 张晓帆; 徐仕琪
2011-01-01
新疆西天山造山带位于古亚洲构造域的中南部,古生代岩浆活动强烈,侵入岩发育.文章系统总结了新疆西天山古生代侵入岩的时空分布、地质特征及其地球化学特征,认为其是南、北天山洋盆演化的产物,早石炭世及其以前的古生代侵入岩呈带状分布于各山系中.主要为一套与洋盆收敛俯冲有关的钙碱性侵入岩,晚石炭世及其之后的古生代侵入岩则具有面状分布的特征,主要为一套与同碰撞有关的富铝花岗岩和后造山的富钾花岗岩.%Western Tianshan orogenic belt of Xinjiang is in the central and southern part of ancient Asian tectonic region where magmatic activities were very intense in the Paleozoic and intrusive rocks extensively developed. This paper sums up the space-time distribution, geological characteristics and geochemical features of Paleozoic intrusive rocks in Western Tianshan, and they are considered as the products of the South and North Tianshan oceanic basin evolution. In the Early Carboniferous and before, Paleozoic intrusive rocks are zonally distributed in the mountains and they are mainly a set of calc-alkaline intrusive rocks related to convergence and subduction ofoceanic basins. In the Late Carboniferous and after, Paleozoic intrusive rocks presents planar distribution, and they are mainly a set of Al-rich granite related to collision and a set of post-orogenic K-rich granite.
16. Petrography and chemical evidence for multi-stage emplacement of western Buem volcanic rocks in the Dahomeyide orogenic belt, southeastern Ghana, West Africa
Science.gov (United States)
Nude, Prosper M.; Kwayisi, Daniel; Taki, Naa A.; Kutu, Jacob M.; Anani, Chris Y.; Banoeng-Yakubo, Bruce; Asiedu, Daniel K.
2015-12-01
The volcanic rocks of the Buem Structural Unit in the Dahomeyide orogenic belt of southeastern Ghana, constitute a unique assemblage among the monocyclic sedimentary formations of this structural unit. Representative volcanic rock samples were collected from the Asukawkaw, Bowiri-Odumase and Nkonya areas which form a roughly north-south trend. The volcanic rocks comprise spherulitic, amygdaloidal, vesicular, phyric and aphyric varieties. Whole rock geochemistry shows that these volcanic rocks exhibit both alkaline and subalkaline characteristics. The alkaline varieties are relatively enriched in REE and incompatible trace element concentrations, similar to OIB; the subalkaline varieties show E-MORB and N-MORB REE and incompatible element characteristics. The rocks have low La/Nb (<1), low K/Nb (<450) and high Nb/U (averagely 47.3) values, suggesting no significant effect of crustal contamination. The key characteristics of these volcanic rocks are the distinct petrography and geochemistry, shown from the three separate localities, which may suggest source fractionation at different depths or modes of emplacement. The association of volcanic rocks of OIB, E-MORB and N-MORB affinities, with no significant crustal contamination, may suggest mantle derived magma that may have been related to rifting event and eventual emplacement at the eastern passive margin of the West African Craton.
17. In search for coastal amplification of rock weathering in polar climates - pilot Schmidt hammer rock tests surveys from sheltered fjords of Svalbard and tsunami-affected coasts of Western Greenland.
Science.gov (United States)
Strzelecki, Matt
2014-05-01
Recent decade has seen the major advance in Arctic coastal geomorphology due to research progress along ice-rich permafrost coastlines of Siberia, Alaska and NW Canada. On the contrary little attention was paid to Arctic rocky coastlines and their response to the reduction of sea ice cover and increased number of storms reaching Arctic region. In this paper I present results from a pilot survey of rock resistance using Schmidt Hammer Rock Tests across rocky cliffs and shore platforms developed in: - sheltered bays of Billefjorden, Svalbard characterised by prolonged sea-ice conditions and very limited operation of wave and tidal action - Vaigat Strait and Isfjorden in W Greenland influenced by landslide-triggered tsunamis and waves induced by ice-berg roll events. The aim of a pilot study was to test the hypothesized coastal impact on the rate of rock weathering in polar climates. To do so I characterise the changes in the rock resistance on the following coastal landforms: - modern and uplifted wave-washed abrasion platforms- focusing on a relation between the degree of rock surface weathering and the distance from the shoreline as well as thickness of sediment cover on shore platform surface - modern and uplifted rocky cliffs - focusing on a relation between the degree of rock surface weathering and the distance from the shoreline as well as difference in height above the sea level and relation to rock lithology. The results present another line of argument supporting intensification of rock weathering processes in the Arctic coastal zone. This work is a contribution to the National Science Centre in Poland research project no. 2011/01/B/ST10/01553.
18. An integrative geologic, geochronologic and geochemical study of Gorgona Island, Colombia: Implications for the formation of the Caribbean Large Igneous Province
Science.gov (United States)
Serrano, Lina; Ferrari, Luca; Martínez, Margarita López; Petrone, Chiara Maria; Jaramillo, Carlos
2011-09-01
The genesis of the Caribbean Large Igneous Province (CLIP) has been associated to the melting of the Galapagos plume head at ~ 90 Ma or to the interaction between the plume and the Caribbean slab window. Gorgona Island, offshore western Colombia, is an accreted fragment of the CLIP and its highly heterogeneous igneous suite, ranging from enriched basalts to depleted komatiites and picrites, was assumed to have formed at ~ 89 Ma from different part of the plume. Here we present new geologic, geochronologic and geochemical data of Gorgona with significant implications for the formation of the CLIP. A new set of 40Ar- 39Ar ages documents a magmatic activity spanning the whole Late Cretaceous (98.7 ± 7.7 to 64.4 ± 5 Ma) followed by a shallower, picritic pyroclastic eruption in the Paleocene. Trace element and isotope geochemistry confirm the existence of an enriched (EDMM: La/Sm N ≥ 1 and ɛNd i of 5.7 to 7.8) and a depleted (DMM: La/Sm N rocks. Higher degree of melting (> 10%) of a mixed DMM + EDMM (40 to 60%) may reproduce the more depleted rocks with temperatures in the range of ambient mantle in absence of plumes. Our results contradict the notion that the CLIP formed by melting of a plume head at ~ 90 Ma. Multiple magmatic pulses over several tens of Ma in small areas like Gorgona, also recognized in other CLIP areas, suggest a long period of diffuse magmatism without a clear pattern of migration. The age span of this magmatism is broadly concurrent with the Caribbean slab window. During this time span the Farallon oceanic lithosphere (later becoming the Caribbean plate) advanced eastward ~ 1500 km, overriding the astenosphere feeding the proto-Caribbean spreading ridge. This hotter mantle flowed westward into, and mixed with, the opening mantle wedge, promoting increasing melting with time. The fortuitous occurrence of a plume passing through the slab gap area cannot be excluded but not required to produce the observed composition and degree of melting.
19. Experimental petrology and origin of Fra Mauro rocks and soil.
Science.gov (United States)
Walker, D.; Longhi, J.; Hays, J. F.
1972-01-01
Results of melting experiments over the pressure range from 0 to 20 kb on Apollo 14 igneous rocks 14310 and 14072, and on comprehensive fines 14259. It is found that low-pressure crystallization of rocks 14310 and 14072 proceeds as predicted from the textural relationships displayed by thin sections of these rocks. The mineralogy and textures of these rocks are the result of near-surface crystallization. The chemical compositions of these lunar samples all show special relationships to multiply saturated liquids in the system anorthite-forsterite-fayalite-silica at low pressure. Partial melting of a lunar crust consisting largely of plagioclase, low-calcium pyroxene, and olivine, followed by crystal fractionation at the lunar surface, is a satisfactory mechanism for the production of the igneous rocks and soil glasses sampled by Apollo 14. The KREEP component of other lunar soils, may have a similar origin.
20. Some Environmental Consequences of Large Igneous Provinces
Science.gov (United States)
Coffin, M. F.
2009-12-01
The formation of large igneous provinces (LIPs)—continental flood basalts, ‘volcanic’ margins, and oceanic plateaus—may impact the atmosphere, oceans, and biosphere by rapidly releasing huge amounts of particulates, magmatic volatiles (CO2, SO2, Cl, F, etc.), and potentially volatiles (CO2, CH4, SO2, etc.) from intruded sediments (e.g., carbonates, organic-rich shales, evaporites). A key factor affecting the magnitude of volatile release is whether eruptions are subaerial or marine; hydrostatic pressure inhibits vesiculation and degassing of relatively soluble volatile components (H2O, S, Cl, F) in deep water submarine eruptions, although low solubility components (CO2, noble gases) are mostly degassed even at abyssal depths. Directly or indirectly, such injections may cause changes in the atmosphere/ocean system that can lead to perturbations of atmosphere/ocean chemistry, circulation, ecology, and biological productivity. These changes can be global in extent, particularly if environmental conditions were at or near a threshold state or tipping point. LIPs may have been responsible for some of the most dramatic and rapid changes in the global environment. For example, between ~145 and ~50 Ma, the global ocean was characterized by chemical and isotopic variations (especially in C and Sr isotope ratios, trace metal concentrations, and biocalcification), relatively high temperatures, high relative sea level, episodic deposition of black shales (oceanic anoxic events), high production of hydrocarbons, mass extinctions of marine organisms, and radiations of marine flora and fauna. Temporal correlations between the intense pulses of igneous activity associated with LIP formation and environmental changes suggest more than pure coincidence. The 1783-84 eruption of Laki on Iceland provides the only historical record of the type of volcanism that constructs transient LIPs. Although Laki produced a basaltic lava flow representing only ~1% of the volume of a typical
1. Evaluation of the nature, origin and potentiality of the subsurface Middle Jurassic and Lower Cretaceous source rocks in Melleiha G-1x well, North Western Desert, Egypt
Directory of Open Access Journals (Sweden)
2015-09-01
Full Text Available The present work aims to evaluate the nature and origin of the source rock potentiality of subsurface Middle Jurassic and Lower Cretaceous source rocks in Melleiha G-1x well. This target was achieved throughout the evaluation of total organic carbon, rock Eval pyrolysis and vitrinite reflectance for fifteen cutting samples and three extract samples collected from Khatatba, Alam El Bueib and Kharita formations in the studied well. The result revealed that the main hydrocarbon of source rocks, for the Middle Jurassic (Khatatba Fm. is mainly mature, and has good capability of producing oil and minor gas. Lower Cretaceous source rocks (Alam El Bueib Fm. are mature, derived from mixed organic sources and have fair to good capability to generate gas and oil. Kharita Formation of immature source rocks originated from terrestrial origin and has poor to fair potential to produce gas. This indicates that Khatatba and Alam El Bueib formations take the direction of increasing maturity far away from the direction of biodegradation and can be considered as effective source potential in the Melleiha G-1x well.
2. The Importance of Geochemical Parameters and Shale Composition on Rock Mechanical Properties of Gas Shale Reservoirs: a Case Study From the Kockatea Shale and Carynginia Formation From the Perth Basin, Western Australia
Science.gov (United States)
2015-05-01
Evaluation of the gas shale mechanical properties is very important screening criteria for determining the potential intervals for hydraulic fracturing and as a result in gas shale sweet spot mapping. Young's modulus and Poisson's ratio are two controlling mechanical properties that dictate the brittleness of the gas shale layers. These parameters can be determined in the laboratory by testing the rock sample under different conditions (static method) or can be calculated using the well-logging data including sonic and density log data (dynamic method). This study investigates the importance of the shale composition and geochemical parameters on the Young's modulus and Poisson's ratio using log data. The data set of this study is coming from five different wells targeting the Kockatea Shale and Carynginia formation, two potential gas shale formations in the Perth Basin, Western Australia. The results show that converse to the common idea the effect of organic matter quantity and maturity on the rock mechanical properties of the gas shale reservoirs is not so much prominent, while the composition of the rock has an important effect on these properties. Considering the weight percentage of shale composition and organic matter quantity it could be concluded that effect of these parameters on rock mechanical properties is dependent on their weight contribution on the shale matrix. As well as effect of thermal maturity on the shale matrix and consequently on the rock mechanical properties of the shales is dependent on the organic matter content itself; therefore, obviously with a low organic matter content thermal maturity has no prominent effect on the brittleness as well.
3. The role of igneous and metamorphic processes in triggering mass extinctions and Earth crises
Science.gov (United States)
Svensen, Henrik; Planke, Sverre; Polozov, Alexander G.; Jerram, Dougal; Jones, Morgan T.
2016-04-01
Mass extinctions and transient climate events commonly coincide in time with the formation of Large igneous provinces (LIPs). The end-Permian event coincides with the Siberian Traps, the end-Triassic with the Central Atlantic Magmatic Event (CAMP), the Toarcian with the Karoo LIP, and the Paleocene-Eocene Thermal Maximum (PETM) with the North Atlantic Igneous Province. Although the temporal relationship between volcanism and the environmental crises has been known for decades, the geological processes linking LIPs to these environmental events are strongly debated: Explosive LIP volcanism should lead to short term cooling (not long term warming), mantle CO2 is too 13C-enriched to explain negative 13C carbon isotope excursions from sedimentary sequences, the LIP volcanism is poorly dated and apparently lasts much longer that the associated environmental events, large portions of the LIPs remain poorly explored, especially the sub-volcanic parts where sills and dikes are emplaced in sedimentary host rocks, and thus gas flux estimates from contact aureoles around sill intrusions are often poorly constrained. In this presentation, we discuss the status of LIP research with an emphasis on the sub volcanic processes. We show that potential for degassing of greenhouse gases, aerosols, and ozone destructive gases is substantial and can likely explain the triggering of both climatic events and mass extinctions.
4. Characterization of mineral coatings associated with a Pleistocene‐Holocene rock art style: The Northern Running Figures of the East Alligator River region, western Arnhem Land, Australia
Directory of Open Access Journals (Sweden)
Penelope L. King
2017-02-01
Full Text Available This data article contains mineralogic and chemical data from mineral coatings associated with rock art from the East Alligator River region. The coatings were collected adjacent to a rock art style known as the “Northern Running Figures” for the purposes of radiocarbon dating (doi:10.1016/j.jasrep.2016.11.016; (T. Jones, V. Levchenko, P.L. King, U. Troitzsch, D. Wesley, 2017 [1]. This contribution includes raw and processed powder X-ray Diffraction data, Scanning Electron Microscopy energy dispersive spectroscopy data, and Fourier Transform infrared spectral data.
5. Characterization of mineral coatings associated with a Pleistocene-Holocene rock art style: The Northern Running Figures of the East Alligator River region, western Arnhem Land, Australia.
Science.gov (United States)
King, Penelope L; Troitzsch, Ulrike; Jones, Tristen
2017-02-01
This data article contains mineralogic and chemical data from mineral coatings associated with rock art from the East Alligator River region. The coatings were collected adjacent to a rock art style known as the "Northern Running Figures" for the purposes of radiocarbon dating (doi:10.1016/j.jasrep.2016.11.016; (T. Jones, V. Levchenko, P.L. King, U. Troitzsch, D. Wesley, 2017) [1]). This contribution includes raw and processed powder X-ray Diffraction data, Scanning Electron Microscopy energy dispersive spectroscopy data, and Fourier Transform infrared spectral data.
6. Zircon U-Pb dating, geochemical and Sr-Nd-Hf isotopic characteristics of the Jintonghu monzonitic rocks in western Fujian Province, South China: Implication for Cretaceous crust-mantle interactions and lithospheric extension
Science.gov (United States)
Li, Bin; Jiang, Shao-Yong; Lu, An-Huai; Zhao, Hai-Xiang; Yang, Tang-Li; Hou, Ming-Lan
2016-09-01
Comprehensive petrological, in situ zircon U-Pb dating, Ti-in-zircon temperature and Hf isotopic compositions, whole rock geochemical and Sr-Nd isotopic data are reported for the Jintonghu monzonitic intrusions in the western Fujian Province (Interior Cathaysia Block), South China. The Jintonghu monzonitic intrusions were intruded at 95-96 Ma. Their Sr-Nd-Hf isotopic compositions are similar to the coeval and nearby enriched lithospheric mantle-derived mafic and syenitic rocks, indicating that the Jintonghu monzonitic rocks were likely derived from partial melting of the enriched mantle sources. Their high Nb/Ta ratios (average 21.6) suggest that the metasomatically enriched mantle components were involved, which was attributed to the modification of slab-derived fluid and melt by the subduction of the paleo-Pacific Plate. The presence of mafic xenoliths, together with geochemical and isotopic features indicates a mafic-felsic magma mixing. Furthermore, the Jintonghu intrusions may have experienced orthopyroxene-, biotite- and plagioclase-dominated crystallization. Crust-mantle interaction can be identified as two stages, including that the Early Cretaceous mantle metasomatism and lithospheric extension resulted from the paleo-Pacific slab subduction coupled with slab rollback, and the Late Cretaceous crustal activation and enhanced extension induced by dip-angle subduction and the underplating of mantle-derived mafic magma.
7. Textures of the soils and rocks at Gusev crater from Spirit's Microscopic Imager
DEFF Research Database (Denmark)
Herkenhoff, K.E.; Squyres, S.W.; Arvidson, R.;
2004-01-01
The Microscopic Imager on the Spirit rover analyzed the textures of the soil and rocks at Gusev crater on Mars at a resolution of 100 micrometers. Weakly bound agglomerates of dust are present in the soil near the Columbia Memorial Station. Some of the brushed or abraded rock surfaces show igneous...
8. Preliminary review of Precambrian Shield rocks for potential waste repository
Energy Technology Data Exchange (ETDEWEB)
Yardley, D.H.; Goldich, S.S.
1975-11-01
This review of the Canadian Shield is primarily concerned with the part (such as in the Lake Superior region) that is seismically the least active of the North American continent. The crystalline metamorphic and igneous rocks of the more stable elements of the shield provide excellent possibilities for dry excavations suitable for long-term storage of radioactive waste materials. (DLC)
9. Origin of igneous meteorites and differentiated asteroids
Science.gov (United States)
Scott, E.; Goldstein, J.; Asphaug, E.; Bottke, W.; Moskovitz, N.; Keil, K.
2014-07-01
Introduction: Igneously formed meteorites and asteroids provide major challenges to our understanding of the formation and evolution of the asteroid belt. The numbers and types of differentiated meteorites and non-chondritic asteroids appear to be incompatible with an origin by fragmentation of numerous Vesta-like bodies by hypervelocity impacts in the asteroid belt over 4 Gyr. We lack asteroids and achondrites from the olivine-rich mantles of the parent bodies of the 12 groups of iron meteorites and the ˜70 ungrouped irons, the 2 groups of pallasites and the 4--6 ungrouped pallasites. We lack mantle and core samples from the parent asteroids of the basaltic achondrites that do not come from Vesta, viz., angrites and the ungrouped eucrites like NWA 011 and Ibitira. How could core samples have been extracted from numerous differentiated bodies when Vesta's basaltic crust was preserved? Where is the missing Psyche family of differentiated asteroids including the complementary mantle and crustal asteroids [1]? Why are meteorites derived from far more differentiated parent bodies than chondritic parent bodies even though C and S class chondritic asteroids dominate the asteroid belt? New paradigm. Our studies of meteorites, impact modeling, and dynamical studies suggest a new paradigm in which differentiated asteroids accreted at 1--2 au less than 2 Myr after CAI formation [2]. They were rapidly melted by 26Al and disrupted by hit-and-run impacts [3] while still molten or semi-molten when planetary embryos were accreting. Metallic Fe-Ni bodies derived from core material cooled rapidly with little or no silicate insulation less than 4 Myr after CAI formation [4]. Fragments of differentiated planetesimals were subsequently tossed into the asteroid belt. Meteorite evidence for early disruption of differentiated asteroids. If iron meteorites were samples of Fe-Ni cores of bodies that cooled slowly inside silicate mantles over ˜50--100 Myr, irons from each core would have
10. Mineralogical and geochemical characteristics of Miocene pelitic sedimentary rocks from the south-western part of the Pannonian Basin System (Croatia: Implications for provenance studies
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Anita Grizelj
2017-01-01
Full Text Available Fifty-two samples of Miocene pelitic sedimentary rock from outcrops on Medvednica, Moslavačka Gora and Psunj Mts., and boreholes in the Sava Depression and the Požega Sub-depression were investigated. These sediments formed in different marine (with normal and reduced salinity, brackish, and freshwater environments, depending on the development stage of the Pannonian Basin System. Carbonate minerals, clay minerals and quartz are the main constituents of all pelitic sedimentary rocks, except in those from Moslavačka Gora Mt in which carbonate minerals are not present. Feldspars, pyrite, opal-CT, and hematite are present as minor constituents in some rocks. Besides calcite, dependent on the sedimentary environment and diagenetic changes, high-magnesium calcite, aragonite, dolomite and ankerite/Ca-dolomite are also present. Smectite or illite-smectite is the main clay minerals in the samples. Minor constituents, present in almost all samples, are detrital illite and kaolinite. In some samples chlorite is also present in a low amount. Major elements, trace elements and rare earth elements patterns used in provenance analysis show that all analysed samples have a composition similar to the values of the upper continental crust (UCC. The contents of major and trace elements as well as SiO2/Al2O3, K2O/Al2O3, Na2O/K2O, Eu/Eu*, La/Sc, Th/Sc, La/Co Th/Co, Th/Cr, Ce/Ce* and LREE/HREE ratios, show that the analysed pelitic sedimentary rocks were formed by weathering of different types of mostly acidic (silicic, i.e. felsic rocks.
11. Experiments and Spectral Studies of Martian Volcanic Rocks: Implications for the Origin of Pathfinder Rocks and Soils
Science.gov (United States)
Rutherford, Malcolm J.; Mustard, Jack; Weitz, Catherine
2002-01-01
The composition and spectral properties of the Mars Pathfinder rocks and soils together with the identification of basaltic and andesitic Mars terrains based on Thermal Emission Spectrometer (TES) data raised interesting questions regarding the nature and origin of Mars surface rocks. We have investigated the following questions: (1) are the Pathfinder rocks igneous and is it possible these rocks could have formed by known igneous processes, such as equilibrium or fractional crystallization, operating within SNC magmas known to exist on Mars? If it is possible, what P (depth) and PH2O conditions are required? (2) whether TES-based interpretations of plagioclase-rich basalt and andesitic terrains in the south and north regions of Mars respectively are unique. Are the surface compositions of these regions plagioclase-rich, possibly indicating the presence of old AI-rich crust of Mars, or are the spectra being affected by something like surface weathering processes that might determine the spectral pyroxene to plagioclase ratio?
12. Log evaluation of fractured igneous reservoirs in Songliao Basin
Institute of Scientific and Technical Information of China (English)
2007-01-01
The petrophysical parameters are bad in most igneous reservoirs of Songliao Basin because of the very low porosity and permeability. The evaluation of igneous reservoirs has not been fully studied so far. The current technique of formation evaluation and interpretation used in sedimentary formations face a series of problems and difficulties. In this study, The PCA was used to identify lithology, a multi-mineral model "QAPM" was proposed. "Surface effect" must be considered when evaluating saturation. A software "SIMPLE" was developed and was used to deal with the logging data in over 70 wells with good results were achieved.
13. Short-lived subduction and exhumation in Western Papua (Wandamen peninsula): Co-existence of HP and HT metamorphic rocks in a young geodynamic setting
Science.gov (United States)
François, Camille; de Sigoyer, Julia; Pubellier, Manuel; Bailly, Vivien; Cocherie, Alain; Ringenbach, Jean-Claude
2016-12-01
Understanding processes of formation of accretionary wedges requires studying young and well preserved examples. The Lengguru wedge (West Papua) is younger than 10 Myr and is a result of oblique and fast subduction (11 cm/yr) of the Bird's Head (a part of the Australian margin beneath the Melanesian Arc). Thus, the rapid formation of this wedge (actually a Fold and Thrust Belt) may be attributed to a single tectonic event. High pressure (HP) metabasic and metasedimentary rocks have been discovered in the core of the wedge in the Wandamen peninsula. Locally, these rocks are overprinted by migmatization during the decompression. Field relationships indicate that migmatites and anatectic leucogranite crosscut the HP metamorphic rocks. This paper reports characterization of petrology and thermobarometry of metasediments and metabasic samples, all included in a former mélange-type rock association, as well as geochronology of metasediments. Pressure-Temperature (P-T) conditions highlight two stages of metamorphism within a small time bracket. In metasediments, a first stage of relatively HP ( 13-17 kbar) is observed as attested by a first paragenesis of garnet-kyanite-phengite. Garnet, kyanite and phengite are then destabilized in favor of biotite during the decompression (5-12 kbar and > 550 °C). Late fractures filled with chlorite and a second generation of white mica crosscut the foliation (< 7 kbar and 500-600 °C). In metabasic rocks, the peak of pressure is reached from 17 to 23 kbar and from 700 to 800 °C. Geochronological study was conducted using U-Pb dating (LA-MC-ICPMS) on zircons from the metasedimentary and migmatitic rocks. Some zircon cores often present high Th/U ratio typical for magmatic origin, as confirmed by trace element signature of metasediments, and recorded ages older than 300 Ma, witness of the activity of a volcanic arc on the former margin of the Australian craton. Most other zircons present a low Th/U ratio attesting their metamorphic
14. Geochemistry, petrography, and zircon U-Pb geochronology of Paleozoic metaigneous rocks in the Mount Veta area of east-central Alaska: implications for the evolution of the westernmost part of the Yukon-Tanana terrane
Science.gov (United States)
Dusel-Bacon, Cynthia; Day, Warren C.; Aleinikoff, John N.
2013-01-01
We report the results of new mapping, whole-rock major, minor, and trace-element geochemistry, and petrography for metaigneous rocks from the Mount Veta area in the westernmost part of the allochthonous Yukon–Tanana terrane (YTT) in east-central Alaska. These rocks include tonalitic mylonite gneiss and mafic metaigneous rocks from the Chicken metamorphic complex and the Nasina and Fortymile River assemblages. Whole-rock trace-element data from the tonalitic gneiss, whose igneous protolith was dated by SHRIMP U–Pb zircon geochronology at 332.6 ± 5.6 Ma, indicate derivation from tholeiitic arc basalt. Whole-rock analyses of the mafic rocks suggest that greenschist-facies rocks from the Chicken metamorphic complex, a mafic metavolcanic rock from the Nasina assemblage, and an amphibolite from the Fortymile River assemblage formed as island-arc tholeiite in a back-arc setting; another Nasina assemblage greenschist has MORB geochemical characteristics, and another mafic metaigneous rock from the Fortymile River assemblage has geochemical characteristics of calc-alkaline basalt. Our geochemical results imply derivation in an arc and back-arc spreading region within the allochthonous YTT crustal fragment, as previously proposed for correlative units in other parts of the terrane. We also describe the petrography and geochemistry of a newly discovered tectonic lens of Alpine-type metaharzburgite. The metaharzburgite is interpreted to be a sliver of lithospheric mantle from beneath the Seventymile ocean basin or from sub-continental mantle lithosphere of the allochthonous YTT or the western margin of Laurentia that was tectonically emplaced within crustal rocks during closure of the Seventymile ocean basin and subsequently displaced and fragmented by faults.
15. Geochemical and zircon isotopic evidence for extensive high level crustal contamination in Miocene to mid-Pleistocene intra-plate volcanic rocks from the Tengchong field, western Yunnan, China
Science.gov (United States)
Li, Linlin; Shi, Yuruo; Williams, Ian S.; Anderson, J. Lawford; Wu, Zhonghai; Wang, Shubing
2017-08-01
SHRIMP zircon Pb/U dating of Cenozoic volcanic rocks in the Tengchong area, western Yunnan Province, China, shows that the dacite and andesitic breccia lavas from Qushi village were intruded at 480 ± 10 ka and 800 ± 40 ka, respectively. Moreover, Pb/U dating of trachyandesite from Tuantian village and olivine basalt from Wuhe village give weighted mean 206Pb/238U ages of 2.82 ± 0.08 Ma and 12.28 ± 0.30 Ma. Corrections for initial 230Th disequilibrium of zircon were used for the former two younger ages. The Tengchong volcanic rocks have a large range of SiO2 (48.6-66.9 wt.%) and mostly belong to a high-K calc-alkaline series. The lavas originated from heterogeneous sources and were modified by subsequent fractional crystallization. The REE and other trace element patterns of the Tengchong volcanic rocks resemble magmas having a large component of continental crust. All have similar degrees of LREE and HREE fractionation and are enriched in LILE, La, Ce and Pb, with depletions in Nb, Ta, Ti, Sr and P relative to primitive mantle. Zircon δ18O values of 6.96 ± 0.17 and 7.01 ± 0.24‰ and highly varied negative εHf(t) values of - 1.5 to - 11.0 and - 10.3 to - 13.7, as well as the presence of inherited zircon grains in the studied samples, indicate that the magmas contain crustal material on a large scale. The Tengchong volcanic rocks have HFSE ratios (e.g., Nb/Ta, La/Nb, Zr/Y) similar to continental flood basalts, indicative of an intra-plate extensional tectonic setting. Widespread distributed faults might have facilitated upwelling of mantle-derived melts and eruptions from shallow crustal magma chambers to form the large volcanic field.
16. Building the EarthChem System for Advanced Data Management in Igneous Geochemistry
Science.gov (United States)
Lehnert, K.; Walker, J. D.; Carlson, R. W.; Hofmann, A. W.; Sarbas, B.
2004-12-01
Several mature databases of geochemical analyses for igneous rocks are now available over the Internet. The existence of these databases has revolutionized access to data for researchers and students allowing them to extract data sets customized to their specific problem from global data compilations with their desktop computer within a few minutes. Three of the database efforts - PetDB, GEOROC, and NAVDAT - have initiated a collaborative effort called EarthChem to create better and more advanced and integrated data management for igneous geochemistry. The EarthChem web site (http://www.earthchem.org/) serves as a portal to the three databases and information related to EarthChem activities. EarthChem participants agreed to establish a dialog to minimize duplication of effort and share useful tools and approaches. To initiate this dialog, a workshop was run by EarthChem in October, 2003 to discuss cyberinfrastructure needs in igneous geochemistry (workshop report available at the EarthChem site). EarthChem ran an information booth with database and visualization demonstrations at the Fall 2003 AGU meeting (and will have one in 2004) and participated in the May 2003 GERM meeting in Lyon, France where we provided the newly established Publishers' Round Table a list of minimum standards of data reporting to ease the assimilation of data into the databases. Aspects of these suggestions already have been incorporated into new data policies at Geochimica et Cosmochimica Acta and Chemical Geology (Goldstein et al. 2004), and are under study by the Geological Society of America. EarthChem presented its objectives and activities to the Solid Earth Sciences community at the Annual GSA Meeting 2003 (Lehnert et al, 2003). Future plans for EarthChem include expanding the types and amounts of data available from a single portal, giving researchers, faculty, students, and the general public the ability to search, visualize, and download geochemical and geochronological data for a
17. The Paleoproterozoic Singo granite in south-central Uganda revealed as a nested igneous ring complex using geophysical data
Science.gov (United States)
Abdelsalam, Mohamed G.; Katumwehe, Andrew B.; Atekwana, Estella A.; Le Pera, Alan K.; Achang, Mercy
2016-04-01
We used high-resolution airborne magnetic and radiometric data and satellite gravity data to investigate the form of occurrence of the Paleoproterozoic Singo granite in west-central Uganda. This granitic body covers an area of ∼700 km2, intrudes Paleoproterozoic crystalline rocks and overlain by Paleoproterozoic-Mesoproterozoic sedimentary rocks, both of which belong to the Rwenzori terrane, and it is host to hydrothermally-formed economic minerals such as gold and tungsten. Our analysis provided unprecedented geometrical details of the granitic body and revealed the following: (1) the margins of the Singo granite are characterized by a higher magnetic signature compared to the interior of the granitic body as well as the surroundings. These anomalies are apparent in both the total magnetic field and horizontal derivative images and define eight overlapping ring features. (2) the depth continuation of these magnetic anomalies define outward but steeply-dipping features as indicated by the tilt images extracted from the airborne magnetic data. This is further supported by forward modeling of the magnetic and gravity data. (3) the Singo granite is characterized by relatively high and evenly-distributed equivalent concentration of Uranium (eU) and Thorium (eTh) compared to the surroundings and this is apparent in the Potassium (K)-eTh-eU radiometric ternary image. (4) the granitic body is defined by a gravity low anomaly that persisted to a depth of three km as shown by the Bouguer anomaly image and its five km upward continuation. We used these observations to identify this granitic body as a nested igneous ring complex and we refer to it as the Singo Igneous Ring Complex (SIRC). We further interpreted the eight ring structures as individual igneous ring complexes aligned in an E-W and NE-SW direction and these were developed due to repeated calderas collapse. Additionally, we interpreted the ring-shaped magnetic anomalies as due to hydrothermally-altered margins
18. Petrochemistry and hydrothermal alteration within the Tyrone Igneous Complex, Northern Ireland: implications for VMS mineralization in the British and Irish Caledonides
Science.gov (United States)
Hollis, Steven P.; Roberts, Stephen; Earls, Garth; Herrington, Richard; Cooper, Mark R.; Piercey, Stephen J.; Archibald, Sandy M.; Moloney, Martin
2014-06-01
Although volcanogenic massive sulfide (VMS) deposits can form within a wide variety of rift-related tectonic environments, most are preserved within suprasubduction affinity crust related to ocean closure. In stark contrast to the VMS-rich Appalachian sector of the Grampian-Taconic orogeny, VMS mineralization is rare in the peri-Laurentian British and Irish Caledonides. Economic peri-Gondwanan affinity deposits are limited to Avoca and Parys Mountain. The Tyrone Igneous Complex of Northern Ireland represents a ca. 484-464 Ma peri-Laurentian affinity arc-ophiolite complex and a possible broad correlative of the Buchans-Robert's Arm belt of Newfoundland, host to some of the most metal-rich VMS deposits globally. Stratigraphic horizons prospective for VMS mineralization in the Tyrone Igneous Complex are associated with rift-related magmatism, hydrothermal alteration, synvolcanic faults, and high-level subvolcanic intrusions (gabbro, diorite, and/or tonalite). Locally intense hydrothermal alteration is characterized by Na-depletion, elevated SiO2, MgO, Ba/Sr, Bi, Sb, chlorite-carbonate-pyrite alteration index (CCPI) and Hashimoto alteration index (AI) values. Rift-related mafic lavas typically occur in the hanging wall sequences to base and precious metal mineralization, closely associated with ironstones and/or argillaceous sedimentary rocks representing low temperature hydrothermal venting and volcanic quiescence. In the ca. 475 Ma pre-collisional, calc-alkaline lower Tyrone Volcanic Group rift-related magmatism is characterized by abundant non-arc type Fe-Ti-rich eMORB, island-arc tholeiite, and low-Zr tholeiitic rhyolite breccias. These petrochemical characteristics are typical of units associated with VMS mineralization in bimodal mafic, primitive post-Archean arc terranes. Following arc-accretion at ca. 470 Ma, late rifting in the ensialic upper Tyrone Volcanic Group is dominated by OIB-like, subalkaline to alkali basalt and A-type, high-Zr rhyolites. These units
19. Slippery Rock University
Science.gov (United States)
Arnhold, Robert W.
2008-01-01
Slippery Rock University (SRU), located in western Pennsylvania, is one of 14 state-owned institutions of higher education in Pennsylvania. The university has a rich tradition of providing professional preparation programs in special education, therapeutic recreation, physical education, and physical therapy for individuals with disabilities.…
20. Geophysical exploration of disseminated and stockwork deposits associated with plutonic intrusive rock: a case study on the eastern flank of Colombia’s western cordillera
Directory of Open Access Journals (Sweden)
Hernández Pardo Orlando
2012-10-01
Full Text Available
Disseminated deposits are low-grade, large tonnage deposits which are mainly mined for gold, copper, molybdenum and tin. These deposits are normally associated with intermediate to acid plutonic intrusive rocks and all are characterized by intense, extensive hydrothermal alteration of host rocks. Disseminated deposit exploration in the tropics suffers from difficult geological mapping due to dense vegetation, lack of rock outcrops and extensive but variable saprolytic weathering. Geophysical exploration of these deposits normally includes magnetic, induced polarization and gamma ray spectrometry surveys. The largest RTP total magnetic field anomaly highs are usually associated with diorite porphyry intrusive bodies. Diorites are usually less magnetic than basaltic rocks; thus when magnetic anomaly highs are related to intrusions they can be explained by basic metals’ intensive mineralization (including magnetite associated with porphyry intrusions. Magnetic anomaly gradients regularly help delineate local discontinuities which can be interpreted as local faults and joints that can be mineralized. Gamma ray spectrometry is useful for determining anomalous potassium, uranium and thorium concentration as it can map alteration halos and linear discontinuities. Statistical analysis of the data also can determine the intermediate intrusive / extrusive nature of porphyry intrusions. Gamma ray spectrometry can help to determine elemental potassium concentration, regardless of the associated potassium mineral species, thereby enabling alteration mapping in a geological setting related to volcanic-associated massive sulphide base metal and gold deposits. An induced polarization survey is useful in outlining disseminated sulphide distribution in porphyry deposits related to chargeability anomaly highs. The results of the Quinchía project’s geophysical exploration program are discussed.
1. Collecting Rocks
Institute of Scientific and Technical Information of China (English)
孙铮
2007-01-01
My hobby is collecting rocks.It is very special,isn’t it?I began to collect rocks about four years ago.I usually go hiking in the mountains,or near the river to look for rocks.When I find a rock,I pick it up and clean it with the brush and water.Then I put it into my bag.Most of the rocks I have collected are quartzite~*.They are really
2. 滇西腾冲新生代火山岩岩石地球化学特征%GEOCHEMISTRY OF CENOZOIC VOLCANIC ROCKS FROM TENGCHONG, WESTERN YUNNAN
Institute of Scientific and Technical Information of China (English)
徐翠玲; 赵广涛; 何雨旸; 李德平
2012-01-01
Tengchong Cenozoic volcanic rocks, which consist of basaltic trachy-andesite, trachy-andesite, and basaltic andesite, belonging to the high-K and calc-alkaline series, are continental intraplate volcanic rocks erupted after the Tethys Ocean was closed. They are distributed near the collision zone of the Indian plate and the Eurasian plate. The geochemical features of the rocks can be used to define the tectonic properties and magma sources. The systematic geochemical study of the typical rock samples by XRF and ICP MS shows that the rocks are characterized by high K2O，CaO, low TiO2，and high Mg # (averaging about 46). REE shows a LREE-enriched pattern with significantly negative Eu. Large ion lithophilc elements (LILE) and high field strength elements (HFSE) are enriched compared to the primitive mantle, and the LILE have higher enrichment than the HFSE. Th shows a significantly positive anomaly. The geochemical composition of the studied volcanic rocks is similar to the volcanic arc magma, suggesting that the magmat-ic activity was triggered by the subduction of the Indian plate down to the Eurasian plate. Characteristic element ratios show that the magma may be derived from the subduction-related EM I mantle.%腾冲新生代火山岩位于印度板块和欧亚板块碰撞带附近,但是喷发时大洋已经闭合,属于大陆板内火山岩.对其进行地球化学研究,可以用来划分构造属性和推测岩浆来源.采用XRF和ICP-MS对典型岩石样品进行了较系统的岩石地球化学研究,结果表明,岩石类型有玄武质粗面安山岩、粗面安山岩和玄武安山岩,属高钾钙碱性系列;岩石化学显示高K2O、CaO和低TiO2,Mg#较高,平均约为46；稀土元素分布呈右倾,显示明显的Eu负异常；相对于原始地幔富集大离子亲石元素和高场强元素,并具有明显的Th正异常；地球化学组成总体上与岛弧岩浆岩相似,推测其成因与印度板块向欧亚板块俯冲引发的岩浆活
3. Tables showing analyses of semiquantitative spectrometry and atomic-absorption spectrophotometry of rock samples collected in the Ugashik, Bristol Bay, and western part of the Karluk quadrangles, Alaska
Science.gov (United States)
Wilson, Frederic H.; O'Leary, Richard M.
1987-01-01
The accompanying tables list chemical analyses of 337 rock samples that were collected in 1979, 1980, and 1981 in conjunction with geologic mapping in the Ugashik, Bristol Bay, and part of Karluk quadrangles. This work was conducted under the auspices of the Alaska Mineral Resource Assessment Program (AMRAP). This report is to accompany Wilson and O'Leary (1986) which inadvertently is missing most of the data tables listed here. Together the two reports contain the complete data from all samples collected for the Ugashik AMRAP.
4. Analysis on structure of igneous formation with fractal dimension of logs
Institute of Scientific and Technical Information of China (English)
2007-01-01
Reflecting the structure of igneous formation by calculating fractal dimension of logs, the fractal dimension of pyroclastic is larger than lava. Structure of pyroclastic is more complicated than that of lava, so reflecting the structure of igneous formation's complexity with fractal dimension is feasible. It is feasible to refleet the structure of igneous formation's complexity with fractal dimension.
5. Igneous composition vaiations determined by ChemCam along Curiosity's traverse from Bradbury to Rocknest area at Gale crater, Mars
Science.gov (United States)
Sautter, Violaine; MSL Science Team
2013-04-01
Since landing in Gale Crater (-4.59, 137,44°) the rover Curiosity, has driven during the first 90 sols, 420 meter east descending ∼ 20m from the Bradbury Landing site towards Glenelg. From sols 13 on, the ChemCam instrument suite performed compositional and imaging analyses of rocks and soils along the route. Each Chem- Cam LIBS observations covers a spot between 350 and 550 μm dia thus individual observations generally do not represent the whole rock composition but rather represent individual grains or a mixture thereof. Most of observations consist of a linear 5-point raster or a 3 x 3 grid. All major elements were regularly reported together with minor and trace elements. During the traverse, two distinct zones have been characterized: Zone I, from sol 0 to sol 47 (i.e. 280 meter traverse), belongs to the Humocky terrains supposed to be a part of the alluvial fan below Peace Vallis, which descends from the crater rim to the Northwest. It is defined by abundant gravels and igneous float rocks and isolated conglomerate outcrops. Rock textures indicate a high ratio of intrusive over extrusive: plutonic rocks vary from homogenous grain size either coarse (1-3mm grains Mara) or fine grained (less than 300 m Coronation) to variable grain size within a given rock (Jake-M). Some contain abundant laths of whitish minerals. ChemCam analyses are Si-rich (up to 60% wt.% or more) together with high Al (more than 15%) and high alkali (Na > K) in a range expected for alkali feldspar compositions. The lowest Si content correlates with low Al and high Fe consistent with ferromagnesian composition. The highest Si content (Stark a white vesicular rock) could indicate the presence of quartz. Clasts analyzed in one conglomerate (Link) had a range of compositions dominated by feldspathic material consistent with loose pebbles in the area and igneous porphyroblast. Beyond Anton soil (sol48), Curiosity entered zone II, transitional to a more distal unit with respect to the fan
6. Fluorine geochemistry in volcanic rock series
DEFF Research Database (Denmark)
Stecher, Ole
1998-01-01
A new analytical procedure has been established in order to determine low fluorine concentrations (30–100 ppm F) in igneous rocks, and the method has also proven successful for higher concentrations (100–4000 ppm F). Fluorine has been measured in a series of olivine tholeiites from the Reykjanes...... Peninsula, a tholeiite to rhyolitic rock series from Kerlingarfjöll, central Iceland, and an alkaline rock series from Jan Mayen that ranges from ankaramites to trachytes. Fluorine is not appreciably degassed during extrusion and appears to be insensitive to slight weathering. The olivine tholeiites from...... the Reykjanes Peninsula have F contents of 30–300 ppm and exhibit linear increases proportional to the incompatible elements K, P, and Ti. Such incompatible behaviour for F has been confirmed for the less evolved rocks of the other series. The tholeiites from Kerlingarfjöll (100–2000 ppm F) show a linear...
7. Inventory of rock avalanches in western Glacier Bay National Park and Preserve, Alaska, 1984-2016: a baseline data set for evaluating the impact of climate change on avalanche magnitude, mobility, and frequency
Science.gov (United States)
Bessette-Kirton, Erin; Coe, Jeffrey A.
2016-01-01
The effects of climate change have the potential to impact slope stability. Negative impacts are expected to be greatest at high northerly latitudes where degradation of permafrost in rock and soil, debuttressing of slopes as a result of glacial retreat, and changes in ocean ice-cover are likely to increase the susceptibility of slopes to landslides. In the United States, the greatest increases in air temperature and precipitation are expected to occur in Alaska. In order to assess the impact that these environmental changes will have on landslide size (magnitude), mobility, and frequency, inventories of historical landslides are needed. These inventories provide baseline data that can be used to identify changes in historical and future landslide magnitude, mobility, and frequency. This data release presents GIS and attribute data for an inventory of rock avalanches in a 5000 km2 area of western Glacier Bay National Park and Preserve, Alaska. We created the inventory from 30 m resolution Landsat imagery acquired from June 1984 to September 2016. For each calendar year, we visually examined a minimum of one Landsat image obtained between the months of May and October. We examined a total of 104 Landsat images. The contrast between the spectral signatures of freshly exposed rock avalanche source areas and deposits and surrounding undisturbed snow and ice was typically significant enough to detect surficial changes. We identified and mapped rock avalanches by locating areas with 1) high contrast compared to surrounding snow and ice, 2) different spectral signatures between successive Landsat images, and 3) lobate forms typical of rock-avalanche deposits. Using these criteria, we mapped a total of 24 rock avalanches ranging in size from 0.1 to 22 km2.Attribute data for each rock avalanche includes: a date, or range in possible dates, of occurrence; the name of the Landsat image(s) used to identify and map the avalanche; the total area covered by the rock avalanche
8. Geochemistry of zircons from basic rocks of the Korosten anorthosite-mangerite-charnockite-granite complex, north-western region of the Ukrainian Shield
Science.gov (United States)
Shumlyanskyy, Leonid; Belousova, Elena; Petrenko, Oksana
2017-09-01
The concentrations of 26 trace elements have been determined by laser ablation ICP-MS in zircons from four samples of basic rocks of the Korosten anorthosite-mangerite-charnockite-granite plutonic complex, the Ukrainian Shield. Zircons from the Fedorivka and Torchyn gabbroic intrusions and Volynsky anorthosite massif have distinctive abundances of many trace elements (REE, Sr, Y, Mn, Th). Zircons from the gabbroic massifs are unusually enriched in trace elements, while zircons from pegmatites in anorthosite are relatively depleted in trace elements. High concentrations of trace elements in zircons from gabbroic intrusions can be explained by their crystallization from residual interstitial melts enriched in incompatible elements. The zircons studied demonstrate a wide range of Ti concentrations, which reflects their temperature of crystallization: the zircons most enriched in Ti, from mafic pegmatites of the Horbuliv quarry (20-40 ppm), have the highest temperature of crystallization (845 ± 40 °C). Lower (720-770 °C) temperatures of zircon crystallization in gabbroic rocks are explained by its crystallization from the latest portions of the interstitial melt or by simultaneous crystallization of ilmenite. The Ce anomaly in zircons correlates with the degree of oxidation of the coexisting ilmenite.
9. The LA-ICP-MS zircons U-Pb ages and geochemistry of the Baihua basic igneous complexes in Tianshui area of West Qinling
Institute of Scientific and Technical Information of China (English)
PEI; XianZhi; DING; SaPing; ZHANG; GuoWei; LIU; HuiBin; LI; ZuoChen; LI; GaoYang; LIU; ZhanQing; MENG; Yong
2007-01-01
Baihua meta-igneous complex consists mainly of pyroxenite-gabbro(diorite)-diorite-quartz diorite. They form a complete comagmatic evolutionary series. The geochemical characteristics of basic-interme- diate basic igneous rocks indicate that they belong to a tholeiite suite. The REE distribution pattern is nearly flat type and LREE is slightly enriched type, and their primitive mantle-normalized and MORB-normalized trace element spider diagrams are generally similar; the LIL elements (LILE) Cs, Ba, Sr, Th and U are enriched, but Rb, K and the HFSEs Nb, P, Zr, Sm, Ti and Y are relatively depleted. All these show comagmatic evolution and origin characteristics. The tectonics environment discrimination of trace element reveals that these igneous complexes formed in an island-arc setting. The LA-ICP-MS single-zircons U-Pb age of Baihua basic igneous complex is 434.6±1.5 Ma (MSWD = 1.3), which proves that the formation time of the island-arc type magmatite in the northern zone of West Qinling is Late Ordovician or Early Silurian, also reveals that the timing of subduction of paleo-ocean basin represented by the Guanzizhen ophiolite and resulting island-arc-type magmatic activities is probably Middle-Late Ordovician to Early Silurian.
10. Rock Stars
Institute of Scientific and Technical Information of China (English)
张国平
2000-01-01
Around the world young people are spending unbelievable sums of money to listen to rock music. Forbes Magazine reports that at least fifty rock stars have incomes between two million and six million dollars per year.
11. KREEP Rocks
Institute of Scientific and Technical Information of China (English)
邹永廖; 徐琳; 欧阳自远
2004-01-01
KREEP rocks with high contents of K, REE and P were first recognized in Apollo-12 samples, and it was confirmed later that there were KREEP rock fragments in all of the Apollo samples, particularly in Apollo-12 and-14 samples. The KREEP rocks distributed on the lunar surface are the very important objects of study on the evolution of the moon, as well as to evaluate the utilization prospect of REE in KREEP rocks. Based on previous studies and lunar exploration data, the authors analyzed the chemical and mineral characteristics of KREEP rocks, the abundance of Th on the lunar surface materials, the correlation between Th and REE of KREEP rocks in abundance, studied the distribution regions of KREEP rocks on the lunar surface, and further evaluated the utilization prospect of REE in KREEP rocks.
12. Rock Art
Science.gov (United States)
Henn, Cynthia A.
2004-01-01
There are many interpretations for the symbols that are seen in rock art, but no decoding key has ever been discovered. This article describes one classroom's experiences with a lesson on rock art--making their rock art and developing their own personal symbols. This lesson allowed for creativity, while giving an opportunity for integration…
13. Rock Art
Science.gov (United States)
Henn, Cynthia A.
2004-01-01
There are many interpretations for the symbols that are seen in rock art, but no decoding key has ever been discovered. This article describes one classroom's experiences with a lesson on rock art--making their rock art and developing their own personal symbols. This lesson allowed for creativity, while giving an opportunity for integration…
14. Rock Finding
Science.gov (United States)
Rommel-Esham, Katie; Constable, Susan D.
2006-01-01
In this article, the authors discuss a literature-based activity that helps students discover the importance of making detailed observations. In an inspiring children's classic book, "Everybody Needs a Rock" by Byrd Baylor (1974), the author invites readers to go "rock finding," laying out 10 rules for finding a "perfect" rock. In this way, the…
15. Geochemical features of texture –forming ground ice in diamondiferous areas of western Yakutia
Directory of Open Access Journals (Sweden)
L. P. Alekseeva
2014-01-01
Full Text Available The unique research results of macro-components, trace elements and rare earth elements (REEs in the structure-forming ground ice in sedimentary and igneous rocks of the diamond-bearing regions of Western Yakutia are presented. It has been found that deep freezing of sedimentary cover in the Yakutian diamond-bearing province gave rise to formation of ice-cement and intrusive ice in the sedimentary strata and kimberlites. Water-rock interaction before the glacial epoch and perennial cryogenesis in the Late Cenozoic resulted in current hydrogeochemical zonality in the diamond-bearing regions and stipulated formation of hydrocarbonate, sulfate-hydrocarbonate, chloride-hydrocarbonate, hydrocarbonate-chloride and chloride types of structure-forming ground ice. Ground ice is enriched in Li, B, Si, S, Br, Sr and is depleted in Sc, Ge, Y, Nb, Th. Concentration of the REE in ground ice is 2–4 orders of magnitude less than in kimberlites and sedimentary rocks, 1–2 orders of magnitude exceed the REE content in the ocean water and approximately equal to the REE content in the river waters. The profiles of REE distribution in the ground ice is characterized by the similar of Ʌ-shape, strongly marked Eu anomaly and approximately equal content of light and heavy REE.
16. Igneous Consequence Modeling for the TSPA-SR
Energy Technology Data Exchange (ETDEWEB)
John McCord
2001-10-29
The purpose of this technical report is to develop credible, defendable, substantiated models for the consequences of igneous activity for the TSPA-SR Model. The effort will build on the TSPA-VA and improve the quality of scenarios and depth of the technical basis underlying disruptive events modeling. Computational models for both volcanic eruptive releases (this is an event that results in ash containing waste being ejected from Yucca Mountain) and igneous intrusion groundwater releases (this is an event that reaches the repository level, impacts the waste packages, and produces releases from waste packages damaged by igneous activity) will be included directly in the TSPA calculations as part of the TSPA-SR Model. This Analysis Model Report (AMR) is limited to development of the conceptual models for these two scenarios. The mathematical implementation of these conceptual models will be done within the TSPA-SR Model. Thus, this AMR will not include any model results or sensitivity analyses. Calculation of any doses resulting from igneous releases will also be done within the TSPA-SR model, as will the probabilistic weighting of these doses. Calculation and analysis of the TSPA-SR Model results for igneous disruption are, therefore, outside the scope of this activity. The reason for not running the mathematical models as part of this AMR is that the models are integrated within the TSPA-SR model and, thus, any model simulations and the corresponding results are out of the scope of this AMR. The scope of this work as defined in the development plan (CRWMS M&O 2000j) involves using data that has been extracted from existing sources to design and support the TSPA-SR models for the transport of radionuclides following igneous disruption of the repository. The development plan states ''applications of the code in this analysis will be limited to testing of the code and sensitivity analyses during analysis design.'' In contrast to the development
17. Geochemistry of ultrapotassic volcanic rocks in Xiaogulihe NE China: Implications for the role of ancient subducted sediments
Science.gov (United States)
Sun, Yang; Ying, Jifeng; Zhou, Xinhua; Shao, Ji'an; Chu, Zhuyin; Su, Benxun
2014-11-01
The unique eruptions of ultrapotassic volcanic rocks in eastern China reported so far took place in the Xiaogulihe area of western Heilongjiang Province, NE China. These ultrapotassic rocks are characterized by extremely high K2O contents (> 7 wt.%), abnormally unradiogenic Pb isotopic compositions (206Pb/204Pb = 16.44-16.55; 207Pb/204Pb = 15.39-15.46; 208Pb/204Pb = 36.35-36.61), and moderately high 87Sr/86Sr ratios (0.7053-0.7057), which can be basically correlated with those of ultrapotassic igneous rocks distributed widely in northwestern America and Aldan Shield. The positive correlation between 187Os/188Os and 1/Os argues that these ultrapotassic rocks have probably experienced negligible lower continental crust addition (less than 1%) during magma ascent. The high contents of K2O and negative correlation between 87Sr/86Sr and 206Pb/204Pb of these ultrapotassic rocks indicate the presence of a potassic phase, mostly phlogopite, in their mantle source. Their strong fractionation of rare earth elements and lack of Nd-Hf isotopic decoupling reveal a low-degree partial melting of garnet-bearing source rocks. In addition, the low CaO and Al2O3 contents of whole-rock compositions and low Fe/Mn ratios of olivine phenocryst chemistries suggest peridotites rather than pyroxenites as dominant source rocks for the Xiaogulihe ultrapotassic rocks. Based on these distinctive geochemical characteristics, we thus propose that the ultimate mantle source of the Xiaogulihe ultrapotassic volcanic rocks is phlogopite-bearing garnet peridotite within the lower part of the sub-continental lithospheric mantle (SCLM) that had been metasomatized by potassium-rich silicate melts. Combined with the unradiogenic Pb compositions, the most likely source of these potassium-rich silicate melts is the ancient subducted continental-derived sediments (> 1.5 Ga). These ancient subducted sediments, possessing relatively low initial Pb isotopic compositions, had experienced large U/Pb fractionation
18. Inelastic deformation in crystalline rocks
Science.gov (United States)
Rahmani, H.; Borja, R. I.
2011-12-01
The elasto-plastic behavior of crystalline rocks, such as evaporites, igneous rocks, or metamorphic rocks, is highly dependent on the behavior of their individual crystals. Previous studies indicate that crystal plasticity can be one of the dominant micro mechanisms in the plastic deformation of crystal aggregates. Deformation bands and pore collapse are examples of plastic deformation in crystalline rocks. In these cases twinning within the grains illustrate plastic deformation of crystal lattice. Crystal plasticity is governed by the plastic deformation along potential slip systems of crystals. Linear dependency of the crystal slip systems causes singularity in the system of equations solving for the plastic slip of each slip system. As a result, taking the micro-structure properties into account, while studying the overall behavior of crystalline materials, is quite challenging. To model the plastic deformation of single crystals we use the so called ultimate algorithm' by Borja and Wren (1993) implemented in a 3D finite element framework to solve boundary value problems. The major advantage of this model is that it avoids the singularity problem by solving for the plastic slip explicitly in sub steps over which the stress strain relationship is linear. Comparing the results of the examples to available models such as Von Mises we show the significance of considering the micro-structure of crystals in modeling the overall elasto-plastic deformation of crystal aggregates.
19. Cretaceous volcanic-intrusive magmatism in western Guangdong and its geological significance
Institute of Scientific and Technical Information of China (English)
GENG; Hongyan; XU; Xisheng; S.Y.O'Reilly; ZHAO; Ming; SUN; Tao
2006-01-01
Systematic zircon LA-ICPMS U-Pb dating reveals that Cretaceous volcanic-intrusive activities developed in western Guangdong. Representative volcanic rocks, i.e. Maanshan and Zhougongding rhyodacites, have zircon U-Pb isotopic ages of 100±1 Ma, and the intrusive ones including the Deqing monzonitic granite body and the Xinghua granodiorite body in the Shidong complex, as well as the Tiaocun granodiorite body in the Guangping complex yield ages of 99±2 Ma, ca.100 Ma, and 104±3 Ma respectively. The biotite-granites of the Shidong complex main body (461±35 Ma) and that of the Guangping complex (444±6 Ma) are Caledonian. In spite of the big time interval between Cretaceous volcanic-intrusive magmatisms and Caledonian intrusive ones, both of them are characterized by enrichment in Rb, Th, Ce, Zr, Hf, Sm, depletion in Ba, Nb, Ta, P, Ti, Eu, and weakly REE tetrad effect. Eu negative anomalies are: Cretaceous volcanic rocks (Eu/Eu*=0.74), Cretaceous intrusive rocks (Eu/Eu*=0.35-0.58), Caledonian biotite granites (Eu/Eu*=0.31-0.34). Studies of Sr-Nd isotope data show that all these igneous rocks have high initial 87Sr/86Sr ratios (0.7105-0.7518), and low εNd(t) values (-7.23--11.39) with their Nd two-stage model ages ranging from 1.6-2.0 Ga, which suggest that they all derived from the Proterozoic crustal basement of southeast China.The occurrence of Cretaceous volcanic-intrusive magmatisms in western Guangdong is related with the important lithospheric extension event in southeast China (including Nanling region) at ca. 100 Ma.The "volcanic line" defined by the large scale Mesozoic intermediate-acidic volcanic magmatisms in southeast China may further extend to the southwest margin of Nanling region.
20. Rocks and geology in the San Francisco Bay region
Science.gov (United States)
Stoffer, Philip W.
2002-01-01
The landscape of the San Francisco Bay region is host to a greater variety of rocks than most other regions in the United States. This introductory guide provides illustrated descriptions of 46 common and important varieties of igneous, sedimentary, and metamorphic rock found in the region. Rock types are described in context of their identification qualities, how they form, and where they occur in the region. The guide also provides discussion about of regional geology, plate tectonics, the rock cycle, the significance of the selected rock types in relation to both earth history and the impact of mineral resources on the development in the region. Maps and text also provide information where rocks, fossils, and geologic features can be visited on public lands or in association with public displays in regional museums, park visitor centers, and other public facilities.
1. A geologic framework for mineralization in the western Brooks Range
Science.gov (United States)
Young, Lorne E.
2004-01-01
The Brooks Range is a 950-km-long north-vergent fold and thrust belt, which was formed during Mesozoic convergence of the continental Arctic Alaska terrane and the oceanic Angayucham terrane and was further shortened and uplifted in Tertiary time. The Arctic Alaska terrane consists of parautochthonous rocks and the Endicott Mountains and De Long Mountains subterranes. The Endicott Mountains allochthon of the western Brooks Range is the setting for many sulfide and barite occurrences, such as the supergiant Red Dog zinc-lead mine. Mineralization is sediment hosted and most commonly is present in black shale and carbonate turbidites of the Mississippian Kuna Formation. The reconstructed Kuna basin is a 200 by +600 km feature that represents the culmination of a remarkable chain of events that includes three fluvial-deltaic and two or more orogenic cycles, Middle Devonian to Mississippian episodes of extension and igneous activity, and the emergence of a seaward Lower Proterozoic landmass that may have constituted a barrier to marine circulation. Mississippian extension and related horst-and-graben architecture in the western Brooks Range is manifested in part by strong facies variability between coeval units of allochthons and structural plates. Shallow marine to possibly nonmarine arkose, platform to shelf carbonate, slope-to-basin shale, chert and carbonate turbidites, and submarine volcanic rocks are all represented in Mississippian time. The structural setting of Mississippian sedimentation, volcanism, and mineralization in the Kuna basin may be comparable to documented Devono-Mississippian extensional sags or half-grabens in the subsurface north of the Brooks Range. Climate, terrestrial ecosystems, multiple fluvial-deltaic aquifers, and structural architecture affected the liberation, movement, and redeposition of metals in ways that are incompletely understood.
2. 'Escher' Rock
Science.gov (United States)
2004-01-01
[figure removed for brevity, see original site] Chemical Changes in 'Endurance' Rocks [figure removed for brevity, see original site] Figure 1 This false-color image taken by NASA's Mars Exploration Rover Opportunity shows a rock dubbed 'Escher' on the southwestern slopes of 'Endurance Crater.' Scientists believe the rock's fractures, which divide the surface into polygons, may have been formed by one of several processes. They may have been caused by the impact that created Endurance Crater, or they might have arisen when water leftover from the rock's formation dried up. A third possibility is that much later, after the rock was formed, and after the crater was created, the rock became wet once again, then dried up and developed cracks. Opportunity has spent the last 14 sols investigating Escher, specifically the target dubbed 'Kirchner,' and other similar rocks with its scientific instruments. This image was taken on sol 208 (Aug. 24, 2004) by the rover's panoramic camera, using the 750-, 530- and 430-nanometer filters. The graph above shows that rocks located deeper into 'Endurance Crater' are chemically altered to a greater degree than rocks located higher up. This chemical alteration is believed to result from exposure to water. Specifically, the graph compares ratios of chemicals between the deep rock dubbed 'Escher,' and the more shallow rock called 'Virginia,' before (red and blue lines) and after (green line) the Mars Exploration Rover Opportunity drilled into the rocks. As the red and blue lines indicate, Escher's levels of chlorine relative to Virginia's went up, and sulfur down, before the rover dug a hole into the rocks. This implies that the surface of Escher has been chemically altered to a greater extent than the surface of Virginia. Scientists are still investigating the role water played in influencing this trend. These data were taken by the rover's alpha particle X-ray spectrometer.
3. 'Escher' Rock
Science.gov (United States)
2004-01-01
[figure removed for brevity, see original site] Chemical Changes in 'Endurance' Rocks [figure removed for brevity, see original site] Figure 1 This false-color image taken by NASA's Mars Exploration Rover Opportunity shows a rock dubbed 'Escher' on the southwestern slopes of 'Endurance Crater.' Scientists believe the rock's fractures, which divide the surface into polygons, may have been formed by one of several processes. They may have been caused by the impact that created Endurance Crater, or they might have arisen when water leftover from the rock's formation dried up. A third possibility is that much later, after the rock was formed, and after the crater was created, the rock became wet once again, then dried up and developed cracks. Opportunity has spent the last 14 sols investigating Escher, specifically the target dubbed 'Kirchner,' and other similar rocks with its scientific instruments. This image was taken on sol 208 (Aug. 24, 2004) by the rover's panoramic camera, using the 750-, 530- and 430-nanometer filters. The graph above shows that rocks located deeper into 'Endurance Crater' are chemically altered to a greater degree than rocks located higher up. This chemical alteration is believed to result from exposure to water. Specifically, the graph compares ratios of chemicals between the deep rock dubbed 'Escher,' and the more shallow rock called 'Virginia,' before (red and blue lines) and after (green line) the Mars Exploration Rover Opportunity drilled into the rocks. As the red and blue lines indicate, Escher's levels of chlorine relative to Virginia's went up, and sulfur down, before the rover dug a hole into the rocks. This implies that the surface of Escher has been chemically altered to a greater extent than the surface of Virginia. Scientists are still investigating the role water played in influencing this trend. These data were taken by the rover's alpha particle X-ray spectrometer.
4. Metamorphic and thermal evolution of large contact aureoles - lessons from the Bushveld Igneous Complex
Science.gov (United States)
Waters, D.
2012-04-01
Large igneous intrusions crystallise, cool, and transfer heat out into their host rocks. The thermal structure of the resulting aureole can be mapped as a series of assemblage zones and isograds, and can in principle be modelled on the assumption that heat transfer is dominantly by conduction. The local peak of contact metamorphism occurs later in time with increasing distance from the igneous contact. The importance of fluids as a metamorphic/metasomatic agent or heat transfer mechanism depends on volatile contents of magma and country rock, and on the geometry of the intrusion. Many of these features are spectacularly illustrated by the aureole beneath the mafic Rustenburg Layered Suite of the Bushveld Complex, which was emplaced at ca. 2060 Ma sub-concordantly into the shale-quartzite succession of the Pretoria Group in the Transvaal Basin. The layered suite reaches a thickness of at least 8 km, and the metamorphic aureole extends 4 km or more downwards into the "floor" of the intrusion. The great extent and relative absence of deformation make this a remarkable natural laboratory for studying the fundamental processes of metamorphism. In quantifying the thermal history, however, a number of second-order factors need to be taken into account. The first relates to the markedly different thermal properties of the major quartzite and shale units, and the second to the importance of endothermic metamorphic reactions in shale units relative to the quartzites. Further insights into metamorphic processes arise from the exquisite detail of poikiloblast growth microstructures preserved in graphite-poor metapelites of the Timeball Hill and Silverton Formations, 2.5 to 3.5 km beneath the igneous contact. These allow a detailed reconstruction of the time sequence of mineral growth and replacement, revealing a marked overlap of the growth intervals of porphyroblastic staurolite, cordierite, biotite, garnet and andalusite at the expense of muscovite, chlorite and chloritoid
5. Unraveling eclogite-facies fluid-rock interaction using thermodynamic modelling and whole-rock experiments: the in-situ eclogitization of metapelites from Val Savenca (Sesia Zone, Western Alps)
Science.gov (United States)
Jentsch, Marie; Tropper, Peter
2015-04-01
A common feature of HP and UHP terranes is the subduction of crustal rocks to great depths. Previous investigations have shown that this process is triggered by fluids present during an eclogite-facies metamorphic overprint. An examples is exposed in the metapelites at Val Savenca in the Sesia-Lanzo Zone, Italy where Alpine eclogite-facies metamorphism and fluid flow led to partial transformation of Variscan amphibolite-eclogite facies metapelites (garnet + biotite + sillimanite + K-feldspar + plagioclase + quartz) to zoisite ± jadeite + kyanite + phengite + quartz. This transformation took place under P-T conditions of 1.7 - 2.1 GPa at 600°C and low a(H2O) of 0.3-0.6. The replacement of plagioclase by jadeite + zoisite + kyanite + quartz takes place also along former fractures. Biotite is replaced by the assemblage phengite + omphacite ± kyanite adjacent to former plagioclase, otherwise by phengite + rutile/titanite. Garnet and clinopyroxene show variable compositions depending in which micro-domain (plagioclase or biotite) they grew. The extreme development of microdomains can best be studied by thermodynamic pseudosection modelling of individual microdomains using stoichiometric mixtures of protolith minerals from this domain and the program DOMINO (De Capitani & Petrakakis, 2010). The aim of these calculations was: 1.) to reproduce the observed mineral assemblage and 2.) to provide constraints on the amount of fluid present in the transformation. The results so far indicate that the amount of fluid was very low, otherwise paragonite would have formed instead of jadeite and reproduction of the observed mineral assemblage has only been partly successful so far since biotite is still stable in the calculations. In addition to understand the role of fluids in the mineralogical and textural transformation piston-cylinder experiments with a fresh, natural orthogneiss granulite from the Moldanubic Unit in upper Austria with the assemblage garnet + biotite + K
6. An outline of tectonic, igneous, and metamorphic events in the Goshute-Toano Range between Silver Zone Pass and White Horse Pass, Elko County, Nevada; a history of superposed contractional and extensional deformation
Science.gov (United States)
Ketner, Keith Brindley; Day, Warren C.; Elrick, Maya; Vaag, Myra K.; Zimmerman, Robert A.; Snee, Lawrence W.; Saltus, Richard W.; Repetski, John E.; Wardlaw, Bruce R.; Taylor, Michael E.; Harris, Anita G.
1998-01-01
Seven kinds of fault-bounded tracts are described. One of the tracts provides a good example of Mesozoic contractional folding and faulting; six exemplify various aspects of Miocene extensional faulting. Massive landslide deposits resulting from Tertiary faulting are described. Mesozoic intrusive rocks and extensive exposures of Miocene volcanic rocks are described and dated. The age ranges of stratigraphic units were based on numerous conodont collections, and ages of igneous rocks were determined by argon/argon and fission-track methods. The geologic complexity of the Goshute-Toano Range provides opportunities for many additional productive structural studies.
7. Hot dry rock geothermal energy: status of exploration and assessment. Report No. 1 of the hot dry rock assessment panel
Energy Technology Data Exchange (ETDEWEB)
1977-06-01
The status of knowledge of attempts to utilize hot dry rock (HDR) geothermal energy is summarized. It contains (1) descriptions or case histories of the ERDA-funded projects at Marysville, MT, Fenton Hill, NM, and Coso Hot Springs, CA; (2) a review of the status of existing techniques available for exploration and delineation of HDR; (3) descriptions of other potential HDR sites; (4) definitions of the probable types of HDR resource localities; and (5) an estimate of the magnitude of the HDR resource base in the conterminous United States. The scope is limited to that part of HDR resource assessment related to the determination of the extent and character of HDR, with emphasis on the igneous-related type. It is estimated that approximately 74 Q (1 Q = 1,000 Quads) of heat is stored in these sites within the conterminous U.S. at depths less than 10 km and temperatures above 150/sup 0/C, the minimum for power generation. (Q = 10/sup 18/ BTU = 10/sup 21/J; the total U.S. consumption for 1972 was approximately 0.07 Q). Approximately 6300 Q are stored in the conduction-dominated parts of the crust in the western U.S. (23% of the total surface area), again at depths less than 10 km and temperatures above 150/sup 0/C. Nearly 10,000 Q are believed to be contained in crustal rocks underlying the entire conterminous U.S., at temperatures above 150/sup 0/C. The resource base is significantly larger for lower grade heat. (JGB)
8. 'Earhart' Rock
Science.gov (United States)
2004-01-01
This false-color image taken by NASA's Mars Exploration Rover Opportunity shows a rock informally named 'Earhart' on the lower slopes of 'Endurance Crater.' The rock was named after the pilot Amelia Earhart. Like 'Escher' and other rocks dotting the bottom of Endurance, scientists believe fractures in Earhart could have been formed by one of several processes. They may have been caused by the impact that created Endurance Crater, or they might have arisen when water leftover from the rock's formation dried up. A third possibility is that much later, after the rock was formed, and after the crater was created, the rock became wet once again, then dried up and developed cracks. Rover team members do not have plans to investigate Earhart in detail because it is located across potentially hazardous sandy terrain. This image was taken on sol 219 (Sept. 4) by the rover's panoramic camera, using its 750-, 530- and 430-nanometer filters.
9. Rock Art
OpenAIRE
Huyge, Dirk
2009-01-01
Rock art, basically being non-utilitarian, non-textual anthropic markings on natural rock surfaces, was an extremely widespread graphical practice in ancient Egypt. While the apogee of the tradition was definitely the Predynastic Period (mainly fourth millennium BCE), examples date from the late Palaeolithic (c. 15,000 BCE) until the Islamic era. Geographically speaking, “Egyptian” rock art is known from many hundreds of sites along the margins of the Upper Egyptian and Nubian Nile Valley and...
10. Rock blocks
OpenAIRE
Turner, W.
2007-01-01
Consider representation theory associated to symmetric groups, or to Hecke algebras in type A, or to q-Schur algebras, or to finite general linear groups in non-describing characteristic. Rock blocks are certain combinatorially defined blocks appearing in such a representation theory, first observed by R. Rouquier. Rock blocks are much more symmetric than general blocks, and every block is derived equivalent to a Rock block. Motivated by a theorem of J. Chuang and R. Kessar in the case of sym...
11. Spectral-induced polarization characteristics of rocks from Shinyemi deposit in Northeastern South Korea
Science.gov (United States)
Park, Samgyu; Shin, Seung Wook; Son, Jeong-Sul; Kim, Changryol
2016-04-01
Contact metasomatism between carbonate and igneous rocks leads to the formation of skarn deposits, and ore minerals are abundant. Geophysical methods that visualize the distributions of physical properties have been utilized to determine lithological boundaries in ore deposits. In particular, spectral-induced polarization (SIP) is the most effective of those methods for mineral exploration because it can obtain not only the boundaries but also the abundance and grain size of ore minerals. It is crucial to characterize the SIP responses of in situ rocks for a more realistic interpretation. Thus, typical rocks composed of igneous rock, skarn rock, skarn ore, and carbonate rock were sampled from drilling cores in the Shinyemi deposit, which is one of the well-known skarn deposits in Northeastern South Korea. The purpose of this study was to characterize the SIP responses of rocks by laboratory measurements. The characterization was performed by evaluating spectra and IP parameters. The IP properties were acquired from equivalent circuit analysis using a circuit model based on the electrochemical theory, and the analysis results of this circuit model were relatively well fit compared with those of the traditional Dias and Cole-Cole models. The frequency responses below 100 Hz in the spectra and the chargeability values of the skarn rocks and ores containing magnetite were relatively strong and high, respectively, compared with those of non-mineralized igneous and carbonate rocks. Therefore, it is considered that these characteristics are dependent on the abundance of magnetite. In case of the skarn ores with high magnetite content, the resistivity values were significantly low and the relaxation time values were influenced by the grain size of magnetite. On the other hand, it is considered that the DC resistivity and the relaxation time values of the igneous and carbonate rocks are slightly related to the porosity and the grade of hydrothermal alteration, respectively.
12. Laboratory duplication of comb layering in the Rhum pluton. [igneous rocks with comb layered texture
Science.gov (United States)
Donaldson, C. H.
1977-01-01
A description is provided of the texture of harrisite comb layers, taking into account the results of crystallization experiments at controlled cooling rates, which have reproduced the textural change from 'cumulate' to comb-layered harrisite. Melted samples of harrisite were used in the dynamic crystallization experiments considered. The differentiation of a cooling rate run with respect to olivine grain size and shape is shown and three possible origins of hopper olivine in differentiated crystallization runs are considered. It is found that olivine nucleation occurred throughout cooling, except for the incubation period during early cooling. The elongate combed olivines in harrisite apparently grew as the magma locally supercooled to at least 30 C. It is suggested that the branching crystals in most comb layers, including comb-layered harrisite, probably grew along thermal gradients.
13. Smectite clay identification and quantification as an indicator of basic igneous rock durability
CSIR Research Space (South Africa)
Leyland, RC
2014-09-01
Full Text Available -Ray Diffraction (XRD), wetting/drying and ethylene glycol tests) should be performed if a petrographic examination shows more than 5% discrete montmorillonite. These statements are unclear and do not suggest rejection or acceptance of a material based... of the saturating cations since these can affect the characteristic d-spacings. Commonly, saturation using glycerol [C3H5(OH)3] or ethylene glycol [C2H6O2] is used to cause diagnostic changes in expansible phyllosilicates by solvation of the interlayer cations...
14. INFLUENCE OF TEXTURE AND MINERALOGY IN APPARENT POROSITY, WATER ABSORPTION AND APPARENT DENSITY OF IGNEOUS ROCKS
Directory of Open Access Journals (Sweden)
Ana Paula Meyer
2014-12-01
Full Text Available The work consists in evaluating the results of physical indices (apparent porosity, water absorption and apparent density obtained in granitoids exploited as ornamental and revetment stones in the state of São Paulo and Espírito Santo. The results of physical indices were qualified as parameters specification published by Abirochas use and compared the characteristics observed in petrographic samples.
15. Implications of Magmatic Events on Hydrocarbon Generation: Occurrences of Gabbroic Rocks in the Orito Field, Putumayo Basin, SW Colombia
Science.gov (United States)
Vásquez, M.; Altenberger, U.; Romer, R. L.
2005-12-01
Mafic dikes and sills intruded the sedimentary succession in the Orito Oil Field, located in the Putumayo Basin, SW Colombia. One sample from the Orito-4 well yields a Late Miocene to Pliocene age (40K/40Ar on amphibole 6.1 ± 0.7 Ma) for the igneous event in the basin. This coincides with the widely recognized regional Andean orogenic uplift that affected most of sub-Andean Peru, Ecuador, and Colombia. Furthermore, the uplift consequently coincides with a second pulse of hydrocarbon generation and expulsion in the Putumayo Basin. This second pulse was thermally more evolved than the first one (Late Oligocene - Miocene). The high content of CO2 in the gas budget recovered in different wells along the basin may be related to the heat flux of the mafic intrusions. There are four geological events that coincide with this large scale evolution during the late Miocene to early Pliocene (13 - 3 Ma): regional orogenic uplift, persistent igneous intrusions, CO2 formation, and a second pulse of hydrocarbon generation and expulsion. The Late Miocene - Pliocene age of the intrusion is the key to formulate a hypothesis where these four events are joined together. Regional uplift and intrusions: The mafic rocks of the Orito Oil Field show Sr-Nd-Pb isotopic compositions that suggest derivation from a mantle source below the western edge of the South American continent. The geochemical signature of these rocks that form part of the Northern Volcanic Zone (NVZ) reflects subduction-related magmatism. Thus, they record subduction and start of the last pervasive uplift episode that took place during the Late Neogene. Intrusions and second migration phase: The Late Miocene pulse of hydrocarbon generation and migration coincides closely with the estimated age of the intrusions; therefore, a causal link with the geothermal anomaly induced by the mafic igneous rocks is likely. The temperature of a mafic magma reaching 1000 to 1200°C is sufficient to heat the host rocks, where the
16. Groundwater flow dynamics of weathered hard-rock aquifers under climate-change conditions: an illustrative example of numerical modeling through the equivalent porous media approach in the north-western Pyrenees (France)
Science.gov (United States)
Jaunat, J.; Dupuy, A.; Huneau, F.; Celle-Jeanton, H.; Le Coustumer, P.
2016-09-01
A numerical groundwater model of the weathered crystalline aquifer of Ursuya (a major water source for the north-western Pyrenees region, south-western France) has been computed based on monitoring of hydrological, hydrodynamic and meteorological parameters over 3 years. The equivalent porous media model was used to simulate groundwater flow in the different layers of the weathered profile: from surface to depth, the weathered layer (5 · 10-8 ≤ K ≤ 5 · 10-7 m s-1), the transition layer (7 · 10-8 ≤ K ≤ 1 · 10-5 m s-1, the highest values being along major discontinuities), two fissured layers (3.5 · 10-8 ≤ K ≤ 5 · 10-4 m s-1, depending on weathering profile conditions and on the existence of active fractures), and the hard-rock basement simulated with a negligible hydraulic conductivity ( K = 1 10 -9 ). Hydrodynamic properties of these five calculation layers demonstrate both the impact of the weathering degree and of the discontinuities on the groundwater flow. The great agreement between simulated and observed hydraulic conditions allowed for validation of the methodology and its proposed use for application on analogous aquifers. With the aim of long-term management of this strategic aquifer, the model was then used to evaluate the impact of climate change on the groundwater resource. The simulations performed according to the most pessimistic climatic scenario until 2050 show a low sensitivity of the aquifer. The decreasing trend of the natural discharge is estimated at about -360 m3 y-1 for recharge decreasing at about -5.6 mm y-1 (0.8 % of annual recharge).
17. Fluid composition and evolution in coesite-bearing rocks (Dora-Maira massif, Western Alps): implications for element recycling during subduction
Science.gov (United States)
Philippot, Pascal; Chevallier, Pierre; Chopin, Christian; Dubessy, Jean
1995-08-01
Fluid inclusions and F, Cl concentration of hydrous minerals were analysed in the coesite-pyrope quartzite, the interlayered jadeite quartzite and their country-rock gneiss from the Dora-Maira massif using a combination of microthermometry, Raman spectrometry, synchrotron X-ray microfiuorescence and electron microprobe analysis. Three populations of fluid inclusions were recognized texturally and can be related to distinct metamorphic stages. A low-salinity aqueous fluid occurs in the retrogressed country gneiss and as late secondary inclusions in jadeite quartzite and chloritized pyrope. An earlier secondary population is found in matrix quartz of the jadeite- and pyro-pe-quartzites. This population can be related to the early decompression and so to incipient breakdown of garnet into phlogopite-bearing assemblages. The inclusion fluid is highly saline (up to 84 wt% equivalent NaCl) and contains Na, Ca, Fe, Cu and Zn as major cations. In pyrope quartzite, additional K was found in these brines, which locally coexist with CO2-rich inclusions. The oldest fluid inclusions are preserved in kyanite grains included in fresh pyrope and in pyrope itself. In pyrope, all inclusions have decrepitated and contain magnesite, an Mg-phosphate, sheet-silicate(s), a chloride and an opaque phase, with no fluid preser ved. In contrast, the kyanite inclusions in pyrope preserve primary H2O-CO2 low-salinity fluid inclusions, probably owing to the low compressibility of the kyanite inclusions and host garnet. In spite of in-situ re-equilibration, these inclusions can be interpreted as relics of the dehydration fluid that attended pyrope growth. These correlations between textural and chemical fluid inclusion data and metamorphic stages are consistent with the fluid composition calculated from the halogen content of different generations of phlogopite and biotite. The preservation of different fluid compositions, both in time and space, is evidence for local control and possibly origin
18. Fractures network analysis and interpretation in carbonate rocks using a multi-criteria statistical approach. Case study of Jebal Chamsi and Jebal Belkhir, South-western part of Tunisia
Science.gov (United States)
Msaddek, Mohamed Haythem; Moumni, Yahya; Chenini, Ismail; Mercier, Eric; Dlala, Mahmoud
2016-11-01
The quantitative analysis of fractures in carbonate rocks across termination folds is important for the understanding of the fractures network distribution and arrangement. In this study, we performed a quantitative analysis and interpretation of fracture network to identify the fracture networks type. For this reason, we used a multi-criteria statistical analysis. The distribution of directional families in all measured stations and their elemental distribution are firstly examined. Then we performed the analysis of directional criteria for each of the two and three neighbouring stations. Finally, the elemental analyses of fracture families crossing others were carried out. This methodology was applied to the folds of Jebal Chamsi and Jebal Belkhir areas located in south western Tunisia characterized by simple folds of carbonate geological formations. The application of the global and the elemental statistical analysis criteria of directional families show a random arrangement of fractures. However, elemental analysis of two and three neighbouring stations for families crossing one another shows a pseudo-organization of fracture arrangements.
19. Art Rocks with Rock Art!
Science.gov (United States)
Bickett, Marianne
2011-01-01
This article discusses rock art which was the very first "art." Rock art, such as the images created on the stone surfaces of the caves of Lascaux and Altimira, is the true origin of the canvas, paintbrush, and painting media. For there, within caverns deep in the earth, the first artists mixed animal fat, urine, and saliva with powdered minerals…
20. Art Rocks with Rock Art!
Science.gov (United States)
Bickett, Marianne
2011-01-01
This article discusses rock art which was the very first "art." Rock art, such as the images created on the stone surfaces of the caves of Lascaux and Altimira, is the true origin of the canvas, paintbrush, and painting media. For there, within caverns deep in the earth, the first artists mixed animal fat, urine, and saliva with powdered minerals…
1. Iron in Precambrian rocks: implications for the global oxygen budget of the ancient Earth.
Science.gov (United States)
Kump, L R; Holland, H D
1992-08-01
Banded iron formations (BIF) are prominent in sediments older than 2 Ga. However, little is known about the absolute abundance of BIF in Archean and Early Proterozoic sediments, and the source of the Fe is still somewhat uncertain. Also unknown is the role that Fe may have played in the maintenance of low oxygen pressures in the Archean and Early Proterozoic atmosphere. An analysis of the chemical composition of Precambrian rocks provides some insight into the role of Fe in Precambrian geochemical cycles. The Fe content of igneous rocks is well correlated with their Ti content. Plots of Fe vs. Ti in Precambrian sandstones and graywackes fall very close to the igneous rock trend. Plots of Fe vs. Ti in Precambrian shales also follow this trend but show a definite scatter toward an excess of Fe. Phanerozoic shales and sandstones lie essentially on the igneous rock trend and show surprisingly little scatter. Mn/Ti relations show a stronger indication of Precambrian Mn loss, perhaps due to weathering under a less oxidizing early atmosphere. These data show that Fe was neither substantially added to nor significantly redistributed in Archean and early Proterozoic sediments. Enough hydrothermal Fe was added to these sediments to increase the average Fe content of shales by at most a factor of 2. This enrichment would probably not have greatly affected the near-surface redox cycle or atmospheric oxygen levels. Continued redistribution of Fe and mixing with weathered igneous rocks during the recycling of Precambrian sediments account for the excellent correlation of Fe with Ti in Phanerozoic shales and for the similarity between their Fe/Ti ratio and that of igneous rocks.
2. Zonation of the Newry Igneous Complex, Northern Ireland, based on geochemical and geophysical data
Science.gov (United States)
Anderson, P. E.; Cooper, M. R.; Stevenson, C. T.; Hastie, A. R.; Hoggett, M.; Inman, J.; Meighan, I. G.; Hurley, C.; Reavy, R. J.; Ellam, R. M.
2016-09-01
The Late Caledonian Newry Igneous Complex (NIC), Northern Ireland, comprises three largely granodioritic plutons, together with an intermediate-ultramafic body at its northeastern end. New whole-rock geochemical data, petrological classifications, and published data, including recent Tellus aeromagnetic and radiometric results, have been used to establish 15 distinct zones across the four bodies of the NIC. These become broadly younger to the southwest of the complex and toward the centres of individual plutons. In places, zones are defined by both current compositional data (geochemistry and petrology) and Tellus results. This is particularly clear at the eastern edge of the NIC, where a thorium-elevated airborne radiometric signature occurs alongside distinct concentrations of various elements from geochemistry. However, in the northeastern-most pluton of the NIC, a prominent ring-shaped aeromagnetic anomaly occurs independent of any observed surface compositional variation, and thus the zones in this area are defined by aeromagnetic data only. The origins of this and other aeromagnetic anomalies are as yet undetermined, although in places, these closely correspond to facies at the surface. The derived zonation for the NIC supports incremental emplacement of the complex as separate, distinct magma pulses. Each pulse is thought to have originated from the same fractionally crystallising source that periodically underwent mixing with more basic magma.
3. Silicic ash beds bracket Emeishan Large Igneous province to < 1 m.y. at ~ 260 Ma
Science.gov (United States)
Huang, Hu; Cawood, Peter A.; Hou, Ming-Cai; Yang, Jiang-Hai; Ni, Shi-Jun; Du, Yuan-Sheng; Yan, Zhao-Kun; Wang, Jun
2016-11-01
Claystone beds directly below and above the Emeishan basalts in SW China formed around the Guadalupian-Lopingian (G - L) boundary. Zircons from both levels give U-Pb ages of 260 Ma, and are identical within-error to ages reported for the Emeishan Large Igneous Province (LIP). The claystones lack Nb - Ta anomalies on primitive mantle normalized elemental diagrams; zircons from these claystones have a geochemical affinity to within-plate-type magmas. These features, combined with the strong negative Eu anomalies in the zircons and high Al2O3/TiO2 ratios, indicate that claystones around the G - L boundary have a silicic volcanic component related to Emeishan LIP. Zircons from the underlying claystone bed have much higher U/Yb and Th/Nb ratios and lower εHf(t) values than those overlying the LIP, suggesting that early-stage silicic volcanic rocks had a higher crustal contamination or assimilation during magmatic processes. In terms of stratigraphic correlation, our data demonstrate that silicic eruptions occurred not only at the end, but also at the beginning of the Emeishan LIP, and the overall duration of the main basaltic phase was short (< 1 m.y).
4. Garnet formation and evolution in Cordilleran source rocks: inherited zircon trace element chemistry from the Transverse Ranges, CA
Science.gov (United States)
Economos, R. C.; Barth, A. P.; Wooden, J. L.; Chapman, A. D.
2011-12-01
Pre-magmatic (inherited) Proterozoic cores are common in Mesozoic plutons from the Transverse Ranges, southern California. These grains record chronological and compositional information that constrains the mineralogy of the source region at the time of its formation. Whole rock geochemical compositions indicate the mineralogy of the source region when re-mobilized in Mesozoic time. These constraints can be compared to yield an impression of major changes in the lower crust between these events. The behavior of garnet is of particular interest due to its role as an indicator of crystallization depth and its distinctive geochemical imprint, both on co-crystallizing zircons and magmatic chemistry as a whole. While the trace element signal of co-crystallization of garnet and zircon is well constrained for metamorphic rocks, similar signals in magmatic rocks have received less thorough treatment. We compare Yb/Gd and Th/U from zircons from garnet bearing granites and tonalites from the deeply-crystallized western Tehachapi Mountains with results for a range of metamorphic environments. A main trend in log-log Yb/Gd vs Th/U space represents the trajectory of magmatic composition in a typical granodiorite as recorded in zircons. A population of zircons from both metamorphic and igneous garnet-bearing rocks falls off this main trend towards lower Yb/Gd, interpreted as a signature of heavy REE depletion via the influence of garnet during co-crystallization. When carrying the signal of garnet co-crystallization, igneous and metamorphic zircons can be distinguished on the basis of Th/U ratio. The Yb/Gd vs. Th/U relationship is generally a better indicator than Th/U alone for discerning the formation environment of zircons, since in the main populations there is significant overlap in Th/U ratio among metamorphic and evolved magmatic zircons that make them difficult to discern. Proterozoic premagmatic zircons sampled by Mesozoic plutons in the Transverse Ranges have a
5. Platinum group elements in stream sediments of mining zones: The Hex River (Bushveld Igneous Complex, South Africa)
Science.gov (United States)
Almécija, Clara; Cobelo-García, Antonio; Wepener, Victor; Prego, Ricardo
2017-05-01
Assessment of the environmental impact of platinum group elements (PGE) and other trace elements from mining activities is essential to prevent potential environmental risks. This study evaluates the concentrations of PGE in stream sediments of the Hex River, which drains the mining area of the Bushveld Igneous Complex (South Africa), at four sampling points. Major, minor and trace elements (Fe, Ca, Al, Mg, Mn, V, Cr, Zn, Cu, As, Co, Ni, Cd, and Pb) were analyzed by FAAS and ETAAS in suspended particulate matter and different sediment fractions (rocks. The highest concentrations were observed closer to the mining area, decreasing with distance and in the cycle, increasing the presence of PGE in the fine fraction of river sediments. We propose that indicators such as airborne particulate matter, and soil and river sediment quality, should be added to the protocols for evaluating the sustainability of mining activities.
6. Metasomatic origin of quartz-pyroxene rock, Akilia, Greenland, and implications for Earth's earliest life.
Science.gov (United States)
Fedo, Christopher M; Whitehouse, Martin J
2002-05-24
A quartz-pyroxene rock interpreted as a banded iron formation (BIF) from the island of Akilia, southwest Greenland, contains (13)C-depleted graphite that has been claimed as evidence for the oldest (>3850 million years ago) life on Earth. Field relationships on Akilia document multiple intense deformation events that have resulted in parallel transposition of Early Archean rocks and significant boudinage, the tails of which commonly form the banding in the quartz-pyroxene rock. Geochemical data possess distinct characteristics consistent with an ultramafic igneous, not BIF, protolith for this lithology and the adjacent schists. Later metasomatic silica and iron introduction have merely resulted in a rock that superficially resembles a BIF. An ultramafic igneous origin invalidates claims that the carbon isotopic composition of graphite inclusions represents evidence for life at the time of crystallization.
7. Significance of an Active Volcanic Front in the Far Western Aleutian Arc
Science.gov (United States)
Yogodzinski, G. M.; Kelemen, P. B.; Hoernle, K.
2015-12-01
Discovery of a volcanic front west of Buldir Volcano, the western-most emergent Aleutian volcano, demonstrates that the surface expression of Aleutian volcanism falls below sea level just west of 175.9° E longitude, but is otherwise continuous from mainland Alaska to Kamchatka. The newly discovered sites of western Aleutian seafloor volcanism are the Ingenstrem Depression, a 60 km-long structural depression just west of Buldir, and an unnamed area 300 km further west, referred to as the Western Cones. These locations fall along a volcanic front that stretches from Buldir to Piip Seamount near the Komandorsky Islands. Western Aleutian seafloor volcanic rocks include large quantities of high-silica andesite and dacite, which define a highly calc-alkaline igneous series and carry trace element signatures that are unmistakably subduction-related. This indicates that subducting oceanic lithosphere is present beneath the westernmost Aleutian arc. The rarity of earthquakes below depths of 200 km indicates that the subducting plate is unusually hot. Some seafloor volcanoes are 6-8 km wide at the base, and so are as large as many emergent Aleutian volcanoes. The seafloor volcanoes are submerged in water depths >3000 m because they sit on oceanic lithosphere of the Bering Sea. The volcanic front is thus displaced to the north of the ridge of arc crust that underlies the western Aleutian Islands. This displacement, which developed since approximately 6 Ma when volcanism was last active on the islands, must be a consequence of oblique convergence in a system where the subducting plate and large blocks of arc crust are both moving primarily in an arc-parallel sense. The result is a hot-slab system where low subduction rates probably limit advection of hot mantle to the subarc, and produce a relatively cool and perhaps stagnant mantle wedge. The oceanic setting and highly oblique subduction geometry also severely limit rates of sediment subduction, so the volcanic rocks, which
8. Regional mapping of hydrothermally altered igneous rocks along the Urumieh-Dokhtar, Chagai, and Alborz Belts of western Asia using Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data and Interactive Data Language (IDL) logical operators: a tool for porphyry copper exploration and assessment: Chapter O in Global mineral resource assessment
Science.gov (United States)
Mars, John L.; Zientek, M.L.; Hammarstrom, J.M.; Johnson, K.M.; Pierce, F.W.
2014-01-01
Regional maps of phyllic and argillic hydrothermal alteration were compiled using Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data and logical operator algorithms. The area mapped extends from northwestern Iran to southeastern Pakistan and includes volcanic and magmatic arcs that make up the Urumieh-Dokhtar volcanic belt (UDVB), the Chagai volcanic belt (CVB), and the central part of the Alborz magmatic belt (AMB). The volcanic belts span the Zagros-Makran transform zone and the present day Baluchistan (Makran) volcanic arc. ASTER visible near infrared (VNIR) data contain three bands between 0.52 and 0.86 micrometers (μm) and the short-wave infrared (SWIR) data consist of six bands spanning 1.6 to 2.43 μm with 15-meter (m), and 30-m resolution, respectively.
9. The offshore basement of Perú: Evidence for different igneous and metamorphic domains in the forearc
Science.gov (United States)
Romero, Darwin; Valencia, Kiko; Alarcón, Pedro; Peña, Daniel; Ramos, Victor A.
2013-03-01
As a result of new studies carried out in the offshore of Perú during the exploration and hydrocarbon evaluation of the forearc basins, new U-Pb SHRIMP and TIMS in zircons and some Ar-Ar data were obtained in the metamorphic and igneous basement. The understanding of this basement was critical to evaluate different hypotheses that have been proposed for the tectonic evolution of pre-Andean crust of Perú. Recent research performed in the basement rocks of the Marañón Massif in northern Perú, claimed that west of this area was a basement-free region in the Paleozoic, where the arc and forearc were developed in a mafic quasi-oceanic crust. However, petrographic studies and new preliminary ages indicate, for the first time, the nature and age of this sialic basement. Reconnaissance studies were performed in several offshore islands, as the Las Hormigas de Afuera Island west of Lima, and Macabí and Lobera islands along the edge of the continental platform. These data were complemented with the studies of some cutting samples obtained in recent exploration wells in northern Perú. The results of the present work show two large crustal domains in the Peruvian offshore forearc. A northern domain contains late Paleozoic igneous rocks that appear to be the southern offshore continuation of the Amotape-Tahuin block, which is interpreted as the southernmost remnant of the Laurentia Alleghenian orogen. The central offshore domain, known as the Paracas High, corresponds to the outer shelf high of previous studies. It contains orthogneisses of Grenville-age, probably recrystallized during an Ordovician magmatic episode. The new results show that the central offshore of Perú is an extension of the Grenville-age basement affected by Famatinian, early Paleozoic magmatism, well exposed in the southern domain in the Arequipa Massif along the coast of southern Perú.
10. ROCK ON
National Research Council Canada - National Science Library
Thomas Grose
2014-01-01
..., however, was music - especially the high-pitched sounds of pop and rock, which boosted energy output by up to 40 percent. By contrast, classical music's lower pitches barely raised effectiveness. O...
11. A modified time-temperature relationship for titanomagnetite and its application to igneous erratic boulders in Hachijo Island, Japan
Science.gov (United States)
Tonosaki, T.; Nakamura, N.; Goto, K.; Sato, T.; Watanabe, M.
2016-12-01
On land along shore line in an island all over the world, there are many huge boulders which seem that they had been broken and transported by errastic events (such as extreme waves). The presence of boulders on land provides geological evidence that the region had been suffered by ancient tsunami or storm waves, establishing the evaluation of risk-management policies for future disasters. In volcanic island of Hachijo, Japan, there are huge (>5000 kg) andesitic boulder (20 m altitude high), and basaltic boulders (4 m altitude high) which seem that they had been broken from an outcrop and emplaced from it. Because radiocarbon dating can not be applied to volcanic rocks, a magnetic viscous dating might be powerful tool to determine the rotation history of rocks. Tyson Smith and Vrosub (1994) succeeded in revealing the age of landslide basaltic rocks by geological evidence, using Pullaiah's time-temperature monogram by Neel's relaxation theory of single domain (SD) particles of magnetite (Pullaiah et al. 1975). However, our application of this monogram to igneous boulders fails to determine the age due to a different magnetic mineralogy including titanomagnetite. Therefore, by introducing a modified monogram for single domain particles of titanomagnetite, we tried to reveal a possible reworked age of the boulders. However, our boulders still fail to identify the reworked age. In this presentation, we will present our current situation of the problem and a working hypothesis to solve it.
12. U-Pb zircon geochronology of rocks in the Salinas Valley region of California: A reevaluation of the crustal structure and origin of the Salinian block
Science.gov (United States)
Barth, A.P.; Wooden, J.L.; Grove, M.; Jacobson, C.E.; Pedrick, J.N.
2003-01-01
The Salinian block in the Salinas Valley region of central California consists of arc granitic and metasedimentary rocks (schist of Sierra de Salinas) sandwiched between coeval high-pressure, low-temperature me??lange belts. U-Pb zircon ages of three granitic plutons from this region range from 88 to 82 Ma, and coexisting biotite yielded 40Ar/39Ar cooling ages of 76-75 Ma. The U-Pb ages from detrital zircons indicate derivation of the protolith of the schist from a 117-81 Ma igneous provenance. Muscovite and biotite 40Ar/ 39Ar cooling ages of 72-68 Ma from the nearby schist are distinctly younger than those from the granitic plutons. These data indicate that deposition and metamorphism of the schist occurred after emplacement of adjacent granitic rocks, contradicting the prevailing view that the schist comprises the local framework for the Salinian arc. We propose that the schist of Sierra de Salinas was thrust beneath the Salinian magmatic arc along a Campanian thrust fault that has not been recognized. This hypothesis implies that the Salinian arc originated as a klippe of basement rocks derived from the vicinity of the western Mojave Desert. Thrusting initiated southeastward-migrating Laramide tectonism of a style similar to that which formed the Vincent thrust and the latest Cretaceous and Paleocene Pelona and Orocopia Schists of southern California and southwestern Arizona.
13. Workshop on Pristine Highlands Rocks and the early History of the Moon
Science.gov (United States)
Longhi, J. (Editor); Ryder, G. (Editor)
1983-01-01
Oxide composition of the Moon, evidence for an initially totally molten Moon, geophysical contraints on lunar composition, random sampling of a layered intrusion, lunar highland rocks, early evolution of the Moon, mineralogy and petrology of the pristine rocks, relationship of the pristine nonmore rocks to the highlands soils and breccias, ferroan anorthositic norite, early lunar igneous history, compositional variation in ferroan anosthosites, a lunar magma ocean, deposits of lunar pristine rocks, lunar and planetary compositions and early fractionation in the solar nebula, Moon composition models, petrogenesis in a Moon with a chondritic refractory lithophile pattern, a terrestrial analog of lunar ilmenite bearing camulates, and the lunar magma ocean are summarized.
14. Igneous banding, schlieren and mafic enclaves in calc-alkaline granites: The Budduso pluton (Sardinia)
Science.gov (United States)
Barbey, P.; Gasquet, D.; Pin, C.; Bourgeix, A. L.
2008-08-01
This study deals with the origin of igneous layering in plutons, and, especially, the extent layering is related to mafic-silicic magma interactions. The Budduso pluton (Sardinia) shows three main scales of organization. (i) Large scale lithological variations correspond to three main magmatic units, with differentiation increasing from the Outer (hornblende-bearing biotite granodiorite/monzogranite) to the Middle (biotite monzogranite) and the Inner (leucomonzogranite) units. The striking homogeneity of 87Sr/ 86Sr initial ratios (0.7090 ± 4) and ɛNd(t) values (- 5.6 ± 0.1) strongly suggests that magma isotopic equilibration was achieved prior to emplacement, whereas mixing/mingling structures observed within the pluton reflect second-stage processes involving broadly cogenetic components. (ii) Metre to decametre-scale igneous layering may be isomodal or modally-graded, locally with cross-layering. Biotite and plagioclase compositions are similar in both biotite-rich and quartzofeldspathic layers, as are the trace-element patterns which differ only by relative abundances. This precludes an origin by fractional crystallization. A penetrative submagmatic fabric superimposed on the layering and corresponding mainly to flattening can be ascribed to interference between pluton growth and regional deformation. (iii) Composite layering and schlieren are commonly associated to mafic microgranular enclaves, locally within synmagmatic shear zones or disrupted synplutonic dykes. In that case, there is a progressive shift in biotite XFe values from the core of enclave (˜ 0.65) to the host monzogranite (˜ 0.72): schlieren in the monzogranite show biotite XFe values similar to that of the host rock, whereas schlieren close to mafic enclaves show lower XFe values (˜ 0.69) towards those of enclave rims. These features can be ascribed to three main processes: (i) assembly of differentiated (± mixed/mingled) magmatic pulses; (ii) local hydrodynamic sorting related to density
15. Tunnel Design by Rock Mass Classifications
Science.gov (United States)
1990-01-01
fact, rock mass classifications have been successfully applied throughout the world : in the United States,2 - Canada,7 8 Western Europe, 9 -12 South...gneiss. Very high strength >30000 >200 Quartzite, dolerite, gabbro , basalt. Table 10 3 Classification for Discontinuity Spacing Spacing of Rock Mass
16. Cenozoic volcanic rocks of Saudi Arabia
Science.gov (United States)
Coleman, R.G.; Gregory, R.T.; Brown, G.F.
2016-01-01
The Cenozoic volcanic rocks of Saudi Arabia cover about 90,000 km2, one of the largest areas of alkali olivine basalt in the world. These volcanic rocks are in 13 separate fields near the eastern coast of the Red Sea and in the western Arabian Peninsula highlands from Syria southward to the Yemen Arab Republic.
17. 辽河盆地东部凹陷火成岩储层特征及成藏模式%Igneous reservoir characteristics and hydrocarbon accumulation model in eastern sag of Liaohe Basin
Institute of Scientific and Technical Information of China (English)
庚琪
2016-01-01
按照成岩方式—化学成分—结构＋矿物等岩性三级分类原则，识别出5大类23种岩性；根据火成岩的结构、构造和特征岩性，将岩相划分为6相16亚相；按成因将火成岩储集空间分为7种类型9种亚类。通过研究认为岩性、岩相是影响火成岩储层储集性能乃至含油气性的主要因素。火成岩油气成藏的主控因素为烃源岩、储层、构造运动；成藏模式有构造成藏模式、岩性成藏模式、构造—岩性成藏模式3种。通过对火成岩岩性、岩相、储层、成藏的研究，为辽河盆地东部凹陷今后的勘探部署奠定了良好的基础。%Based on the principle of three -level classification of lithology such as diagenetic model ,chemical composi-tion,and structure and mineral ,etc.,the igneous rocks was identified as 5 main classes and 23 types of lithology .Accord-ing to the texture ,structure and characteristic lithology ,the igneous rocks were divided into 6 lithofacies and 16 subfacies . The reservoir spaces were divided into 7 categories and 9 subclasses by the genesis of the igneous rocks .It is considered that the lithology and the lithofacies were main facors controlling reservoir performance and oil -bearing properties .Hydro-carbon accumulation in igneous rocks was mainly controlled by source rock ,reservoir and tectonic movement .Three types of reservoir-forming patterns mainly consist of structural ,lithological ,and structural-lithological patterns .The studies on li-thology ,lithofacies ,reservoir ,and accumulation of igneous rocks have laid a good foundation for future exploration in east -ern Sag of Liaohe Basin .
18. The occurrence of microdiamonds in Mesoproterozoic Chapada Diamantina intrusive rocks--Bahia/Brazil.
Science.gov (United States)
Battilani, Gislaine A; Gomes, Newton S; Guerra, Wilson J
2007-06-01
The origin of diamonds from Serra do Espinhaço in Diamantina region (State of Minas Gerais) and in Chapada Diamantina, Lençóis region (State of Bahia) remains uncertain, even taking into account the ample research carried out during the last decades. The lack of typical satellite minerals in both districts makes a kimberlitic source for these diamonds uncertain. In mid 18th century the occurrence of a metamorphosed igneous rock composed of martite, sericite and tourmaline was described in Diamantina region and named hematitic phyllite, considered by some researchers as a possible diamond source. Similar rocks were found in Lençóis and examined petrographically and their heavy mineral concentration was investigated by means of scanning electron microscopy (SEM). Petrographic analyses indicated an igneous origin for these rocks and SEM analyses showed the discovery of microdiamonds. Geochronological studies using the Ar/Ar technique in muscovites yielded minimum ages of 1515+/-3 Ma, which may correlate with 1710+/-12 Ma from U-Pb method in igneous zircons from the hematitic phyllites. Both rock types also have the same mineral and chemical composition which leads to the conclusion that the intrusive rocks were protolith of the hematitic phyllites. This first discovery of microdiamonds in intrusive rocks opens the possibility of new investigation models for diamond mineralization in Brazilian Proterozoic terrains.
19. Kinematics of syn- and post-exhumational shear zones at Lago di Cignana (Western Alps, Italy): constraints on the exhumation of Zermatt-Saas (ultra)high-pressure rocks and deformation along the Combin Fault and Dent Blanche Basal Thrust
Science.gov (United States)
Kirst, Frederik; Leiss, Bernd
2017-01-01
Kinematic analyses of shear zones at Lago di Cignana in the Italian Western Alps were used to constrain the structural evolution of units from the Piemont-Ligurian oceanic realm (Zermatt-Saas and Combin zones) and the Adriatic continental margin (Dent Blanche nappe) during Palaeogene syn- and post-exhumational deformation. Exhumation of Zermatt-Saas (U)HP rocks to approximately lower crustal levels at ca. 39 Ma occurred during normal-sense top-(S)E shearing under epidote-amphibolite-facies conditions. Juxtaposition with the overlying Combin zone along the Combin Fault at mid-crustal levels occurred during greenschist-facies normal-sense top-SE shearing at ca. 38 Ma. The scarcity of top-SE kinematic indicators in the hanging wall of the Combin Fault probably resulted from strain localization along the uppermost Zermatt-Saas zone and obliteration by subsequent deformation. A phase of dominant pure shear deformation around 35 Ma affected units in the direct footwall and hanging wall of the Combin Fault. It is interpreted to reflect NW-SE crustal elongation during updoming of the nappe stack as a result of underthrusting of European continental margin units and the onset of continental collision. This phase was partly accompanied and followed by ductile bulk top-NW shearing, especially at higher structural levels, which transitioned into semi-ductile to brittle normal-sense top-NW deformation due to Vanzone phase folding from ca. 32 Ma onwards. Our structural observations suggest that syn-exhumational deformation is partly preserved within units and shear zones exposed at Lago di Cignana but also that the Combin Fault and Dent Blanche Basal Thrust experienced significant post-exhumational deformation reworking and overprinting earlier structures.
20. Petrología y geoquímica de la unidad ígnea Quebrada Blanca, sierra de la Huerta, Provincia de San Juan Petrology and geochemistry of the Quebrada Blanca Igneous Unit, Sierra de La Huerta, province of San Juan.
Directory of Open Access Journals (Sweden)
Brígida Castro de Machuca
2011-12-01
group of similar age and magmatic features distributed in the cited range. It comprises a hypabyssal rhyolite porphyry, a hydrothermal-intrusive breccia wherein two facies with contrasting texture and composition were distinguished, and felsite/rhyolite dikes. This association defines the root zone of a diatreme-type breccia which has been exposed by erosion. Breccia formation was associated with crystallization of the porphyry rhyolite, explosive brecciation, and exsolution of magmatic hydrothermal fluids which broke off and carried upward fragments of the solidified porphyry carapace and metamorphic wall rocks. The rhyolite porphyry was emplaced afterwards probably occupying the feeder conduit. The geochemistry data indicate a high-silica, subalkaline, high-K calk-alkaline and metaluminous to slightly peraluminous affinity for the Quebrada Blanca igneous Unit. Large-ion lithophile elements contents are high whilst Sr, P and Ti contents are low. They show enrichment of LREE and HREE depletion (La/YbN = 3.37 to 13.67. Geochemical characteristics are compatible with igneous rocks related to volcanic arcs. The studied rocks are tentatively correlated to the dacitic-rhyolitic upper section of the Choiyoi Group and could be assigned to the final stages of the continental magmatic arc developed along the western margin of Gondwana since the Late Carboniferous.
1. Characterizing silicic rocks in the Parana Magmatic Province: an update in their origin and emplacement
Science.gov (United States)
Luchetti, A. F.; Nardy, A. R.; Machado, F. B.; Gravley, D. M.; Gualda, G. A.
2013-12-01
The Paraná Magmatic Province (PMP), a large igneous province in southern Brazil (with correlative rocks in western Africa), includes 800,000 km3 of flood basalts generated during the rifting that ultimately led to the opening of the South Atlantic and covers nearly 75% of the surface of the Paraná Basin. Towards the top of the volcanic pile, silicic rocks are observed in many areas. They comprise a small proportion of the total erupted volume (2.5%), yet correspond to a significant flare-up of silicic volcanism over a period of only a few million years. In Brazil, the silicic rocks are divided into two groups, the Chapecó Member, which appears more northerly and includes porphyritic, crystal-rich, high-Ti dacites and trachydacites; and the Palmas Member, which includes fine-grained, crystal-poor, low-Ti dacites and rhyolites. The mode of emplacement (lavas vs. pyroclastic flows) of the volcanic units has been the subject of much controversy. The aim of this project is to better understand the origin and evolution of the PMP silicic rocks. We are combining information from the regional to the thin section scale to better characterize eruption dynamics and magma distribution prior to eruption. In both Palmas and Chapecó units, we observe features consistent with emplacement in the form of pyroclastic density currents, e.g. fiamme, variable weathering patterns consistent with local variations in welding at the outcrop scale, vertical gas-escape structures, sedimentary dykes, and lythophysae. Some ignimbrite units can be traced for 10's of kilometers and with more research on their spatial distribution could reveal the location of eruptive centers. In the Palmas, ignimbrites can be observed juxtaposed against or overlying discrete eruptive centers in the form of discordant structures that resemble domes and coulees typical of lava extrusion and flow. However, many of the silicic rocks are ambiguous and difficult to characterize, with features that could be related
2. Using Modeling Clay to Model the Rock Cycle
Science.gov (United States)
Cook, H. M.
2016-12-01
During this interactive exploration, students will be guided through the rock cycle using modeling clay as a medium. Each student will be given a ball of red clay and a ball of yellow clay. The instructor will introduce students to igneous rocks as they use their red clay to create a volcano. Students will then learn about weathering and erosion as they break their yellow ball of clay into smaller and smaller pieces that they will round into spheres. The "sand" created from the yellow clay gets accumulated and lithified (via gentle compression by the students) to form a sandstone. This sandstone then becomes covered by a lava flow, created by smashing the red clay volcanoes. The process of metamorphism is introduced as students gently cover their sandstone using the lava flow. This also serves a segue for a discussion about the various types of metamorphism beginning with contact metamorphism. Metamorphic grade is discussed as increased pressure further alters the sedimentary rock and lava flow. Ultimately a migmatite is formed by mixing the red and yellow clay together. Finally, they clays become so intermingled that a new larger orange ball is created, beginning the rock cycle anew with an igneous melt. This activity is engaging and effective with students of all ages. Intended as a fun, light-hearted approach to introducing rocks in an undergraduate earth science class, this can be effectively customized for use in an elementary, middle, or high school classroom.
3. 'Wopmay' Rock
Science.gov (United States)
2004-01-01
This approximate true-color image taken by NASA's Mars Exploration Rover Opportunity shows an unusual, lumpy rock informally named 'Wopmay' on the lower slopes of 'Endurance Crater.' The rock was named after the Canadian bush pilot Wilfrid Reid 'Wop' May. Like 'Escher' and other rocks dotting the bottom of Endurance, scientists believe the lumps in Wopmay may be related to cracking and alteration processes, possibly caused by exposure to water. The area between intersecting sets of cracks eroded in a way that created the lumpy appearance. Rover team members plan to drive Opportunity over to Wopmay for a closer look in coming sols. This image was taken by the rover's panoramic camera on sol 248 (Oct. 4, 2004), using its 750-, 530- and 480-nanometer filters.
4. Petrogenesis and tectonic implications of the Neoproterozoic Datian mafic-ultramafic dykes in the Panzhihua area, western Yangtze Block, SW China
Science.gov (United States)
Yang, Yi-Jin; Zhu, Wei-Guang; Bai, Zhong-Jie; Zhong, Hong; Ye, Xian-Tao; Fan, Hong-Peng
2017-01-01
Mafic-ultramafic dykes are important geological markers that can punctuate the onset of crustal extension during the breakup of a continent and provide valuable information on the mantle source. This study reports secondary ion mass spectroscopy zircon and baddeleyite U-Pb ages, elemental and Nd isotopic data for the Datian mafic-ultramafic dykes in the Panzhihua area, western Yangtze Block, SW China. Two kinds of rocks are confirmed: the picritic rock and the dolerite. Based on petrographic and geochemical features, the dolerite dykes are further subdivided into two groups: Group I mafic and Group II mafic dykes, which emplaced at 760 Ma (zircon U-Pb) and 800 Ma (zircon and baddeleyite U-Pb), respectively. All samples from the picritic rocks and the Group I mafic rocks show the features of high-Ti and alkaline basaltic magma in composition as well as "humped" trace element patterns, which are similar to those of typical alkaline basalts associated with continental rifts except for the slightly negative Nb-Ta anomalies. The Group II mafic rocks display the features of low-Ti and tholeiitic magma, moderately enriched in LILE and LREE, and characterized by distinctively negative Nb-Ta anomalies. The primary magmas of the picritic rocks and the Group I mafic rocks were generated from ca 25 % partial melting of an OIB-like, Nd isotopically depleted but incompatible elements relatively enriched mantle source within a garnet stable field. The Group II mafic rocks crystallized from crustal contaminated mafic magmas that were derived from a spinel-bearing sub-continental lithospheric mantle source, because of low ratios of La/Yb, Ti/Y and Sm/Yb. Geochemical features suggest that these groups of mafic-ultramafic dykes were formed in a continental rift setting, but derived from different mantle sources. In combination with other Neoproterozoic igneous rocks in the western margin of Yangtze Block, it is suggested that the Datian mafic-ultramafic dykes in the Panzhihua area
5. LA-ICP-MS U-Pb apatite dating of Lower Cretaceous rocks from teschenite-picrite association in the Silesian Unit (southern Poland
Directory of Open Access Journals (Sweden)
Szopa Krzysztof
2014-08-01
Full Text Available The main products of volcanic activity in the teschenite-picrite association (TPA are shallow, sub-volcanic intrusions, which predominate over extrusive volcanic rocks. They comprise a wide range of intrusive rocks which fall into two main groups: alkaline (teschenite, picrite, syenite, lamprophyre and subalkaline (dolerite. Previous 40Ar/39Ar and 40K/40Ar dating of these rocks in the Polish Outer Western Carpathians, performed on kaersutite, sub-silicic diopside, phlogopite/biotite as well as on whole rock samples has yielded Early Cretaceous ages. Fluorapatite crystals were dated by the U-Pb LA-ICP-MS method to obtain the age of selected magmatic rocks (teschenite, lamprophyre from the Cieszyn igneous province. Apatite-bearing samples from Boguszowice, Puńców and Lipowa yield U-Pb ages of 103± 20 Ma, 119.6 ± 3.2 Ma and 126.5 ± 8.8 Ma, respectively. The weighted average age for all three samples is 117.8 ± 7.3 Ma (MSWD = 2.7. The considerably smaller dispersion in the apatite ages compared to the published amphibole and biotite ages is probably caused by the U-Pb system in apatite being less susceptible to the effects of hydrothermal alternation than the 40Ar/39Ar or 40K/40Ar system in amphibole and/or biotite. Available data suggest that volcanic activity in the Silesian Basin took place from 128 to 103 Ma with the the main magmatic phase constrained to 128-120 Ma.
6. The Upper Triassic alkaline magmatism of the western Neo-Tethys (Bajo Ebro, NE Spain): age and geodynamic implications
Science.gov (United States)
Sanz, T.; Lago, M.; Gil, A.; Pocoví, A.; Galé, C.; Ubide, T.; Larrea, P.; Ramajo, J.; Tierz, P.
2012-04-01
A set of mafic rocks crop out in the north-western margin of the Neo-Tethys (eastern Spain and France). These rocks show three common features: 1) they were emplaced into Upper Triassic sediments (Keuper facies), 2) they are mainly basalts and dolerites and show an alkaline geochemical affinity and 3) these magmas rose to their emplacement level through deep fractures; some of the fractures were newly opened as a result of the Triassic extension (Triassic-Liassic rifting), whereas others had been generated during the Permian extension (Lower Permian rifting) and were reopened. Magmatic activity has also been recognized in these areas during the Jurassic, the Cretaceous and the Quaternary. The Bajo Ebro sector (NE Spain) comprises two types of Upper Triassic mafic rocks: 1) massive rocks emplaced as dikes, sills and basaltic lavas (10-12 meters in thickness and up to kilometric in extension) and 2) a wide range of pyroclasts (from ash grains to bombs) forming layers more than 100 meters thick, which are usually interbedded with argillites and carbonates. Protrusions of the sills into the overlying sediments, together with spilitization of the igneous rocks, suggest that the magmas emplaced into unconsolidated sediments. Furthermore, a level of epiclastic-basaltic breccias is recognized overlying the magmatic levels and below the dolostones of the Imón Formation (Rhaetian in age); these breccias are interpreted to represent an erosive episode which affected the magmatic rocks in emerged areas. According to these criteria, these rocks can be considered Upper Triassic (pre-Rhaetian) in age. The basaltic lavas show alkaline mineral assemblages composed of: olivine (Fo79-65), Ti-rich clinopyroxene (Fs3-15, En52-35, Wo50-42), plagioclase (An80-50), Ti-rich magnetite and apatite. Their major and trace element whole rock compositions show contents in SiO2 (41,3-49,3 w.%), Nb/Y (1,5-4,1), Zr/TiO2 (0,0057-0,013), V (157,8-292,1 ppm) and Ti/1000 (11,3-18,53) which indicate
7. Rock Paintings.
Science.gov (United States)
Jones, Julienne Edwards
1998-01-01
Discusses the integration of art and academics in a fifth-grade instructional unit on Native American culture. Describes how students studied Native American pictographs, designed their own pictographs, made their own tools, and created rock paintings of their pictographs using these tools. Provides a list of references on Native American…
8. Ayers Rock
Institute of Scientific and Technical Information of China (English)
王慧茹
2002-01-01
Ayers Rock is right in the centre of Australia.It's nearly two thousand kilometres______Sydney.So we flew most of the way.h was rather cloudy______But after we left the mountains behind us, there was hardly a cloud in thesky.
9. Intellektuaalne rock
Index Scriptorium Estoniae
2007-01-01
Briti laulja-helilooja ja näitleja Toyah Willcox ning Bill Rieflin ansamblist R.E.M. ja Pat Mastelotto King Krimsonist esinevad koos ansamblitega The Humans ja Tuner 25. okt. Tallinnas Rock Cafés ja 27. okt Tartu Jaani kirikus
10. Intellektuaalne rock
Index Scriptorium Estoniae
2007-01-01
Briti laulja-helilooja ja näitleja Toyah Willcox ning Bill Rieflin ansamblist R.E.M. ja Pat Mastelotto King Krimsonist esinevad koos ansamblitega The Humans ja Tuner 25. okt. Tallinnas Rock Cafés ja 27. okt Tartu Jaani kirikus
11. Source rock potential in Pakistan
Energy Technology Data Exchange (ETDEWEB)
Raza, H.A. (Hydrocarbon Development Institute of Pakistan, Islamabad (Pakistan))
1991-03-01
Pakistan contains two sedimentary basins: Indus in the east and Balochistan in the west. The Indus basin has received sediments from precambrian until Recent, albeit with breaks. It has been producing hydrocarbons since 1914 from three main producing regions, namely, the Potwar, Sulaisman, and Kirthar. In the Potwar, oil has been discovered in Cambrian, Permian, Jurassic, and Tertiary rocks. Potential source rocks are identified in Infra-Cambrian, Permian, Paleocene, and Eocene successions, but Paleocene/Eocene Patala Formation seems to be the main source of most of the oil. In the Sulaiman, gas has been found in Cretaceous and Tertiary; condensate in Cretaceous rocks. Potential source rocks are indicated in Cretaceous, Paleocene, and Eocene successions. The Sembar Formation of Early Cretaceous age appears to be the source of gas. In the Kirthar, oil and gas have been discovered in Cretaceous and gas has been discovered in paleocene and Eocene rocks. Potential source rocks are identified in Kirthar and Ghazij formations of Eocene age in the western part. However, in the easter oil- and gas-producing Badin platform area, Union Texas has recognized the Sembar Formation of Early Cretaceous age as the only source of Cretaceous oil and gas. The Balochistan basin is part of an Early Tertiary arc-trench system. The basin is inadequately explored, and there is no oil or gas discovery so far. However, potential source rocks have been identified in Eocene, Oligocene, Miocene, and Pliocene successions based on geochemical analysis of surface samples. Mud volcanoes are present.
12. Mineral growth in melt conduits as a mechanism for igneous layering in shallow arc plutons: mineral chemistry of Fisher Lake orbicules and comb layers (Sierra Nevada, USA)
Science.gov (United States)
McCarthy, Anders; Müntener, Othmar
2017-07-01
Different processes have been proposed to explain the variety of igneous layering in plutonic rocks. To constrain the mechanisms of emplacement and crystallization of ascending magma batches in shallow plutons, we have studied comb layers and orbicules from the Fisher Lake Pluton, Northern Sierra Nevada. Through a detailed study of the mineralogy and bulk chemistry of 70 individual layers, we show that comb layers and orbicule rims show no evidence of forming through a self-organizing, oscillatory crystallization process, but represent crystallization fronts resulting from in situ crystallization and extraction of evolved melt fractions during decompression-driven crystallization, forming a plagioclase-dominated cres-cumulate at the mm- to m-scale. We propose that the crystal content of the melt and the dynamics of the magmatic system control the mechanisms responsible for vertical igneous layering in shallow reservoirs. As comb layers crystallize on wall rocks, the higher thermal gradients will increase the diversity of comb layering, expressed by inefficient melt extraction, thereby forming amphibole comb layers and trapped apatite + quartz saturated evolved melt fractions. High-An plagioclase (An90-An97.5) is a widespread phase in Fisher lake comb layers and orbicule rims. We show that a combination of cooling rate, latent heat of crystallization and pressure variations may account for high-An plagioclase in shallow melt extraction zones.
13. Ca. 1.5 Ga mafic magmatism in South China during the break-up of the supercontinent Nuna/Columbia: The Zhuqing Fe-Ti-V oxide ore-bearing mafic intrusions in western Yangtze Block
Science.gov (United States)
Fan, Hong-Peng; Zhu, Wei-Guang; Li, Zheng-Xiang; Zhong, Hong; Bai, Zhong-Jie; He, De-Feng; Chen, Cai-Jie; Cao, Chong-Yong
2013-05-01
Secondary ion mass spectroscopy (SIMS) zircon and baddeleyite U-Pb ages, elemental, and Nd isotopic data are reported for the Zhuqing Fe-Ti-V oxide ore-bearing mafic intrusions in western Yangtze Block, South China. The mafic intrusions are dated at 1494 ± 6 Ma (zircon U-Pb), 1486 ± 3 Ma (baddeleyite U-Pb) and 1490 ± 4 Ma (baddeleyite U-Pb). The intrusions are dominantly gabbros that experienced variable degrees of alteration. All the studied rocks are high-Ti and alkaline in composition, and exhibit light rare earth element enrichment and "humped" incompatible trace-element patterns with no obvious Nb-Ta depletion, similar to intraplate alkali basaltic rocks in continental flood basalt (CFB) and ocean island basalt (OIB) provinces. Negative ɛNd(T) values (- 0.97 to - 3.58) and fractionation of the HREE of these rocks indicate that they were derived from a time-integrated, slightly enriched asthenospheric mantle source with minor crustal contamination. Like other Fe-Ti oxide mineralized rocks in plume-related layered intrusions or large igneous provinces around the world, the Zhuqing gabbros likely occurred in an intraplate setting. The ~ 1.5 Ga mafic magmatism was likely part of the global 1.6-1.2 Ga anorogenic magmatism related to the break-up of the supercontinent Nuna/Columbia, suggesting that the Yangtze Block may have been a component of the supercontinent.
14. IGNEOUS INTRUSION IMPACTS ON WASTE PACKAGES AND WASTE FORMS
Energy Technology Data Exchange (ETDEWEB)
P. Bernot
2004-04-19
The purpose of this model report is to assess the potential impacts of igneous intrusion on waste packages and waste forms in the emplacement drifts at the Yucca Mountain Repository. The models are based on conceptual models and includes an assessment of deleterious dynamic, thermal, hydrologic, and chemical impacts. The models described in this report constitute the waste package and waste form impacts submodel of the Total System Performance Assessment for the License Application (TSPA-LA) model assessing the impacts of a hypothetical igneous intrusion event on the repository total system performance. This submodel is carried out in accordance with Technical Work Plan for Waste Form Degradation Modeling, Testing, and Analyses in Support of LA (BSC 2004 [DIRS:167796]) and Total System Performance Assessment-License Application Methods and Approaches (BSC 2003 [DIRS: 166296]). The technical work plan was prepared in accordance with AP-2.27Q, Planning for Science Activities. Any deviations from the technical work plan are documented in the following sections as they occur. The TSPA-LA approach to implementing the models for waste package and waste form response during igneous intrusion is based on identification of damage zones. Zone 1 includes all emplacement drifts intruded by the basalt dike, and Zone 2 includes all other emplacement drifts in the repository that are not in Zone 1. This model report will document the following model assessments: (1) Mechanical and thermal impacts of basalt magma intrusion on the invert, waste packages and waste forms of the intersected emplacement drifts of Zone 1. (2) Temperature and pressure trends of basaltic magma intrusion intersecting Zone 1 and their potential effects on waste packages and waste forms in Zone 2 emplacement drifts. (3) Deleterious volatile gases, exsolving from the intruded basalt magma and their potential effects on waste packages of Zone 2 emplacement drifts. (4) Post-intrusive physical
15. Characterize Framework for Igneous Activity at Yucca Mountain, Nevada
Energy Technology Data Exchange (ETDEWEB)
F. Perry; B. Youngs
2000-11-06
The purpose of this Analysis/Model (AMR) report is twofold. (1) The first is to present a conceptual framework of igneous activity in the Yucca Mountain region (YMR) consistent with the volcanic and tectonic history of this region and the assessment of this history by experts who participated in the Probabilistic Volcanic Hazard Analysis (PVHA) (CRWMS M&O 1996). Conceptual models presented in the PVHA are summarized and extended in areas in which new information has been presented. Alternative conceptual models are discussed as well as their impact on probability models. The relationship between volcanic source zones defined in the PVHA and structural features of the YMR are described based on discussions in the PVHA and studies presented since the PVHA. (2) The second purpose of the AMR is to present probability calculations based on PVHA outputs. Probability distributions are presented for the length and orientation of volcanic dikes within the repository footprint and for the number of eruptive centers located within the repository footprint (conditional on the dike intersecting the repository). The probability of intersection of a basaltic dike within the repository footprint was calculated in the AMR ''Characterize Framework for Igneous Activity at Yucca Mountain, Nevada'' (CRWMS M&O 2000g) based on the repository footprint known as the Enhanced Design Alternative [EDA II, Design B (CRWMS M&O 1999a; Wilkins and Heath 1999)]. Then, the ''Site Recommendation Design Baseline'' (CRWMS M&O 2000a) initiated a change in the repository design, which is described in the ''Site Recommendation Subsurface Layout'' (CRWMS M&O 2000b). Consequently, the probability of intersection of a basaltic dike within the repository footprint has also been calculated for the current repository footprint, which is called the 70,000 Metric Tons of Uranium (MTU) No-Backfill Layout (CRWMS M&O 2000b). The calculations for both
16. Low-Ti melts from the southeastern Siberian Traps Large Igneous Province: Evidence for a water-rich mantle source?
Alexei V Ivanov; Elena I Demonterova; Sergei V Rasskazov; Tatyana A Yasnygina
2008-02-01
Siberian Traps Large Igneous Province (STLIP) is one of the most voluminous volcanic provinces on Earth. The dominant erupted rocks are low-Ti basalts, which make up 80% by volume of the classical Noril’sk lava sequence. In the west Siberian basin and Maymecha-Kotuy area, the low- Ti basalts make up about 99% and 50% by volume, respectively. Dolerite sills in the Angara– Taseevskaya Syncline at the southeastern STLIP exhibit trace element patterns and Sr isotope ratios typical of the low-Ti basalts of the Noril’sk sequence. The most Mg-rich (MgO 9.5–11 wt%) and hence least differentiated dolerites are characterized by trace element patterns with Ta-Nb depletion, low Ce/Pb and high Sr/Pr. These trace element features are similar to water-saturated, mantle wedge-derived island arc basalts. These imply an important role of subduction fluid-derived trace elements in the source of melting beneath the Angara–Taseevskaya Syncline and other regions of the STLIP. Less magnesium rocks (MgO 3.8–6.1 wt%) with less prominent Ta-Nb depletion, higher Ce/Pb and lower Sr/Pr could be produced via olivine-plagioclase fractionation of primary high-magnesium melts.
17. Petrology of Igneous Clasts in Regolithic Howardite EET 87503
Science.gov (United States)
Hodges, Z. V.; Mittlefehldt, D. W.
2017-01-01
The howardite, eucrite and diogenite (HED) clan of meteorites is widely considered to originate from asteroid 4 Vesta, as a result of a global magma ocean style of differentiation. A global magmatic stage would allow silicate material to be well mixed, destroying any initial heterogeneity that may have been present resulting in the uniformity of eucrite and diogenite delta(exp 17)O, for example. The Fe/Mn ratio of mafic phases in planetary basalts can be diagnostic of different source bodies as this ratio is little-affected by igneous processes, so long as the oxygen and sulphur fugacities are buffered. Here, pyroxene Fe/Mn ratios in mafic clasts in howardite EET 87503 have been determined to further evaluate whether the HED parent asteroid is uniform. Uniformity would suggest that the parent asteroid was subject to homogenization prior to the formation of HED lithologies, likely through an extensive melting phase. Whereas, distinct differences may point towards heterogeneity of the parent body.
18. Targeting ROCK2 rather than ROCK1 inhibits Ewing sarcoma malignancy
Science.gov (United States)
Pinca, Rosa Simona; Manara, Maria Cristina; Chiadini, Valentina; Picci, Piero; Zucchini, Cinzia; Scotlandi, Katia
2017-01-01
Understanding the molecular processes characterizing Ewing sarcoma (EWS) cell migration is crucial to highlight novel therapies for patients with disseminated disease. In this study we analyzed the role of ROCK kinases in the regulation of cell migration, growth and differentiation of EWS cells. Overexpression of ROCK promotes invasion and metastasis in many solid tumors. However, the effect of ROCK in EWS has not been extensively investigated. Expression of ROCK1 and ROCK2 was analyzed by western blotting in a representative panel of human EWS cell lines, in comparison with the parameters of in vitro malignancy. We investigated the effects of a ROCK2 specific inhibitor toward those of a pan-ROCK inhibitor on the growth, migration and differentiation of two EWS cell lines. ROCK2 but not ROCK1 expression was found to be associated with in vitro cell migration and anchorage-independent growth capabilities. Exposure of EWS cells to ROCK inhibitors significantly reduced migration and growth, while favoring morphology changes and neural differentiation. These effects were more striking when cells were specifically deprived of ROCK2 activity. Our findings lead to consider ROCK2, rather than ROCK1, as a possible molecular target for the treatment of EWS. PMID:28112365
19. Creep of mafic dykes infiltrated by melt in the lower continental crust (Seiland Igneous Province, Norway)
Science.gov (United States)
Degli Alessandrini, G.; Menegon, L.; Malaspina, N.; Dijkstra, A. H.; Anderson, M. W.
2017-03-01
A dry mafic dyke from a continental lower-crustal shear zone in the Seiland Igneous Province (northern Norway) experienced syn-kinematic melt-rock interaction. Viscous shearing occurred at T ≈ 800 °C, P ≈ 0.75-0.95 GPa and was coeval with infiltration of felsic melt from adjacent migmatitic metapelites. The dyke has a mylonitic microstructure where porphyroclasts of orthopyroxene, clinopyroxene and plagioclase are wrapped by a fine-grained (4-7 μm) polyphase mixture of clinopyroxene + orthopyroxene + plagioclase + quartz + ilmenite ± K-feldspar ± apatite. Microstructural observations and electron backscatter diffraction analysis indicate that the porphyroclasts deformed by a combination of dislocation glide and fracturing, with only a limited record of dislocation creep, recovery and dynamic recrystallization. We identified diffusion creep as the dominant deformation mechanism in the mixture based on the small grain size, phase mixing and weak crystallographic preferred orientation of all phases (interpreted as the result of oriented grain growth during viscous flow). The polyphase mixture did not form by dynamic recrystallization or by mechanical fragmentation of the porphyroclasts, but rather by melt-rock interaction. Thermodynamic models indicate that the syn-kinematic mineral assemblage results from the chemical interaction between a pristine mafic dyke and ca. 10 vol.% of felsic melt infiltrating from the adjacent partially molten metapelites. Extrapolation of laboratory-derived flow laws to natural conditions indicates that the formation of interconnected layers of fine-grained reaction products deforming by diffusion creep induces a dramatic weakening in the mafic granulites, with strain rates increasing up to 2-3 orders of magnitude. The reaction weakening effect is more efficient than the weakening associated with melt-assisted diffusion creep in the presence of up to 10 vol.% of infiltrated melt without formation of fine-grained reaction products
20. Basement faults and volcanic rock distributions in the Ordos Basin
Institute of Scientific and Technical Information of China (English)
2010-01-01
Volcanic rocks in the Ordos Basin are of mainly two types: one in the basin and the other along the margin of the basin. Besides those along the margin, the marginal volcanic rocks also include the volcanic rocks in the Yinshanian orogenic belt north of the basin. Based on the latest collection of gravitational and aeromagnetic data, here we interpret basement faults in the Ordos Basin and its peripheral region, compare the faults derived from aeromagnetic data with those from seismic data, and identify the geological ages of the fault development. Two aeromagnetic anomaly zones exist in the NE-trending faults of the southern basin, and they are in the volcanic basement formed in pre-Paleozoic. These NE-trending faults are the channel of volcanic material upwelling in the early age (Archean-Neoproterozoic), where igneous rocks and sedimentary rocks stack successively on both sides of the continental nucleus. In the Cambrian, the basin interior is relatively stable, but in the Late Paleozoic and Mesozoic, the basin margin underwent a number of volcanic activities, accompanied by the formation of nearly north-south and east-west basement faults in the basin periphery and resulting in accumulation of great amount of volcanic materials. Volcanic tuff from the basin periphery is discovered in the central basin and volcanic materials are exposed in the margins of the basin. According to the source-reservoir-cap rock configuration, the basin peripheral igneous traps formed in the Indosinian-Early Yanshanian and Late Hercynian are favorable exploration objectives, and the volcanic rocks in the central basin are the future target of exploration.
1. SHRIMP U-Pb zircon dates from igneous rocks from the Fontana Lake region, Patagonia: Implications for the age of magmatism, Mesozoic geological evolution and age of basement Datación de circón por U-Pb SHRIMP en rocas ígneas de la región del lago Fontana, Patagonia: Implicancia para la edad del magmatismo, la evolución geológica mesozoica y edad del basamento
Directory of Open Access Journals (Sweden)
A.P. Rolando
2004-12-01
Full Text Available In the eastern margin of the Patagonian Andes and between 44° 30´S and 45° 30´S (Fontana Lake region, Middle Jurassic to Early Cretaceous volcanic and sedimentary rocks were intruded by granitic bodies during the Cretaceous. The reconstruction of the Jurassic-Cretaceous magmatic evolution in the Fontana Lake region and in the adjacent Patagonian Batholith was made possible by the consideration of the following characteristics: distribution in time and space of several intrusive bodies, retro-arc basin formation and volcanic intensity. U-Pb SHRIMP dating of zircon crystals from an ignimbrite, a dacitic porphyry and two granitoid rocks yielded dates of 148.7 ± 2.3, 144.5 ± 1.6, 117 ± 1.7 and 99.6 ± 2.8 Ma, respectively. The Cerro Bayo Ignimbrite (148.7 ± 2.3 Ma, Late Jurassic was included in the Lago La Plata Formation; this unit hosts an epithermal ore deposit. The Laguna Escondida dacitic porphyry (144.5 ± 1.6 Ma, Jurassic-Cretaceous boundary intruded metasedimentary rocks of the Lago La Plata Formation; this sub-volcanic body can chronologically be linked to the Patagonian Batholith. After the Jurassic volcanic events, a retro-arc basin formed in the eastern sector of the Patagonian Range at about 140-115 Ma (Late Berriasian-Barremian and magmatism ceased during this event. The dating of granitoids (117 ± 1.7 and 99.6 ± 2.8 Ma in the Fontana Lake region confirms a temporal magmatic continuity with the Patagonian Batholith. These dates also are in agreement with the volcanic rocks of the Divisadero Group and epithermal deposits in the region (La Ferrocarrilera deposit. One of the analyzed granitoids (Dedo Chico, 99.6 ± 2.8 Ma has inherited zircon crystals of about 2,100 and 3,410 Ma, in agreement with other previous isotopic evidence for the occurrence of an underlying Precambrian basement in the region.En la margen oriental de la cordillera Patagónica, entre los 44° 30´ L.S. y 45° 30´ L.S. (región del lago Fontana, rocas volc
2. Tilting, burial, and uplift of the Guadalupe Igneous Complex, Sierra Nevada, California
Science.gov (United States)
Haeussler, Peter J.; Paterson, Scott R.
1993-01-01
It is often incorrectly assumed that plutons have a relatively uneventful structural history after emplacement. The 151 Ma Guadalupe Igneous Complex (GIC) in the Foothills Terrane, California, was involved in three post-emplacement events: (1) ∼30° of southwestside-up tilting during ductile regional faulting and contraction, (2) burial of the pluton from ∼4 to 12 km during crustal thickening of the wall rocks, and (3) uplift with only minor tilting in the Late Cretaceous. Tilting of the pluton is indicated by (1) southwest to northeast gradational changes from layered gabbros and diorites to granites and granophyres; (2) northeastward dips of layering in gabbro, internal contacts, and bedding of overlying coeval(?) volcanic rocks; (3) northeastward decrease in wall-rock metamorphic grade; and (4) paleomagnetic data from 14 localities across the pluton. We argue that tilting occurred between 146-135 Ma during southwest-northeast-directed regional contraction. This contraction is indicated by widespread folds and cleavages and by reverse motion on the Bear Mountains fault zone (BMFZ), a large northeast-dipping shear zone that bounds the GIC on its southwest side. Burial of the GIC, which overlapped in time but outlasted tilting, is suggested by (1) post-emplacement contractional faulting, folding, and cleavage development; (2) analyses of strains associated with widespread cleavage that indicate vertical thickening of ∼100% and (3) microstructural and mineral assemblage data that indicate shallow emplacement of the GIC, in contrast to mineral assemblage and limited geobarometric data from adjacent 120-110 Ma plutons that indicate moderate emplacement levels. Late Cretaceous uplift is indicated by 95-75 Ma sedimentary rocks that unconformably overlie the 120-110 Ma plutons.This geologic history is interesting for several reasons. First, although the GIC participated in extensive post-emplacement deformation, it lacks internal structural evidence of these events
3. Inherited igneous zircons in jadeitite predate high-pressure metamorphism and jadeitite formation in the Jagua Clara serpentinite mélange of the Rio San Juan Complex (Dominican Republic)
Science.gov (United States)
Hertwig, Andreas; McClelland, William C.; Kitajima, Kouki; Schertl, Hans-Peter; Maresch, Walter V.; Stanek, Klaus; Valley, John W.; Sergeev, Sergey A.
2016-05-01
This study utilizes zircon SIMS U-Pb dating, REE and trace-element analysis as well as oxygen isotope ratios of zircon to distinguish jadeite-rich rocks that formed by direct crystallization from a hydrous fluid from those that represent products of a metasomatic replacement process. Zircon was separated from a concordant jadeitite layer and its blueschist host, as well as from loose blocks of albite-jadeite rock and jadeitite that were all collected from the Jagua Clara serpentinite-matrix mélange in the northern Dominican Republic. In the concordant jadeitite layer, three groups of zircon domains were distinguished based on both age as well as geochemical and oxygen isotope values: age groups old (117.1 ± 0.9 Ma), intermediate (three dates: 90.6, 97.3, 106.0 Ma) and young (77.6 ± 1.3 Ma). Zircon populations from the blueschist host as well as the other three jadeite-rich samples generally match zircon domains of the old age group in age as well as geochemistry and oxygen isotope ratios. Moreover, these older zircon populations are indistinguishable from zircon typical of igneous oceanic crust and hence are probably inherited from igneous protoliths of the jadeite-rich rocks. Therefore, the results suggest that all investigated jadeite-rich rocks were formed by a metasomatic replacement process. The younger domains might signal actual ages of jadeitite formation, but there is no unequivocal proof for coeval zircon-jadeite growth.
4. Whole-rock Pb and Sm-Nd isotopic constraints on the growth of southeastern Laurentia during Grenvillian orogenesis
Science.gov (United States)
Fisher, C.M.; Loewy, S.L.; Miller, C.F.; Berquist, P.; Van Schmus, W. R.; Hatcher, R.D.; Wooden, J.L.; Fullagar, P.D.
2010-01-01
The conventional view that the basement of the southern and central Appalachians represents juvenile Mesoproterozoic crust, the final stage of growth of Laurentia prior to Grenville collision, has recently been challenged. New whole-rock Pb and Sm-Nd isotopic data are presented from Meso protero zoic basement in the southern and central Appalachians and the Granite-Rhyolite province, as well as one new U-Pb zircon age from the Granite-Rhyolite province. These data, combined with existing data from Mesoproterozoic terranes throughout southeastern Laurentia, further substantiate recent suggestions that the southern and central Appalachian basement is exotic with respect to Laurentia. Sm-Nd isotopic compositions of most rocks from the southern and central Appalachian basement are consistent with progressive growth through reworking of the adjacent Granite-Rhyolite province. However, Pb isotopic data, including new analyses from important regions not sampled in previous studies, do not correspond with Pb isotopic compositions of any adjacent crust. The most distinct ages and isotopic compositions in the southern and central Appalachian basement come from the Roan Mountain area, eastern Tennessee-western North Carolina. The data set indicates U-Pb zircon ages up to 1.8 Ga for igneous rocks, inherited and detrital zircon ages >2.0 Ga, Sm-Nd depleted mantle model (TDM) ages >2.0 Ga, and the most elevated 207Pb/204Pb observed in southeastern Laurentia. The combined U-Pb geochronologic and Sm-Nd and Pb isotopic data preclude derivation of southern and central Appalachian basement from any nearby crustal material and demonstrate that Grenville age crust in southeastern Laurentia is exotic and probably was transferred during collision and assembly of Rodinia. These new data better define the boundary between the exotic southern and central Appalachian basement and adjacent Laurentian Granite-Rhyolite province. ?? 2010 Geological Society of America.
5. Petrography, geochemistry and tectonic setting of Salmabad Tertiary volcanic rocks, southeast of Sarbisheh, eastern Iran
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Masoumeh Goodarzi
2014-10-01
is attributed to the mantle source, presumably metasomatized by the Sistan ocean subduction. The trace element features are consistent with the roles played by subducted sediments and fluid released from the subducted slab in magma genesis. Acknowledgements The authors would like to thank reviewers for the constructive comments which greatly contributed to the improvement of the manuscript. References Berberian, F., Muir, I.D., Pankhurst, R.J. and Berberian, M., 1982. Late Cretaceous and early Miocene Andean type plutonic activity in northern Makran and Central Iran. Journal of the Geological Society, 139(5: 605-614. Camp, V.E. and Griffis, R., 1982. Character, genesis and tectonic setting of igneous rocks in the Sistan suture zone, eastern Iran. Lithos, 15(3: 221-239. Gill, R., 2010. Igneous rocks and processes. Wiley-Blackwell, Malaysia, 428 pp. Harangi, S., Downes, H., Thirlwall, M., Gmeling, K., 2007. Geochemistry, Petrogenesis and Geodynamic Relationships of Miocene Calc-alkalineVolcanic Rocks in the Western Carpathian arc, Eastern Central Europe. Journal of petrology, 48(12: 2261-2287. Jung, D., Keller, J., Khorasani, R., Marcks, Chr., Baumann, A. and Horn, P., 1983. Petrology of the Tertiary magmatic activity the northern Lut area, East of Iran. Ministry of mines and metals, Geological survey of Iran, geodynamic project (geotraverse in Iran, Tehran, Report 51, pp. 285-336. Karimpour, M.H., Stern, C.R., Farmer, L., Saadat, S. and Malekezadeh, A., 2011. Review of age, Rb-Sr geochemistry and petrogenesis of Jurassic to Quaternary igneous rocks in Lut Block, Eastern Iran. Geopersia, 1(1:19-36. Kuscu, G.G. and Geneli, F., 2010. Review of post-collisional volcanism in the central Anatolian volcanic province(Turkey, with special reference to the Tepekoy volcanic complex. International Journal of Earth Sciences, 99(3: 593-621. Richards, J.P., Spell, T., Rameh, E., Razique, A. and Fletcher T., 2012. High Sr/Y Magmas Reflect Arc Maturity,High Magmatic Water Content, and
6. Ultramafic rocks in the Namurian C series in the Zebrzydowice area (Rybnik coal region)
Energy Technology Data Exchange (ETDEWEB)
Jochemczyk, L.
1984-08-01
The chemical and physical properties as well as origin of ultramafic rock samples from the Zebrzydowice area in the Rybnik coal region are evaluated. The ultramafic rocks detected by drilling were situated at depths of 1035 m in the top of dacite-andesite system and thermally alterated claystones. Chemical analyses and X-ray examination show that the ultramafic rock consists of secondarily alterated peridotite. The peridotite consists of chlorite-serpentite, phlogopite, bastite, nepheline and opaque minerals. Its chemical composition is characterized by reduced content of silica and a high content of ferric oxide. The ultramafic rock in the Zebrzydowice area differs from mineral and chemical composition of igneous rocks which occur in Carboniferous strata in the west and the southwest of the Upper Silesia basin. Rock of this type has been recorded in the Upper Silesia basin for the first time. 12 references.
7. Characterize Framework for Igneous Activity at Yucca Mountain, Nevada
Energy Technology Data Exchange (ETDEWEB)
F. Perry; R. Youngs
2004-10-14
The purpose of this scientific analysis report is threefold: (1) Present a conceptual framework of igneous activity in the Yucca Mountain region (YMR) consistent with the volcanic and tectonic history of this region and the assessment of this history by experts who participated in the probabilistic volcanic hazard analysis (PVHA) (CRWMS M&O 1996 [DIRS 100116]). Conceptual models presented in the PVHA are summarized and applied in areas in which new information has been presented. Alternative conceptual models are discussed, as well as their impact on probability models. The relationship between volcanic source zones defined in the PVHA and structural features of the YMR are described based on discussions in the PVHA and studies presented since the PVHA. (2) Present revised probability calculations based on PVHA outputs for a repository footprint proposed in 2003 (BSC 2003 [DIRS 162289]), rather than the footprint used at the time of the PVHA. This analysis report also calculates the probability of an eruptive center(s) forming within the repository footprint using information developed in the PVHA. Probability distributions are presented for the length and orientation of volcanic dikes located within the repository footprint and for the number of eruptive centers (conditional on a dike intersecting the repository) located within the repository footprint. (3) Document sensitivity studies that analyze how the presence of potentially buried basaltic volcanoes may affect the computed frequency of intersection of the repository footprint by a basaltic dike. These sensitivity studies are prompted by aeromagnetic data collected in 1999, indicating the possible presence of previously unrecognized buried volcanoes in the YMR (Blakely et al. 2000 [DIRS 151881]; O'Leary et al. 2002 [DIRS 158468]). The results of the sensitivity studies are for informational purposes only and are not to be used for purposes of assessing repository performance.
8. Late Paleozoic tectonomagmatic evolution of the western southern Tian Shan, Tajikistan
Science.gov (United States)
2015-04-01
The 2500-km-long Tian Shan orogenic belt constitutes a dominantly Paleozoic amalgmation of Eurasia that has been overprinted by the Mesozoic and Cenozoic Cimmerian and Indo-Eurasian collisions. This southernmost unit of the Central Asian Orogenic System (CAOS) is divided N-S by discontinuous suture zones that reflect its complex assemblage and E-W by the Talas-Fergana dextral (modern kinematics) fault zone. The western southern Tian Shan in Tajikistan/Uzbekistan is poorly studied compared to the rest of the orogen in Kyrgyzstan/China, but a dominant signal of late Paleozoic magmatism synchronous to widespread magmatism documented along strike provides an intriguing opportunity to investigate regional tectonic processes at this time. The late Carboniferous-early Permian Gissar batholith is the southern Tian Shan's southernmost lithotectonic unit. Zircon U-Pb weighted-mean crystallization ages for Gissar granitoids range from ~310-290 Ma, are youngest in the east, and define a primary stage of arc magmatism related to closure of the Turkestan ocean. A ~280 Ma crystallization age was obtained for a Ne syenite, which corresponds to small, 'post-collisional,' alkaline intrusions in 1:200,000 Soviet geologic maps. Zircon ɛHf in Gissar granitoids generally decreases with decreasing zircon U-Pb age from +5'10. Zircon ɛHf in the young Ne syenite is +1-+6. Taken together, these trends indicate a progressive shift from juvenile to intermediate magmatism over 20 Myr, followed by a marked return to juvenile magmatism within 10 Myr. The Garm 'metamorphic' massif is situated within the eastern Gissar batholith and is derived from greater depths than the rest of the batholith, as indicated by its defining features: (i) Discontinuous outcrops of Bt+Grt quartzofeldspathic gneisses/schists; and (ii) Presence of igneous garnet in granitoids. Zircons from the Garm quartzofeldspathic gneisses/schists exhibit pronounced Pb-loss discordia that are consistent with ~amphibolite
9. Contact metamorphism in Middle Ordovician arc rocks (SW Sardinia, Italy): New paleogeographic constraints
Science.gov (United States)
Costamagna, Luca Giacomo; Elter, Franco Marco; Gaggero, Laura; Mantovani, Federico
2016-11-01
In the early Cambrian Bithia Formation in the Variscan foreland of Sardinia, a Middle Ordovician granitic intrusion (478-457 Ma) is hosted by marly metasedimentary rocks that were affected by high-temperature (HT) metamorphism. A detailed structural-petrographical transect was conducted through the granitic intrusion and its host rocks. Field data and relationships between HT/low-pressure (LP) mineral assemblages in the metasedimentary rocks (Grt + Wo + Ves in carbonate lenses and And in pelite) demonstrate that the study area was affected by a polyphase HT overprint (I: T = 520-620 °C at XCO2 = 0.1, P: 0.2-0.4 GPa; and II: T = 600-670 °C at XCO2 = 0.1, P = 0.2-0.4 GPa) that pre-dates the Variscan tectonic, metamorphic, and igneous phases. In the Canigò or Canigou Massif (Eastern Pyrenees), the Somail Massif (Montagne Noire), and the Ruitor Massif (Internal Massifs, NW Alps), Middle Ordovician orthogneiss with relict igneous textures are deciphered despite being overprinted by Variscan amphibolite-to-granulite-facies metamorphism and subsequent Alpine low-grade metamorphism. Comparisons of associated igneous and metasedimentary rocks in the Sardinia foreland with the High-Grade Metamorphic Complex in the Variscan Axial Zone and the Canigou Massif indicate a convergent Middle Ordovician evolution that was overprinted by HT Variscan metamorphism.
10. Igneous pyrometamorphism in the Potiguar Basin, Northeastern Brazil
Directory of Open Access Journals (Sweden)
Larissa dos Santos
2014-06-01
Full Text Available In the Potiguar Basin (NE Brazil, cretaceous rocks (sandstones, siltstones, shales, limestones are intruded by Paleogene to Neogene basic bodies. As a result, were formed buchites, pyrometamorphic rocks indicating very low pressures and very high temperatures. Field descriptions permitted distinguishing light buchites (LB and dark buchites (DB, which were investigated throughout petrographic, electron microprobe and X-ray diffraction studies. LBs contain abundant clasts of quartz surrounded by radial tridymite needles, besides phenocrysts of sanidine and clinopyroxene included in a vitreous groundmass. DBs have mainly microcrystals of Fe-cordierite (sekaninaite, mullite, armalcolite, ilmenite and spinel, dispersed within a black cryptocrystalline matrix. Chemically, LBs are richer in SiO2 (~76.7% and K2O (~5.7% and poorer in Al2O3 (~12.8% when compared to DBs (respectively ~51.5, ~0.2 and ~42.7%. Based on phase diagrams published in the literature, the habit of crystals (acicular, elongated sometimes hollow crystals and the significant content of glassy material we consider that the liquid formed by melting at ~1100 – 1150o C of sedimentary material cooled quickly at very high temperatures and pressures below 1 kbar. The results obtained are relevant in petrological terms, and may also have economic implications since a large number of basic bodies intrude rocks with hydrocarbon reservoirs.
11. Evaluation of garnet discrimination diagrams using geochemical data of garnets derived from various host rocks
Science.gov (United States)
Krippner, Anne; Meinhold, Guido; Morton, Andrew C.; von Eynatten, Hilmar
2014-06-01
This work is an attempt to evaluate six different garnet discrimination diagrams (one binary diagram and five ternary diagrams) commonly used by many researchers. The mineral chemistry of detrital garnet is a useful tool in sedimentary provenance studies, yet there is no clear-cut understanding of what garnet type originates from which host lithology. Several discrimination diagrams exist for garnet showing distinct compositional fields, separated by strict boundaries that are thought to reflect specific types of source rocks. For this study, a large dataset was compiled (N = 3532) encompassing major element compositions of garnets derived from various host lithologies, including metamorphic, igneous, and mantle-derived rocks, in order to test the applicability of the various discrimination schemes. The dataset contains mineral chemical data collected from the literature complemented with some new data (N = 530) from garnet-bearing metamorphic and ultramafic rocks in Austria and Norway. Discrimination of the tested diagrams only works for a small group of garnets derived from mantle rocks, granulite-facies metasedimentary rocks, and felsic igneous rocks. For other garnet types, the assignment to a certain type of host rock remains ambiguous. This is considered insufficient and therefore the evaluated diagrams should be used with great care. We further apply compositional biplot analysis to derive some hints towards future perspectives in detrital garnet discrimination.
12. Search for magnetic monopoles in polar volcanic rocks
CERN Document Server
Bendtz, K; Hächler, H -P; Hirt, A M; Mermod, P; Michael, P; Sloan, T; Tegner, C; Thorarinsson, S B
2013-01-01
For a broad range of values of magnetic monopole mass and charge, the abundance of monopoles trapped inside the Earth would be expected to be enhanced in the mantle beneath the geomagnetic poles. A search for magnetic monopoles was conducted using the signature of an induced persistent current following the passage of igneous rock samples through a SQUID-based magnetometer. A total of 24.6 kg of rocks from various selected sites, among which 23.4 kg are mantle-derived rocks from the Arctic and Antarctic areas, was analysed. No monopoles were found and a 90% confidence level upper limit of $1.6\\cdot 10^{-28}$ is set on the monopole to nucleon ratio in the search samples.
13. Search for Magnetic Monopoles in Polar Volcanic Rocks
DEFF Research Database (Denmark)
Bendtz, K.; Milstead, D.; Hächler, H. -P.
2013-01-01
For a broad range of values of magnetic monopole mass and charge, the abundance of monopoles trapped inside Earth would be expected to be enhanced in the mantle beneath the geomagnetic poles. A search for magnetic monopoles was conducted using the signature of an induced persistent current...... following the passage of igneous rock samples through a SQUID-based magnetometer. A total of 24.6 kg of rocks from various selected sites, among which 23.4 kg are mantle-derived rocks from the Arctic and Antarctic areas, was analyzed. No monopoles were found, and a 90% confidence level upper limit of 9.8 x...... 10(-5)/g is set on the monopole density in the search samples. DOI:10.1103/PhysRevLett.110.121803...
14. Electrical resistivity measurements to predict abrasion resistance of rock aggregates
Sair Kahraman; Mustafa Fener
2008-04-01
The prediction of Los Angeles (LA) abrasion loss from some indirect tests is useful for practical applications. For this purpose, LA abrasion, electrical resistivity, density and porosity tests were carried out on 27 different rock types. LA abrasion loss values were correlated with electrical resistivity and a good correlation between the two parameters was found. To see the effect of rock class on the correlation, regression analysis was repeated for igneous rocks, metamorphic rocks and sedimentary rocks, respectively. It was seen that correlation coefficients were increased for the rock classes. In addition, the data were divided into two groups according to porosity and density, respectively. After repeating regression analysis for these porosity and density groups, stronger correlations were obtained compared to the equation derived for all rocks. The validity of the derived equations was statistically tested and it was shown that all derived equations were significant. Finally, it can be said that all derived equations can alternatively be used for the estimation of LA abrasion loss from electrical resistivity.
15. Zircon U-Pb age of the Pescadero felsite: A late Cretaceous igneous event in the forearc, west-central California Coast Ranges
Science.gov (United States)
Ernst, W.G.; Martens, U.C.; McLaughlin, R.J.; Clark, J.C.; Moore, Diane E.
2011-01-01
Weathered felsite is associated with the late Campanian-Maastrichtian Pigeon Point Formation near Pescadero, California. Poorly exposed, its age and correlation are uncertain. Is it part of the Pigeon Point section west of the San Gregorio-Hosgri fault? Does it rest on Nacimiento block basement? Is it dextrally offset from the Oligocene Cambria Felsite, ~185 km to the southeast? Why is a calc-alkaline hypabyssal igneous rock intrusive into the outboard accretionary prism? To address these questions, we analyzed 43 oscillatory-zoned zircon crystals from three incipiently recrystallized pumpellyite ?? prehnite ?? laumontite-bearing Pescadero felsite samples by sensitive high-resolution ion microprobe-reverse geometry (SHRIMPRG) and laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) techniques. Thirty-three zircons gave late Mesozoic U-Pb ages, with single-grain values ranging from 81 to 167 Ma; ten have pre-Mesozoic, chiefl y Proterozoic ages. A group of the four youngest Pescadero zircons yielded an apparent maximum igneous age of ca. 86-90 Ma. Refl ecting broad age scatter and presence of partly digested sandstone inclusions, we interpret the rest of the zircons (perhaps all) as xenocrysts. Twenty-three zircons were separated and analyzed from two samples of the similar Cambria Felsite, yielding a unimodal 27 Ma U-Pb age. Clearly, the origin of the Upper Oligocene Cambria Felsite is different from that of the Upper Cretaceous Pescadero felsite; these rocks are not correlated, and do not constrain displacement along the San Gregorio-Hosgri fault. Peak ages differ slightly, but relative probability curves for Mesozoic and pre-Mesozoic Pescadero zircons compare well, for example, with abundant U-Pb age data for detrital zircons from Franciscan metaclastic strata ~100 km to the east in the Diablo Range- San Francisco Bay area, San Joaquin Great Valley Group turbidites, Upper Cretaceous Nacimiento block Franciscan strata, and Upper Cretaceous
16. Zircon U-Pb geochronology and petrogenesis of metabasites from the western Beihuaiyang zone in the Hong'an orogen, central China: Implications for detachment within subducting continental crust at shallow depths
Science.gov (United States)
Liu, Yi-Can; Liu, Li-Xiang; Li, Yuan; Gu, Xiao-Feng; Song, Biao
2017-09-01
Deformed low-grade metabasites from the western segment of the Beihuaiyang zone in the Hong'an orogen, central China can be divided into two types, i.e. meta-gabbro and meta-basalt. These lithologies have been studied by using whole-rock elemental and Sr-Nd-Pb isotopic analyses, and zircon SHRIMP U-Pb dating. Concordant zircon U-Pb ages of 631 ± 5 Ma and 623 ± 14 Ma are obtained for the meta-gabbros, consistent with a previously reported U-Pb age of 635 ± 5 Ma. The meta-basalt was dated to have a protolith age of middle Neoproterozoic (∼750 Ma) and a metamorphic age at ca. 240 Ma. The all studied metabasites occur as block or slice within a metamorphosed Ordovician volcanic zone (originally named as the Dingyuan Formation) and are in tectonic contact to each other. The gabbro and basalt emplaced at ∼630 Ma and ∼750 Ma, respectively in a continental rifting setting, whereas their present country rocks were erupted at ∼465 Ma in an arc setting. The Pb-isotope compositions of the low-grade meta-gabbros and meta-basalts are similar to those from the Dabie ultrahigh-pressure (UHP) meta-igneous rocks with an upper continental crust affinity. The protolith ages of the studied relatively low-grade meta-basic rocks are in good agreement not only with ages for two episodes of middle and late Neoproterozoic mafic and felsic magmatism in the Suizhou to Zaoyang areas at the northern margin of the South China Block, but are also in agreement with the protolith ages of UHP meta-igneous rocks in the Dabie-Sulu orogenic belt. Therefore, these Neoproterozoic low-grade metabasites are considered to be exotic and they may have been detached and offscraped from the subducting upper crust of the South China Block at shallow depths during continental collision in the Triassic. They were subsequently exhumed in the initial stage of continental subduction, and thrusted over the Paleozoic metamorphosed rocks in the southern margin of the North China Block or as foreign slices
17. Age and tectonic setting of the Mesozoic McCoy Mountains Formation in western Arizona, USA
Science.gov (United States)
Spencer, J.E.; Richard, S.M.; Gehrels, G.E.; Gleason, J.D.; Dickinson, W.R.
2011-01-01
The McCoy Mountains Formation consists of Upper Jurassic to Upper Cretaceous siltstone, sandstone, and conglomerate exposed in an east-west-trending belt in southwestern Arizona and southeastern California. At least three different tectonic settings have been proposed for McCoy deposition, and multiple tectonic settings are likely over the ~80 m.y. age range of deposition. U-Pb isotopic analysis of 396 zircon sand grains from at or near the top of McCoy sections in the southern Little Harquahala, Granite Wash, New Water, and southern Plomosa Mountains, all in western Arizona, identifi ed only Jurassic or older zircons. A basaltic lava fl ow near the top of the section in the New Water Mountains yielded a U-Pb zircon date of 154.4 ?? 2.1 Ma. Geochemically similar lava fl ows and sills in the Granite Wash and southern Plomosa Mountains are inferred to be approximately the same age. We interpret these new analyses to indicate that Mesozoic clastic strata in these areas are Upper Jurassic and are broadly correlative with the lowermost McCoy Mountains Formation in the Dome Rock, McCoy, and Palen Mountains farther west. Six samples of numerous Upper Jurassic basaltic sills and lava fl ows in the McCoy Mountains Formation in the Granite Wash, New Water, and southern Plomosa Mountains yielded initial ??Nd values (at t = 150 Ma) of between +4 and +6. The geochemistry and geochronology of this igneous suite, and detrital-zircon geochronology of the sandstones, support the interpretation that the lower McCoy Mountains Formation was deposited during rifting within the western extension of the Sabinas-Chihuahua-Bisbee rift belt. Abundant 190-240 Ma zircon sand grains were derived from nearby, unidentifi ed Triassic magmatic-arc rocks in areas that were unaffected by younger Jurassic magmatism. A sandstone from the upper McCoy Mountains Formation in the Dome Rock Mountains (Arizona) yielded numerous 80-108 Ma zircon grains and almost no 190-240 Ma grains, revealing a major
18. The behaviour of copper isotopes during igneous processes
Science.gov (United States)
Savage, P. S.; Moynier, F.; Harvey, J.; Burton, K. W.
2015-12-01
Application of Cu isotopes to high temperature systems has recently gained momentum and has the potential for probing sulphide fractionation during planetary differentiation [1]. This requires robust estimates for planetary reservoirs, and a fundamental understanding of how igneous processes affect Cu isotopes; this study aims to tackle the latter. Cogenetic suites affected by both fractionation crystallisation and cumulate formation were analysed to study such effects on Cu isotopes. In S-undersatured systems, Cu behaves incompatibly during melt evolution and the Cu isotope composition of such melt is invariant over the differentiation sequence. In contrast, S-saturated systems show resolvable Cu isotope variations relative to primitive melt. Such variations are minor but imply a slightly heavy Cu isotope composition for continental crust compared to BSE, consistent with granite data [2]. Although olivine accumulation does not affect Cu isotopes, spinel-hosted Cu is isotopically light relative to the bulk. Analysis of variably melt-depleted cratonic peridotites shows that partial melting can affect Cu isotope composition in restite, with the depleted samples isotopically light compared to BSE. This could be due to residual spinel and/or incongruent melting of sulphides - individual sulphides picked from a single xenolith reveal a range of Cu isotope compositions, dependent on composition. Although partial melting may fractionate Cu isotopes, models suggest most mantle-derived melt will have δ65Cu ≈ BSE, as most source Cu will be transferred to the melt. Small degree melts such as ocean island basalts are predicted to be isotopically heavier than MORB, if derived from a primitive mantle source. OIBs have a range of Cu isotope compositions: some are heavier than MORB as predicted; however, some have much lighter compositions. Since Cu isotopes can be significantly fractionated in the surface environment [e.g. 3] OIB Cu isotopic variations may be linked to
19. The World's Largest Submarine Canyon—Kroenke Canyon in the Western Equatorial Pacific
Science.gov (United States)
Coffin, M. F.; Adams, N.; Whittaker, J. M.; Lucieer, V.; Heckman, M.; Ketter, T.; Neale, J. F.; Reyes, A.; Travers, A.
2015-12-01
Kroenke Canyon lies on the Ontong Java Plateau (OJP) in the western Equatorial Pacific, between the Solomon Islands and the Federated States of Micronesia. In late 2014 aboard the Schmidt Ocean Institute's RV Falkor, we mapped, albeit incompletely, the Canyon for the first time, revealing that it is both the longest (>700 km) and the most voluminous (>6800 km3) submarine canyon yet discovered on Earth. Kroenke Canyon appears to originate in the vicinity of Ontong Java (Solomon Islands) and Nukumanu (Papua New Guinea) atolls, and presumably began to develop when the atolls were high-standing volcanic islands surmounting the ~120 Ma igneous basement of the OJP. The Canyon is characterised by numerous tributaries and significant mass wasting. Kroenke Canyon incises the layer-cake stratigraphy of OJP sediment and sedimentary rock, mostly carbonate with some interbedded chert, which has provided numerous slip surfaces for submarine landslides. The carbonate compensation depth (CCD) roughly coincides with the depth of the transition between the OJP and the neighbouring Nauru Basin. As a result, despite the large volume of sediment eroded and transported by canyon-forming processes, only a minor fan is evident in the Nauru Basin because most of the carbonate has dissolved.
20. The Guerrero suspect terrane (western Mexico) and coeval arc terranes (the Greater Antilles and the Western Cordillera of Colombia): a late Mesozoic intra-oceanic arc accreted to cratonal America during the Cretaceous
Science.gov (United States)
Tardy, M.; Lapierre, H.; Freydier, C.; Coulon, C.; Gill, J.-B.; de Lepinay, B. Mercier; Beck, C.; Martinez R., J.; O. Talavera, M.; E. Ortiz, H.; Stein, G.; Bourdier, J.-L.; Yta, M.
1994-02-01
The Guerrero suspect terrane, composed of Late Jurassic-Early Cretaceous sequences, extends from Baja California to Acapulco and is considered to be coeval with the late Mesozoic igneous and sedimentary arc sequences of the Greater Antilles, the West Indies, Venezuela and the Western Cordillera of Colombia. These sequences represent the remnants of an arc which accreted to the North American and northern South American cratons at the end of the Cretaceous. In western Mexico, the arc sequences built on continental crust consist of high-K calc-alkaline basalts, andesites and rhyolites enriched in LREE with abundant siliceous pyroclastic rocks interbedded either with Aptian-Albian reefal limestones or red beds. They do not show magmatic changes during the arc development. In contrast, the arc sequences built on oceanic crust show an evolution with time. Arc activity began with the development of depleted low K-tholeiitic mafic suite (Guanajuato igneous sequence), followed first by mature tholeiitic basalts and then by calc-alkaline olivine basalts interbedded with micritic limestones and radiolarian oozes of Early Cretaceous age. At the end of the arc growth, during Aptian-Albian times, calc-alkaline pillow basalts and and esites poured out in the volcanic front while shoshonitic olivine basalts extruded in the back arc. The tholeiitic and shoshonitic mafic rocks as well as the calc-alkaline lavas are mildly enriched in LREE, Y and Nb and show high ɛNd ratios, typical of oceanic arcs. In contrast, the calc-alkaline mafic suite enriched in LREE, Y and Nb exhibits lower ɛNd ratios suggesting that it was derived by the partial melting of a mantle source contaminated either by Paleozoic subducted sediments or old source enrichments (OIB). The Cretaceous arc rocks of the Greater Antilles, interbedded with and/or capped by Aptian-Albian limestones, the Cretaceous andesites of northern Colombia, the Cretaceous tholeiitic and calc-alkaline volcanic rocks of Venezuela, and
1. Petrogenesis of Eocene granitoids and microgranular enclaves in the western Tengchong Block: Constraints on eastward subduction of the Neo-Tethys
Science.gov (United States)
Zhao, Shao-wei; Lai, Shao-cong; Qin, Jiang-feng; Zhu, Ren-Zhi
2016-11-01
Eocene granitic and related igneous rocks in the western Tengchong Block are considered to be the result of eastward subduction of Neo-Tethyan oceanic lithosphere beneath the Tengchong Block. In this paper we show that the granitic and mafic rocks in the western Tengchong Block exhibit a systematic compositional variation from west to east, with Na-rich granodiorites in the Nabang area (west) that differ from coeval high-K calc-alkaline granodiorites in the Bangwan area (east), and with tholeiitic mafic rocks in the Nabang area that differ from shoshonitic mafic microgranular enclaves (MMEs) in granodiorites of the Bangwan area. In addition, high-silica biotite granites were intruded into the granodiorites in the Bangwan area. The host granodiorites, MMEs, and biotite granites in the Bangwan area yield zircon U-Pb ages of ca. 50 Ma. The MMEs have relatively low SiO2 contents (53.1-64.95 wt%) and Mg# values (37-45), and high K2O (4.14-5.02 wt%) and ∑ REE contents (331-509 ppm); the MMEs contain acicular apatites that indicate quenching. The host granodiorites also have high K2O (4.48-5.95 wt%) and ∑ REE compositions (320-459 ppm), and together with the MMEs they are enriched in Th but depleted in Nb and Ti. The Sr-Nd-Pb isotopic compositions of the host granodiorites and the MMEs are similar, with εHf(t) values of - 1.0 to - 10.8 and 3.3 to - 11.1, respectively. The geochemical data and igneous textures suggest that the MMEs represent a mafic magma that was derived from the partial melting of mantle pyroxenite, with the melting induced by the influx of fluids/melts from the recycling of sediments in the subducted slab. The mafic melts then caused the partial melting of lower crustal tonalitic rocks to produce granodioritic magma that was subsequently mixed with mafic magma. The biotite granites have relatively high SiO2 contents and low Mg# values that indicate a purely crustal origin and derivation from the partial melting of upper crustal metagraywacke. The
2. The Effect of Water on the Flow of Stress-Activated Electric Currents through Rocks
Science.gov (United States)
Jahoda, A. M.; Cyr, G. G.; Dahlgren, R.; Freund, F. T.
2011-12-01
When igneous or high-grade metamorphic rocks are subjected to deviatoric stresses, dormant defects in the matrix of common rock-forming minerals become activated. These defects consist of pairs of oxygen anions in the 1- valence state, e.g. peroxy links such as O3Si-OO-SiO3. When a peroxy bond breaks, O3Si-O:O-SiO3, an electron is transferred from a neighboring O2- causing the donor oxygen, now O-, to turn into a defect electron, also known as a positive hole, that can propagate as a highly mobile positive charge through the rocks1. The current outflow is driven by the battery potential that builds up during this process. The question is how this electric current through rocks is affected by water. When positive holes flow into bulk water, they oxidize H2O to H2O2 and are thereby consumed2. This electrochemical reaction is driven by the potential drop across the rock-water interface. However, no such potential drop occurs across water that fills pores inside the rocks along the path of the electronic charge carriers. We present evidence that the presence of water in the pore space does indeed not "kill" the current flow. This observation leads to the conclusion that stress-activated positive hole currents should be able to flow through water-saturated rocks maybe as well as, possibly even better than through dry rocks. 1 Freund, F. T., et al.: Electric currents streaming out of stressed igneous rocks - A step towards understanding pre-earthquake low frequency EM emissions, Phys. Chem. Earth, 2006, 31, 389-396. 2 Balk, M., et al.: Oxidation of water to hydrogen peroxide at the rock-water interface due to stress-activated electric currents in rocks, Earth Planet. Sci. Lett. 2009, 283, 87-92 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6179191470146179, "perplexity": 15782.11504020432}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813691.14/warc/CC-MAIN-20180221163021-20180221183021-00397.warc.gz"} |
https://qoto.org/@ssokolow/104969427786602118 | PSA:
If you're trying to write a utility using Open Watcom C/C++ that works both on DOS and on the Linux machine you normally cross-compile from, and you're getting mysterious misbehaviours on one platform, check your INCLUDE path.
Having INCLUDE=$WATCOM/lh when cross-building for DOS or having INCLUDE=$WATCOM/h when building natively for Linux can result in successfull builds with confusing runtime misbehaviours.
QOTO: Question Others to Teach Ourselves. A STEM-oriented instance.
An inclusive free speech instance.
All cultures and opinions welcome.
Explicit hate speech and harassment strictly forbidden.
We federate with all servers: we don't block any servers. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2212829291820526, "perplexity": 26448.484061496692}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320299927.25/warc/CC-MAIN-20220129032406-20220129062406-00481.warc.gz"} |
https://en.wikibooks.org/wiki/Multibody_Mechanics/Euler_Parameters | # Multibody Mechanics/Euler Parameters
The Euler parameters are defined by an axis and angle, i.e. the relative orientation of frames is described by a rotation about a common axis. If the axis defined by the vector ${\displaystyle {\vec {u}}}$ decomposed as ${\displaystyle u_{1},u_{2},u_{2}}$ in both frames (the axis is common), and the rotation by an angle ${\displaystyle \phi }$ (right-handed about the vector) to arrive at orientation of the second frame, then the Euler parameters are
${\displaystyle e_{0}=\cos \left({\frac {\phi }{2}}\right)|{\vec {u}}|}$
${\displaystyle e_{i}=\sin \left({\frac {\phi }{2}}\right)u_{i},i=1...3}$
Note that it is common for one to consider Euler parameters in normalized form where the vector ${\displaystyle {\vec {u}}}$ is a unit vector ${\displaystyle {\hat {u}}}$, in which case the Euler parameters will, by definition, satisfy the constraint that their squares sum to one. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 7, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.962554395198822, "perplexity": 260.3628076766765}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257830064.24/warc/CC-MAIN-20160723071030-00047-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://www.cplusplus.com/forum/beginner/111278/ | ### bobble sort algorithm, need help
you are asked to read 10 names (String type) from an input file let's call it in.text, save it to an array
(called name [10]), sort them (alphabetically). Print the result to an output file calls it out.txt you need
to use bobble sort algorithm.
Here is my problem, my output shows only 9 names on the list, and sometimes one of the names shows more than once.
Thanks for help!
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263 #include #include #include #include #include using namespace std; int main() { vector names; ifstream inFileNames; ofstream outFileNames; //Open names file inFileNames.open("d:\\in.txt"); //read names string readName; for(; getline(inFileNames, readName);) { names.push_back(readName); } //close name file inFileNames.close(); //create names file outFileNames.open("d:\\out.txt"); //output to the namegrades file for(int k=1; k<=9; k++) { for(int n=0; n<=8; n++) { if (names[n] > names[n+1]) names[n].swap(names[n+1]); } outFileNames< names[n+1]) names[n].swap(names[n+1]); } cout<
First fundamental issue:
How many elements does the "names" contain at line 26? You don't check.
Nevertheless, you do assume some number in the following loops.
You do appear to sort the list twice for no reason. Sort first, then output to the two destinations (outfile and cout).
To your question: You do print elements [1-9]. That is 9 values.
I have long forgotten the algorithm for bubble, so I just have an eerie feeling about your implementation.
Here is my take on your problem.
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061 #include #include #include using namespace std; #define NUMNAMES 20 void bubbleSort(string list[], int length); int main(int argc, const char * argv[]) { string names[NUMNAMES]; ifstream inFile; inFile.open("inData.txt", ifstream::in); if (!inFile) { cerr << "Error: in file could not be opened" << endl; return -1; } int count = 0; while (getline(inFile, names[count++], '\n')) { } inFile.close(); bubbleSort(names, NUMNAMES); return 0; } // BubbleSort algorithm source: //C++ PROGRAMMING: FROM PROBLEM ANALYSIS TO PROGRAM DESIGN // By D.S. MALIK 5th Edition void bubbleSort(string list[], int length){ string temp; int iteration; int index; for (iteration = 0; iteration < length; iteration++) { for (index = 0; index < length - iteration; index++) { if (list[index] > list[index + 1]) { temp = list[index]; list[index] = list[index + 1]; list[index + 1] = temp; } } } // printing list. for (int i = 0; i < length; i ++) { cout << list[i] << endl; } }
Last edited on
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http://ams.org/bookstore?fn=20&arg1=hmathseries&ikey=HMATH-14.S | New Titles | FAQ | Keep Informed | Review Cart | Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education
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History of Mathematics
1998; 574 pp; softcover
Volume: 14
Reprint/Revision History:
reprinted with corrections 1999
ISBN-10: 0-8218-1923-2
ISBN-13: 978-0-8218-1923-4
List Price: US$60 Member Price: US$48
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This book presents a fascinating story of the long life and great accomplishments of Jacques Hadamard (1865-1963), who was once called "the living legend of mathematics". As one of the last universal mathematicians, Hadamard's contributions to mathematics are landmarks in various fields. His life is linked with world history of the 20th century in a dramatic way. This work provides an inspiring view of the development of various branches of mathematics during the 19th and 20th centuries.
Part I of the book portrays Hadamard's family, childhood and student years, scientific triumphs, and his personal life and trials during the first two world wars. The story is told of his involvement in the Dreyfus affair and his subsequent fight for justice and human rights. Also recounted are Hadamard's worldwide travels, his famous seminar, his passion for botany, his home orchestra, where he played the violin with Einstein, and his interest in the psychology of mathematical creativity.
Hadamard's life is described in a readable and inviting way. The authors humorously weave throughout the text his jokes and the myths about him. They also movingly recount the tragic side of his life. Stories about his relatives and friends, and old letters and documents create an authentic and colorful picture. The book contains over 300 photographs and illustrations.
Part II of the book includes a lucid overview of Hadamard's enormous work, spanning over six decades. The authors do an excellent job of connecting his results to current concerns. While the book is accessible to beginners, it also provides rich information of interest to experts.
Vladimir Maz'ya and Tatyana Shaposhnikova were the 2003 laureates of the Insitut de France's Prix Alfred Verdaguer. One or more prizes are awarded each year, based on suggestions from the Académie française, the Académie de sciences, and the Académie de beaux-arts, for the most remarkable work in the arts, literature, and the sciences. In 2003, the award for excellence was granted in recognition of Maz'ya and Shaposhnikova's book, Jacques Hadamard, A Universal Mathematician, which is both an historical book about a great citizen and a scientific book about a great mathematician.
Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
General mathematical audience; beginners and experts interested in mathematical history.
Reviews
"The book is filled with brief and fascinating biographies of many of these colleagues, with amusing anecdotes and incisive quotations, and with an illuminating description of the academic milieu in which Hadamard was trained. In the second part of the book, Maz'ya and Shaposhnikova discuss the major fields of Hadamard's mathematics. These chapters, written with clarity and authority, manage simultaneously to be accessible to the novice (with a good undergraduate training in mathematics or science) and to be enlightening to the professional."
-- SIAM Review
"This is a fascinating book on the life and work of J. Hadamard (1865-1963). In fact, it is also a book on mathematics and mathematicians from the last quarter of the 19th century until today--extremely rich material collected, ordered and presented in an interesting, attractive and readable form. The authors have done an excellent job and the result deserves much attention from professional mathematicians and historians of science, as well as from students with an interest in mathematics. This book is warmly recommended to everybody who likes mathematics."
"Maz'ya and Shaposhnikova have created an authoritative source for biographical information on Jacques Hadamard. The authors describe Hadamard's life with numerous interesting details contained in the references of those close to him and give many illustrations of the wide-ranging mathematical impact of this "living legend". Furthermore, the authors enhance the utility of their text as a research tool by organizing and listing hundreds of references to other pertinent materials about the life and works of Hadamard."
-- MAA Online
"[This volume] will be of great interest to mathematicians and those with an interest in the science and mathematics of the period of Hadamard's life. The authors have neatly divided the book into 300 pages on the life of Hadamard, profusely illustrated with photographs and facsimiles of important documents, followed by 200 pages of detailed description of Hadamard's mathematics. Mathematicians and historians of mathematics will particularly appreciate this second part, with its lucid exposition ... The papers are arranged by topic in eight chapters, like the biographical part, profusely illustrated with photographs and facsimiles. The reader gets a really clear idea of the significance of each paper and the meaning of the major results it contains ... The reviewer recommends the book highly for both enjoyment and information. The authors have a masterful grasp of both the mathematics and the biography, and they tell the story in a very interesting way."
-- Mathematical Reviews
"An account of one of the great mathematicians of all time. Thoroughly researched biography plus summary of contributions to analytic function theory, number theory, geometry, calculus of variations, mathematical physics, PDEs, and other subjects."
-- American Mathematical Monthly
"Some mathematicians are well remembered without being well acknowledged: the name circulates, but the contributions which caused the fame are largely forgotten or at least not distinguished from others': An outstanding case for this century is Jacques Hadamard ... All the more reason to welcome this fine and exhaustive book, which treats in detail both his exceptionally long life and comparably important work ... The quality of the book is greatly strengthened by very full bibliographies, in three parts: i) Hadamard's own publications, ii) writings on him, and iii) everything else ... The authors cover a remarkable amount of Hadamard's output and also his concerns outside mathematics: family life (he lost two sons in the First World War and the other one in the Second), a deep interest in botany, concern with the victimization of his distant relative Alfred Dreyfus, and pacifism."
-- Bulletin of the AMS
"Hadamard's life is described in a readable and inviting way. The authors humorously weave throughout the text of his jokes and myths about him. They also movingly recount the tragic side of his life. Stories about his relatives and friends, and old letters and documents create an authentic and colorful picture. The book contains over 300 photographs and illustrations. Part II of the book includes a lucid overview of Hadamard's enormous work, spanning over six decades. The authors do an excellent job of connecting his results to current concerns. While the book is accessible to beginners, it also provides rich information of interest to experts."
-- Resonance -- journal of science education
• Prologue
• The beginning
• The turn of the century
• Mature years
• After the Great War
• Le Maître
• In the thirties
• World War II
• After eighty
• Analytic function theory
• Number theory
• Analytical mechanics and geometry
• Calculus of variations and functionals
• Miscellaneous topics
• Elasticity and hydrodynamics
• Partial differential equations | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17039832472801208, "perplexity": 2845.0837655242062}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163051992/warc/CC-MAIN-20131204131731-00096-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/can-ke-be-reformulated-using-v-instead-of-v-2.931568/ | # A Can KE be reformulated using |v| instead of v^2?
Tags:
1. Nov 13, 2017
### BallisticDisks
While doing some calculations on v_rms using the Maxwell-Boltzmann distribution, I noticed that v_rms and v_avg are pretty similar (https://casper.berkeley.edu/astrobaki/index.php/File:MaxwellSpeedDist.png).
In fact, really it's just the choice of using the 1-norm (|v|_avg) vs. 2-norm sqrt(v^2 avg). When deriving v_rms or <KE> from the Maxwell-Boltzmann distribution , we get <KE> = 0.5m<v^2> = 3kT/2; however, using v_avg from the Maxwell-Boltzmann distribution we get v_avg = sqrt(8kT/(pi*m)) and then 0.5m<v>^2 = 4kT/pi.
In computer science/statistics, people often choose the distance metric <|x|> vs. sqrt<(x^2)> based on their needs, and generally <|x|> is thought to be better and more robust to outliers (yet has far worse properties, e.g., no convergence). I'm familiar with the work-energy theorem and the derivation of KE = 0.5mv^2 from Newton's 2nd law, but am trying to figure out if there are alternative formulations using |v|. I'm also familiar with the equipartition theorem with energies of form Ax^2 being assigned 0.5kT energy and am not sure how this would be reformulated using |v|.
So two questions:
1. Can KE/classical laws be reformulated using |v| instead of |v^2|, or has anything been published using the 1-norm (absolute value) or any other norm besides the 2-norm (square)? I realize the units of energy won't make sense with just changing how KE is computed. But, for example, speed could be defined as (sum |v|) instead of (sum v^2), though I'm not sure if people do this.
2. Are there cases where v_avg is useful to use instead of v_rms?
Thanks in advance for the help/dicussion! This has been gnawing at me since in CS/stats we usually have the choice of using |v| or v^2 to compare distributions, but I'm not sure if we're "forced" to use v^2 in physics because of fundamental laws (and if so which ones?).
Image is from: https://casper.berkeley.edu/astrobaki/index.php/Maxwellian_velocity_distribution
Last edited: Nov 13, 2017
2. Nov 14, 2017
### Staff: Mentor
Are you familiar with momentum?
3. Nov 14, 2017
### BallisticDisks
Yep! I know that momentum = mv. I've only seen momentum used as a property of individual molecules as opposed to ensembles in stat mech (and also never seen a scalar formulation of momentum analogous to speed for velocity) . Is the average momentum of a system ever considered in a way similar to KE? Maybe (q1) is better posed as -- is there a macroscopic energy-like description of a system using |v| instead of v^2? For example, this could be useful in non-equillibrium settings where few particles have very high velocity and are outliers, and where v^2 could be misleading.
(q2) still remains -- is there a case where v_avg is useful to describe systems instead of v_rms? Or, is it really only used to describe the momentum of particles.
Last edited: Nov 14, 2017
4. Nov 14, 2017
### Staff: Mentor
The units don’t work out as written. However, since v is a vector over the reals then |v^2|=|v|^2
5. Nov 14, 2017
### BallisticDisks
Poor notation on my part. I meant reformulated with <|v|> instead of <v^2>. But also curious about if <|v|>^2 is ever useful to use.
6. Nov 15, 2017
### Khashishi
Both total energy and total momentum are conserved. But total speed is not conserved, so it is less physically relevant. Of course, there are some uses, but not nearly as many.
Energy, momentum, and speed will all change depending on your frame of reference. But energy and momentum form a 4-vector, so laws involving them are covariant. Speed isn't a component of a tensor, so any laws involving speed will have to change depending on your frame of reference.
Also, the absolute value function is hard to work with since it's nonholomorphic. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9800738096237183, "perplexity": 1441.3405492745833}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826842.56/warc/CC-MAIN-20181215083318-20181215105318-00506.warc.gz"} |
https://www.zbmath.org/?q=ai%3Astan.ilie+se%3A00002252+in%3A00089665 | ×
# zbMATH — the first resource for mathematics
On interpolation of compact operators for Banach triples. (English) Zbl 1004.46046
Summary: We investigate the behaviour of compact operators under $$\mathcal J$$ and $$\mathcal K$$ interpolation methods with a parameter function of Banach triples. We begin with the case when one of the triples reduces to a single Banach space; then, using the connection between interpolation functors of different orders, we treat the general case for particular Banach triples.
##### MSC:
46M35 Abstract interpolation of topological vector spaces 47B07 Linear operators defined by compactness properties | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7631301879882812, "perplexity": 843.6258689329577}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178368608.66/warc/CC-MAIN-20210304051942-20210304081942-00407.warc.gz"} |
http://nrich.maths.org/9858/solution?nomenu=1 | ## 'A Brief Introduction to Complex Numbers' printed from http://nrich.maths.org/
The students from St Stephens School, Australia, found the following examples:
• Pairs of complex numbers whose sum is a real number:
2+i, 2-i
4+5i, 3-5i
• Pairs of complex numbers whose sum is an imaginary number:
2i+1, -i-1
i+2, i-2
• Pairs of complex numbers whose product is a real number:
1+2i, 1-2i
2+3i, 4-6i
• Pairs of complex numbers whose product is an imaginary number:
3+3i, 3+3i
1, i
Sina Sanaizadeh from Hinde House Secondary School, Sheffield, sent in the following explanations:
• In general, what would you need to add to a+bi to get a real number?
We want to remove the imaginary part of a+bi to get a real number, so we want to add a complex number of the form c-bi.
• Or an imaginary number?
We want to remove the real part of a+bi to get an imaginary number, so we want to add a complex number of the form -a+ci.
• In general, what would you need to multiply by a+bi to get a real number?
Consider the product of the complex numbers a+bi and c+di:
(a+bi)(c+di) = (ac-bd) + (ad+bc)i
For this product to be real, the imaginary part must be 0, so ad+bc = 0
As a and b are fixed, must have $\frac{c}{d}$ = $\frac{-a}{b}$.
So, in general, for the product of two complex numbers to be real, the ratio of the real to imaginary parts of each complex number must be equal up to a minus sign.
• Or an imaginary number?
Again, consider (a+bi)(c+di) = (ac-bd) + (ad+bc)i
For this product to be imaginary, the real part must be 0, so ac-bd = 0
As a and b are fixed, must have $\frac{d}{c}$ = $\frac{a}{b}$.
So, in general, for the product of two complex numbers to be imaginary, the ratios of the real to imaginary parts of each complex number must be the reciprocal of the other. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7650567889213562, "perplexity": 603.251842759459}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246651727.46/warc/CC-MAIN-20150417045731-00200-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://trac-hacks.org/ticket/12062 | Opened 4 years ago
Closed 3 years ago
Doubleclick on checkbox labels doesn't work on filters added through the OR menu
Reported by: Owned by: Ryan J Ollos Matoba Akihiro normal QueryUiAssistPlugin normal
Description
Thank you for the nice plugin. I found it very useful and I'm working on adding the features to the Trac core in trac:#11417. Please feel free to comment on that ticket. Most likely the QueryUiAssistPlugin won't be needed by Trac 1.2. One fewer plugin is always nice :)
The issue I encountered is that the double-click doesn't function on the label of a checkbox when a filter is added using the OR selector.
I set off to fix this, and ended up making a few other changes as well:
• Fixed implicitly declared variables
• Optimized some jQuery selectors by limiting the scope of the search
• Some PEP-0008 changes in the Python code.
• Use prop rather than attr since Trac 1.0 uses jQuery 1.8.
The patch is attached. I hope it doesn't seem like I'm picking at your code. I learned far more from studying it than I'm contributing with the minor list of issues above :)
Attachments (3)
t12062.diff (3.7 KB) - added by Ryan J Ollos 4 years ago.
CustomQuery.png (31.9 KB) - added by Ryan J Ollos 4 years ago.
t12062-delegated-events.diff (2.2 KB) - added by Jun Omae 4 years ago.
comment:1 Changed 4 years ago by Matoba Akihiro
Status: new → accepted
comment:2 Changed 4 years ago by Jun Omae
I think it would be simple and easy to use .on() method to handle delegated events rather than setTimeout(). See t12062-delegated-events.diff.
comment:3 Changed 3 years ago by Matoba Akihiro
Resolution: → fixed accepted → closed
In 14387:
closes #12062
comment:4 Changed 3 years ago by Ryan J Ollos
There's a minor regression in [14387]. Double-click on a checkbox still selects the checkbox and clears all the neighbours, but double-click on the label of a checkbox no longer clear all the neighbours.
• queryuiassistplugin/1.0/uiassist/htdocs/js/enabler.js
diff --git a/queryuiassistplugin/1.0/uiassist/htdocs/js/enabler.js b/queryuiassi
index f0dc07e..8ecd52d 100644
a function binder() { var $filters =$("#filters"); $filters.on('dblclick', 'label', flip);$filters.on('dblclick', ':checkbox', selectone); $filters.on('dblclick', ':checkbox, :checkbox + label', selectone); }$(document).ready(function() { binder() })
comment:5 Changed 3 years ago by Matoba Akihiro
Resolution: fixed closed → reopened
thanks! I'll update soon...
comment:6 Changed 3 years ago by Matoba Akihiro
Resolution: → fixed reopened → closed
comment:7 Changed 3 years ago by Ryan J Ollos
One more change. Although it appears to be harmless, the flip function is executed when double-clicking on a checkbox or its label. The following fixes the issue:
• queryuiassistplugin/1.0/uiassist/htdocs/js/enabler.js
diff --git a/queryuiassistplugin/1.0/uiassist/htdocs/js/enabler.js b/queryuiassi
index 8ecd52d..de5ce4c 100644
a // bind "flip" above to labels in page. function binder() { var $filters =$("#filters"); $filters.on('dblclick', 'label', flip);$filters.on('dblclick', ':checkbox, :checkbox + label', selectone); $filters.on('dblclick', 'th label', flip);$filters.on('dblclick', 'td :checkbox, td :checkbox + label', selectone); } \$(document).ready(function() { binder() })
The addition of the th selector is what fixes the issue. The td selectors were just added for code clarity.
comment:8 Changed 3 years ago by Matoba Akihiro
Resolution: fixed closed → reopened
comment:9 Changed 3 years ago by Ryan J Ollos
New ticket for integrating this plugin to the Trac core is trac:#11970.
comment:10 Changed 3 years ago by Ryan J Ollos
I added a notice in QueryUiAssistPlugin@9. Please let us know if you have any suggestions about the changes in trac:#11970. My aim is to make this plugin no longer necessary by Trac 1.2, by having equivalent functionality in Trac.
comment:11 Changed 3 years ago by Matoba Akihiro
Glad to hear that the function is now in Trac core, thank you!
comment:12 Changed 3 years ago by Ryan J Ollos
Is it okay to commit the change in comment:7?
yes!
comment:14 Changed 3 years ago by Ryan J Ollos
Resolution: → fixed reopened → closed
Thanks! Fixed in [14862].
comment:15 Changed 3 years ago by Ryan J Ollos
Changes in trac:#11970 have finally been committed (changeset:14225). Thanks Matobaa!
Last edited 3 years ago by Ryan J Ollos (previous) (diff)
Modify Ticket
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https://brilliant.org/problems/parabola-6/ | # Parabola
Geometry Level 4
Akul draws a Tangent from any point $$(x_{1},y_{1})$$ on the parabola $$y^{2}$$=4ax. He then draws tangents are from any point on this tangent to a circle centred at origin, having radius $$a$$. Mayank obsserves that All the chords of contact pass through a fixed point $$(x_{2},y_{2})$$.
Find k given that $$k(x_{1}/x_{2})+(y_{1}/y_{2})^2$$=0
We've got more for you at the set Mayank and Akul
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https://notes.reasoning.page/html/derivatives-sums | # A calculus of the absurd
#### 10.2 Derivatives of sums
Let’s suppose we have a function $$f(x) = q(x) + r(x)$$, then the derivative of $$f(x)$$ is 6868 Note that this relies on the property that the limit of two things added together is the same as the sum of the limits of the two things
$\lim _{x \to a} (z(x) + q(x)) = \lim _{x \to a} z(x) + \lim _{x \to a} q(x)$
Where $$z(x)$$ and $$q(x)$$ are any functions of $$x$$ whose limit is defined as $$x \to a$$.
\begin{align} \frac {df}{dx} &= \lim _{h \to 0} \frac {f(x+h) - f(x)}{h} \\ &= \lim _{h \to 0} \frac {q(x+h) + r(x+h) - q(x) - r(x)}{h} \\ &= \lim _{h \to 0} \frac {q(x+h) - q(x) + r(x+h) - r(x)}{h} \\ &= \lim _{h \to 0} \frac {q(x+h)-q(x)}{h} + \lim _{h \to 0} \frac {r(x+h)-r(x)}{h} \\ &= \frac {dq}{dx} + \frac {dr}{dx} \end{align}
That is to say that
$$\label {linearity of differentiation} \frac {d}{dx}(a(x) + b(x)) = \frac {d}{dx} (a) + \frac {d}{dx} (b)$$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 1.0000100135803223, "perplexity": 658.9815897562772}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711394.73/warc/CC-MAIN-20221209080025-20221209110025-00666.warc.gz"} |
https://www.hackmath.net/en/math-problem/2431 | # Grass garden
Mr. Grass would itself be mowed garden for 5 hours. His son Michael could do it for 7 hours. They agreed that they wake up at 5 am and begins to mow together. Ms. Grass needs drive into town at 8.30. Michael says that at that time they're done with work. Is he right?
Result
#### Solution:
$x(1/5+1/7) = 1 \ \\ x = 35⁄12 \ h ≐ 2.916667 \ h \ \\ x < 8.50 - 5.00 \ \\ 2.916667 < 3.50$
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Gabrielle is 9 years younger than Mikhail. The sum of their ages is 87. What is Mikhail's age? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4135451912879944, "perplexity": 2233.7415974701116}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370506477.26/warc/CC-MAIN-20200401223807-20200402013807-00271.warc.gz"} |
https://comnuan.com/cmnn01006/ | ## Matrix Transpose Calculator
Given an $m\times n$ real or complex matrix $A$, this application calculate its transpose $A^T$, if $A$ is a real matrix, or conjugate transpose $A^\star$ , if $A$ is a complex matrix. $A^T$ is an $n\times m$ real matrix and has the property: $[A^T]_{ij} = [A]_{ji}$ i.e. the $i^{\mbox{th}}$ row, $j^{\mbox{th}}$ column element of $A^T$ is the $j^{\mbox{th}}$ row, $i^{\mbox{th}}$ column element of $A$. In the case of conjugate transpose matrix $A^\star$, it has the property $[A^\star]_{ij} = \overline{[A]_{ji}}$
See Input Data for the description of how to enter matrix or just click Example for a simple example. Note that this calculator can be used as a scientific calculator. Just enter math expression (without white space) and click Calculate. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9174673557281494, "perplexity": 199.5420814694546}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027321160.93/warc/CC-MAIN-20190824152236-20190824174236-00395.warc.gz"} |
https://axiomsofchoice.org/product_type | ## Product type
### Type
context $X, Y$ … type rule ${\large\frac{a\ :\ X\hspace{1cm}b\ :\ Y}{\langle a,b\rangle\ :\ X\times Y}}(\times\mathcal I)$ rule ${\large\frac{p :\ X\times Y}{\pi_{\mathcal l}(p)\ :\ X\hspace{1cm}\pi_{\mathcal r}(p)\ :\ Y}}(\times\mathcal E)$ rule ${\large\frac{a\ :\ X\hspace{1cm}b\ :\ Y}{\pi_{\mathcal l}(\langle a,b\rangle)\ \leftrightsquigarrow\ a \hspace{1cm}\pi_{\mathcal r}(\langle a,b\rangle)\ \leftrightsquigarrow\ b}}(\times\beta)$ rule ${\large\frac{p\ :\ X\times Y}{\langle\pi_{\mathcal l}(p),\pi_{\mathcal r}(p)\rangle\ \leftrightsquigarrow\ p}}(\times\eta)$ rule ${\large\frac{a\ \leftrightsquigarrow\ a'\ :\ X\hspace{1cm}b\ \leftrightsquigarrow\ b'\ :\ Y}{\langle a,b\rangle\ \leftrightsquigarrow\ \langle a',b'\rangle}}$ rule ${\large\frac{p\ \leftrightsquigarrow\ p'\ :\ X\times Y}{\pi_{\mathcal l}(p)\ \leftrightsquigarrow\ \pi_{\mathcal l}(p')\hspace{1cm}\pi_{\mathcal l}(p)\ \leftrightsquigarrow\ \pi_{\mathcal r}(p')}}$
### Discussion
These are constructors (introduction and elimination), computational rules for $\pi$ (alpha and beta) and defining property of the pair.
##### Computational vs. logical point of view
Depending on what we want to do with the type system, we might just replace expressions of computational equivalence $\rightsquigarrow$ by equality '$=$'. This symbol denotes a term rewriting, i.e. a computations alla
$\left(\lambda x.\,3+x\right)\,4\ \rightsquigarrow_\beta\ 3+4,$
or
$\lambda x.\,\sin\,x\ \rightsquigarrow_\eta\ \sin$
##### Logic
Note how the rules reflect the logical “and”. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.967391312122345, "perplexity": 3924.8840614467917}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703587074.70/warc/CC-MAIN-20210125154534-20210125184534-00632.warc.gz"} |
http://mathhelpforum.com/algebra/1702-what-print.html | # What the?
• Jan 22nd 2006, 11:22 AM
MOODYtarqi
What the?
Can anyone help me with these..?!
1) 3i/2+5i
and...
2) square root of -2(square root of -9 - square root of 7)
i would appreicate it if you can reply asap.
• Jan 22nd 2006, 11:49 AM
CaptainBlack
Quote:
Originally Posted by MOODYtarqi
Can anyone help me with these..?!
1) 3i/2+5i
This is ambiguous (you need to use brackets to make this unambiguous),
but I will presume you are asking for:
$\frac{3i}{2+5i}$
to be reduced to standard form $a+b.i$.
Multiply the top and bottom by the complex conjugate of the bottom:
$\frac{3i}{2+5i} = \frac{3i (2-5i)}{(2+5i)(2-5i)}$,
so:
$\frac{3i}{2+5i} = \frac{15+6i}{29}=\frac{15}{29}+\frac{6i}{29}$.
RonL
• Jan 22nd 2006, 11:51 AM
MOODYtarqi
thanks man you're smart . . . or I'm an idiot.
appreciate it.
• Jan 22nd 2006, 12:02 PM
CaptainBlack
Quote:
Originally Posted by MOODYtarqi
2) square root of -2(square root of -9 - square root of 7)
This again is ambiguous, it could mean either:
$\sqrt{-2(\sqrt{-9}-\sqrt{7}})$,
or:
$\sqrt{-2}(\sqrt{-9}-\sqrt{7})$.
I will assume that you mean the latter of these, then:
$\sqrt{-2}(\sqrt{-9}-\sqrt{7})=\sqrt{2}i(3i-\sqrt{7})$
so:
$\sqrt{-2}(\sqrt{-9}-\sqrt{7})=-3\sqrt{2}-\sqrt{14}i$
RonL
• Jan 22nd 2006, 12:04 PM
MOODYtarqi
thanks again. but what if the tell me "write it in standard form?"
• Jan 22nd 2006, 12:10 PM
CaptainBlack
Quote:
Originally Posted by MOODYtarqi
thanks again. but what if the tell me "write it in standard form?"
They have both been reduced to standard form (or near enough to get marked as correct).
RonL
• Jan 22nd 2006, 12:12 PM
MOODYtarqi
thanks man... have a Gday. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9158691167831421, "perplexity": 4902.455475558204}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886106865.74/warc/CC-MAIN-20170820170023-20170820190023-00236.warc.gz"} |
https://math.eretrandre.org/tetrationforum/showthread.php?tid=895&pid=7233 | • 0 Vote(s) - 0 Average
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Easy tutorial on hyperoperations and noptiles MikeSmith Junior Fellow Posts: 40 Threads: 16 Joined: Nov 2011 06/26/2014, 09:09 AM This is an introduction to hyperoperations and noptiles The tutorial gives a sketch outline for the noptile concept Easy to understand for school and college students and other learners of math Introduction.pdf (Size: 417.4 KB / Downloads: 577) I think you ought to know I'm feeling very depressed. Marvin the Paranoid Android, in The Hitchhiker's Guide to the Galaxy (1979), Ch. 11. In addition to my other numerous acquaintances, I have one more intimate confidant.... My depression is the most faithful mistress I have known—no wonder, then, that I return the love. Søren Kierkegaard (1813–1855), Danish existentialist philosopher. “Diapsalmata,” Vol. 1, Either/Or (1843, trans. 1987). ~,~'~,~",~,~'~,~",~,~'~,~",~,~'~,~",~,~'~,~",~,~'~ MphLee Fellow Posts: 184 Threads: 19 Joined: May 2013 06/26/2014, 01:31 PM I'm starting to understand something.. thanks for the introduction... but I'm far from the other parts of your work. Seems interesting but large number is not my favourite field... MathStackExchange account:MphLee Fundamental Law $(\sigma+1)0=\sigma (\sigma+1)$ MikeSmith Junior Fellow Posts: 40 Threads: 16 Joined: Nov 2011 06/26/2014, 11:58 PM large numbers are covered extensively in the xkcd my number is bigger debate and more coherently described and compared in the Googology Wiki. my ideas are a mixture of things within the positive integer realm, transitional sequences and their patterns, emergent phenomena such as coordinate systems for these patterns and binate features, Catalan numbers, recursion theory, generalised recursion and subrecursive hierarchies, paradoxes and inconsistencies, pattern commonalities between hyperoperations and their compositions and transfinite ordinals and also how COH expressions are in some sense more general than transfinite ordinals, such as the epsilon numbers, these days I'm trying to learn more about normal topics within elementary and recreational number theory. my weaker areas are complex analysis, Lambert's W, special kinds of matrices, Stirling numbers, Bernoulli numbers, Riemann hypothesis, every now and then I pick up a few more ideas « Next Oldest | Next Newest »
Possibly Related Threads... Thread Author Replies Views Last Post @Andydude References about the formalization of the Hyperoperations MphLee 3 7,035 07/25/2014, 10:41 AM Last Post: MphLee how to create pure noptiles MikeSmith 0 2,570 06/25/2014, 11:30 AM Last Post: MikeSmith Negative, Fractional, and Complex Hyperoperations KingDevyn 2 10,149 05/30/2014, 08:19 AM Last Post: MphLee A relaxed $$\zeta$$-extensions of the Recursive Hyperoperations MphLee 0 3,284 06/14/2013, 09:57 PM Last Post: MphLee Wonderful new form of infinite series; easy solve tetration JmsNxn 1 6,694 09/06/2012, 02:01 AM Last Post: JmsNxn
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https://datascience.stackexchange.com/questions/27003/catboost-categorical-features-handling-options-ctr-settings | # Catboost Categorical Features Handling Options (CTR settings)?
I am working with a dataset with large number of categorical features (>80%) predicting a continuous target variable (i.e. Regression). I have been reading quite a bit about ways to handle categorical features. And learned that one-hot encoding I have been using in past is really bad idea especially when it comes to lots of categorical features with many levels (read these post, and this).
While I've come across methods like target-based encoding (smoothing) of categorical features often based on mean of target values for each feature perhaps this post/kernel in Kaggle. Still I am struggling to find a more concrete way till I found CatBoost an open-source gradient boosting on decision trees released last year by Yandex group. They seem to offer extra statistical counting options for categorical features likely much more efficient than simple one-hot encoding or smoothing.
The problem is the documentation is not helpful how to set CTR settings. I have tried different ways but it just does not work. The doc says CTR setting as simple_ctr, to be given as (CTR setting section):
['CtrType[:TargetBorderCount=BorderCount][:TargetBorderType=BorderType][:CtrBorderCount=Count][:CtrBorderType=Type][:Prior=num_1/denum_1]..[:Prior=num_N/denum_N]',
'CtrType[:TargetBorderCount=BorderCount][:TargetBorderType=BorderType][:CtrBorderCount=Count][:CtrBorderType=Type][:Prior=num_1/denum_1]..[:Prior=num_N/denum_N]',
...]
Here is a super simple example, the data looks like this:
import pandas as pd
import catboost
data = [{'profit': '342','country': 'holland','account': 'Jones LLC', 'saving': 150, 'debt': -60, 'age': 28},
{'profit': '875','country': 'germany','account': 'Alpha Co', 'saving': 200, 'debt': -10, 'age': 42},
{'profit': '127','country': 'italy','account': 'Blue Inc', 'saving': 50, 'debt': -300, 'age': 38 }]
df = pd.DataFrame(data)
Here is a simple Catboost Regressor:
X_train = df.drop(['profit'],axis=1)
Y_train = df['profit']
categorical_features_indices = [0,2]
train_pool = catboost.Pool(X_train, Y_train, cat_features=categorical_features_indices)
model = catboost.CatBoostRegressor(
depth=3,
iterations=5,
eval_metric='RMSE',
simple_ctr=None)
model.fit(train_pool);
The simple_ctr, one of CTR settings, is the problem!! It is pity because it looks like it the package offers various methods, so far no way to access them.
UPDATE Aug. 9th, 2018: A few days ago I raised this problem to Catboost developer, see here, and they opened a ticket for it to provide a tutorial.
• Here is the description about catboost on categorical vaiable: tech.yandex.com/catboost/doc/dg/concepts/… – DiveIntoML May 28 '18 at 0:07
• Yes, I know the link; it gives a detailed theoretical description. Yet not enough description on how to use it is given; I mean practical usage instructions. I have have tried it a few months ago and it was not straightforward. – TwinPenguins May 28 '18 at 5:39
• I am currently only using the one_hot_max_size param and my understanding is that everything that is not one hot encoded, will be encoded using target mean expanding encoding. I am looking forward to the additional official documentation to understand the ctr settings better and how I can play with them. – Garima Jain Mar 13 '19 at 16:13
Did you try using the format provided like below:
['CtrType[:TargetBorderCount=BorderCount][:TargetBorderType=BorderType][:CtrBorderCount=Count][:CtrBorderType=Type][:Prior=num_1/denum_1]..[:Prior=num_N/denum_N]'
['BinarizedTargetMeanValue[:TargetBorderCount=1][:TargetBorderType=Uniform][:CtrBorderCount=5][:CtrBorderType=Uniform][:Prior=1]']
• Is this an answer? It feels more like a question/comment. – Stephen Rauch Aug 9 '18 at 20:34
• @Interested_Programmer: It does not work, try it yourself in the example I just provided. Have you tested it or you simply found it in the documentation? – TwinPenguins Aug 9 '18 at 21:13
• I apologize @StephenRauch. I was unable to run my notebook but found it usable in other functions to follow the format. In hindsight, I should have added it as a comment. I am also waiting for the creators to put out the new tutorial. – Interested_Programmer Aug 10 '18 at 21:06
• also this works. simple_ctr=['BinarizedTargetMeanValue']) – Interested_Programmer Aug 10 '18 at 21:20
• Thanks. But as you shown it only works as simple_ctr=['BinarizedTargetMeanValue'])! The other options can not be fed like [:TargetBorderCount=BorderCount] etc. If you know how to feed others together with CtrType, let me know. – TwinPenguins Aug 11 '18 at 7:21
I found out that in order to set the ctr parameters and all the components one should pass a list of strings, each string should contain the ctrType and one of its component:
• The first word of the string should be a ctrType for example Borders: (click here for catboost parameters)
• Then one component of the ctrType should follow. For example TargetBorderType=5.
• All together 'Borders:TargetBorderType=5'.
• Repeat the procedure to set an other component and add the new string to the list.
Example with two components set:
simple_ctr = ['Borders:TargetBorderType=Uniform', 'Borders:TargetBorderCount=50'] | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2670528292655945, "perplexity": 2520.5767598009315}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251783000.84/warc/CC-MAIN-20200128184745-20200128214745-00011.warc.gz"} |
https://math.stackexchange.com/questions/1387109/help-with-spivaks-calculus-chapter-1-problem-21 | # Help with Spivak's Calculus: Chapter 1 problem 21
I've been stuck on this problem for over a day, and the answerbook simply says "see chapter 5" for problems 20,21, and 22. But I want to complete the problem without using knowledge given later in the book, so I've been banging my head against the wall trying all sorts of things, but nothing I do seems to lead me anywhere.
The problem is as follows:
Prove that if
$|x - x_0| < min (\frac{\varepsilon}{2(|y_0| + 1)}, 1)$ and $|y - y_0| < min (\frac{\varepsilon}{2(|x_0| + 1)}, 1)$
then
$|xy - x_0 y_0| < \varepsilon$.
Here are some of the things I've been thinking about, I don't know which of these are useful (if any), but they somewhat outline the logic behind my various attempts.
Since at most $|x - x_0| < 1$ and $|y - y_0| < 1$ then it follows that $(|x-x_0|)(y-y_0|) < |x-x_0|$ and $(|x-x_0|)(y-y_0|) < |y-y_0|$
Also, $(|x - x_0|)(|y_0| + 1) < \frac{\varepsilon}{2}$ and $(|y - y_0|)(|x_0| + 1) < \frac{\varepsilon}{2}$ so $(|x - x_0|)(|y_0| + 1) + (|y - y_0|)(|x_0| + 1) < \varepsilon$. and since $|a + b| \leq |a| + |b| < \varepsilon$ I've tried multiplying things out, and then adding them together to see if anything cancels, but I can't make anything meaningful come out of it.
Also since $|a - b| \leq |a| + |b|$ I've also tried subtracting one side from the other, but to no avail.
I was also thinking that since $(|x-x_0|)(y-y_0|) < |x-x_0|$, then I could try something along the lines of $(|x-x_0|)(y-y_0|)(|x_0| + 1) + (|x-x_0|)(y-y_0|)(|y_0| + 1)< \varepsilon$ and various combinations as such, but I just can't seem to get anything meaningful to come out of any of these attempts.
I have a sneaking suspicion that the road to the solution is simpler than I'm making it out to be, but I just can't see it.
• Hint: $(xy-x_{0}y_{0}) = x(y-y_{0}) + y_{0}(x-x_{0})$. – Geoff Robinson Aug 6 '15 at 20:25
• @GeoffRobinson Thanks for the hint. I'll try to see if I can put it to use. – Shane T Aug 6 '15 at 20:30
• The game is given away in the answer below, although if you follow the hint, there is a natural progression to the necessary inequalities. – Geoff Robinson Aug 6 '15 at 21:42
• @GeoffRobinson my only remaining question is how or why you recognized that (xy−x_0y_0)=x(y−y_0)+y_0(x−x_0)? I don't know if I would have seen that without you telling me. – Shane T Aug 6 '15 at 23:17
• Some things you just have to see- they come with experience- the intuition is that you know that if $x$ is close to $x_{0}$ and $y$ is close to $y_{0}$, then $xy$ is close to $x_{0}y_{0}$. But to make that a reality, you have to see that step. If you want to break it down further, you know that $x(y-y_{0})$ is small, but that isn't $xy - x_{0}y_{0}$. To get that, you have to add $xy_{0}- x_{0}y_{0} = y_{0}(x-x_{0}).$ – Geoff Robinson Aug 6 '15 at 23:47
By reverse triangle inequality $|x| - |x_0| \leq |x-x_0| < 1$ giving $|x| < 1 + |x_0|$. Now \begin{align*} |xy - x_0y_0| & = |x(y-y_0) + y_0(x-x_0)| \leq |x||y-y_0| + |y_0||x-x_0| \\ & < (1 + |x_0|)\frac{\varepsilon}{2(|x_0| + 1)} + |y_0|\frac{\varepsilon}{2(|y_0| + 1)} \\ & < \frac{\varepsilon}{2} + \frac{\varepsilon}{2} = \varepsilon \end{align*} To my mind the difficult part of this argument is writing down the equality proceeding the string of inequalities and this certainly isn't the only way to do that.
I just solved this today - which for me was really amazing because I was just as lost as the earlier post - so please forgive my enthusiasm. The breakthrough for me was the hint $|x - x_0|$ < 1 and a relaxation of mind.
$|y - y_0|$ < ${\frac{\epsilon}{2(|x_0| + 1)}}$ < ${\frac{\epsilon}{2(|x_0| + |x - x_0|)}}$.
This was the application of the hint.
$|y - y_0|$ < ${\frac{\epsilon}{2(|x_0| + |x - x_0|)}}$ < ${\frac{\epsilon}{2(|x_0 + x - x_0|)}}$
$|y - y_0|$ < ${\frac{\epsilon}{2|x|}}$
(1) $|x||y - y_0|$ < ${\frac{\epsilon}{2}}$
Working with the given inequality:
$|x - x_0|$ < ${\frac{\epsilon}{2(|y_0| + 1)}}$
Simplifying:
(2) $|x - x_0|(|y_0| + 1) < {\frac{\epsilon}{2}}$
Add (1) and (2) following: if a < b and c < d, then a+c < b+d.
$|x||y - y_0| + |x - x_0|(|y_0| + 1) < \epsilon$
$|xy - xy_0| + |x-x_0||y_0| + |x - x_0| < \epsilon$
$|xy - xy_0 + xy_0 - x_0y_0| + |x - x_0|$ < $|x||y - y_0| + |x - x_0|(|y_0| + 1) < \epsilon$
$|xy - x_0y_0| + |x - x_0| < \epsilon$
$|xy - x_0y_0| < |xy - x_0y_0| + |x - x_0| < \epsilon$
$|xy - x_0y_0| < \epsilon$
• Nice! I'm glad you were able to figure it out. It took me a while too. – Shane T Aug 17 '15 at 18:35
I think I figured it out thanks to GeoffRobinson's hint, and from RJS (thanks guys!) so I figured I'd write out my own work here.
$|xy-x_0y_0| = |x(y-y_0) + y_0(x-x_0)| \leq |x(y-y_0)| + |y_0(x-x_0)|$
So in essence we're going to show that $|x(y-y_0)| + |y_0(x-x_0)| \leq \varepsilon$ which implies that $|xy-x_0y_0| \leq \varepsilon$.
So let's start. From
$|x - x_0| < \frac{\varepsilon}{2(|y_0| + 1)}$
then
$(|x - x_0|)(|y_0| + 1) = |y_0(x-x_0)| + |x - x_0| < \frac{\varepsilon}{2}$
Which in turn implies that $|y_0(x-x_0)|< \frac{\varepsilon}{2}$
We're halfway done with our inequality.
Next by looking at $|x-x_0| < 1$, we can observe that $|x| - |x_0| \leq |x-x_0| \Rightarrow |x| < |x_0| + 1$
Then consider the given inequality:
$|y-y_0| < \frac{\varepsilon}{2(|x_0| + 1)}$
We can see that $|x||y-y_0| < (|x_0| + 1) \frac{\varepsilon}{2(|x_0| + 1)} = \frac{\varepsilon}{2}$ and so $|x(y-y_0)| < \frac{\varepsilon}{2}$
So finally we can show that:
$|y_0(x-x_0)| + |x(y-y_0)| < \frac{\varepsilon}{2} + \frac{\varepsilon}{2} = \varepsilon$
and because $|xy-x_0y_0| \leq |x(y-y_0)| + |y_0(x-x_0)|$
We can say $|xy-x_0y_0| < \varepsilon$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8863750100135803, "perplexity": 254.0567450513526}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487655418.58/warc/CC-MAIN-20210620024206-20210620054206-00548.warc.gz"} |
http://clay6.com/qa/30095/identify-the-end-product-in-the-following-sequence | Browse Questions
# Identify the end product in the following sequence
Hence (a) is the correct answer. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8686962723731995, "perplexity": 2026.77444574433}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423774.37/warc/CC-MAIN-20170721122327-20170721142327-00507.warc.gz"} |
https://abitofcs.blogspot.com/2015/05/codeforces-529c-rooks-and-rectangles.html | ## Wednesday, May 6, 2015
### Codeforces 529C - Rooks and Rectangles
Problem Statement:
529C - Rooks and Rectangles
Solution:
Just learnt a new technique for solving a segment tree problem, which involves an idea in computational geometry referred to as vertical/horizontal sweeping. To solve the problem effectively we need the following observation: a rectangle is well defended if (1) either every row of that rectangle contains a rook, or (2) every column in that rectangle contains a rook. We can check these two cases (1) and (2) separately. Let's focus on one of them.
We will follow the notation in the problem, where x denotes the column wise index, while y is the row indices. First we sort all the rectangles in x direction, by using their x2 values, and also similarly sort the rooks by their x values. Then left to right, we consider the rectangle one by one:
1. Let rightmost[y] be the rightmost rook in row y. Update rightmost[y] for all y using all rooks with x <= x2 of the current rectangle.
2. Then the current rectangle is well defended if rightmost[y] >= x1 for all y1 <= y <= y2. This is equivalent to saying that the minimum rightmost[y] in segment y1 and y2 must be at least x1. This can be checked efficiently using a segment tree.
Repeat the same procedure in the y direction, and as long as a rectangle satisfies one of the checks, output YES.
Implementation: (PS square in the code actually denotes an array of rectangles)
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <vector>
#include <utility>
using namespace std;
int N, M, K, Q;
vector<pair<pair<int,int>,pair<int,int> > > square;
vector<pair<int,int> > point;
int mark[200005];
int a[200005];
int seg[400005];
int rmq(int p, int S, int T, int L, int R) {
if(R<S || T<L)return -1;
if(S<=L && R<=T){
return seg[p];
}
int M = (L+R)/2;
int left = rmq(2*p,S,T,L,M);
int right = rmq(2*p+1,S,T,M+1,R);
if(left==-1)return right;
if(right==-1)return left;
return min(left,right);
}
void upd(int p, int L, int R, int S){
if(R<S || S<L) return;
if(L==R && R == S){
seg[p] = a[S];
return;
}
int M = (L+R)/2;
upd(2*p,L,M,S);
upd(2*p+1,M+1,R,S);
seg[p] = min(seg[2*p+1],seg[2*p]);
}
bool cmp(const pair<int,int>& L, const pair<int,int>& R) {
if(R.second == L.second) {
return L.first < R.first;
}
return L.second < R.second;
}
void solve() {
// sorted by x
sort(point.begin(), point.end());
vector<pair<int,int> > st;
for(int i=0;i<Q;++i){
st.push_back(make_pair(square[i].second.first, i));
}
sort(st.begin(), st.end());
int next = 0;
for(int i=0;i<Q;++i){
int cur = st[i].second;
while(next < K && point[next].first <= st[i].first){
int x = point[next].first;
int y = point[next].second;
a[y] = max(a[y], x);
upd(1, 1, M, y);
++next;
}
int y1 = square[cur].first.second;
int y2 = square[cur].second.second;
int x1 = square[cur].first.first;
int low = rmq(1,y1,y2,1,M);
if(low >= x1) {
mark[cur]++;
}
}
// sort by y
sort(point.begin(), point.end(), cmp);
st.clear();
for(int i=0;i<=N;++i)a[i]=0;
for(int i=0;i<=4*N;++i)seg[i]=0;
for(int i=0;i<Q;++i){
st.push_back(make_pair(square[i].second.second, i));
}
sort(st.begin(), st.end());
next = 0;
for(int i=0;i<Q;++i){
int cur = st[i].second;
while(next < K && point[next].second <= st[i].first){
int x = point[next].first;
int y = point[next].second;
a[x] = max(a[x], y);
upd(1, 1, N, x);
++next;
}
int x1 = square[cur].first.first;
int x2 = square[cur].second.first;
int y1 = square[cur].first.second;
if(rmq(1,x1,x2,1,N) >= y1) {
mark[cur]++;
}
}
for (int i=0;i<Q;++i){
if(mark[i]>0)printf("YES\n");
else printf("NO\n");
}
}
int main(){
scanf("%d%d%d%d",&N,&M,&K,&Q);
int x,y;
for(int i=0;i<K;++i){
scanf("%d%d",&x,&y);
point.push_back(make_pair(x,y));
}
int x1,y1;
for(int i=0;i<Q;++i){
scanf("%d%d%d%d",&x,&y,&x1,&y1);
square.push_back(make_pair(make_pair(x,y),make_pair(x1,y1)));
}
solve();
return 0;
} | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6495767831802368, "perplexity": 11612.733368590503}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084886758.34/warc/CC-MAIN-20180116224019-20180117004019-00308.warc.gz"} |
https://anadat-r.davidzeleny.net/doku.php/en:suppl_vars_r | # Analysis of community ecology data in R
David Zelený
### Site Tools
en:suppl_vars_r
Section: Ordination analysis
## Supplementary variables (unconstrained ordination)
### R functions
• envfit (vegan) - fits supplementary variables on ordination scores, using multiple regression. Tests the significance of each variable using permutation test1). Results can be plotted onto ordination diagram using plot function; use argument p.max if only significant variables should be plotted. This function is a wrapper for functions vectorfit and factorfit applied on quantitative or qualitative environmental variables, respectively.
• scores (vegan) - extract scores of samples or species on ordination axes.
• ordisurf (vegan) - projects supplementary environmental variable as a non-linear surface onto ordination diagram (using GAM model).
• p.adjust.envfit - custom-built function (author: D. Zelený) to adjust the P-values in the object created by the function envfit, using p.adjust function. Definition is here.
1)
Note that the option to test the significance of supplementary variables passively projected onto ordination diagram is not available in CANOCO 5, where it would have to be done manually. CANOCO 5 alternative is to check the t-values reported together with results of regression coefficients - if absolute value of these t-values exceeds 2.1, one can consider them as significant (in case that number of samples minus number of supplementary variables is higher than 18) - see the CANOCO 5 manual (ter Braak & Šmilauer 2012), page 226. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23272544145584106, "perplexity": 8204.101164007698}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499946.80/warc/CC-MAIN-20230201144459-20230201174459-00600.warc.gz"} |
https://chemistry.stackexchange.com/questions/2438/determining-enthalpy-and-internal-energy-of-formation-for-potassium-superoxide | # Determining enthalpy and internal energy of formation for potassium superoxide
Given $2.14\ \mathrm g$ of $\ce{K(s)}$, determine $\Delta H^\circ_\mathrm{f,m}$ and $\Delta U^\circ_\mathrm{f,m}$ for $\ce{K2O}$.
We know:
• The calorimeter's constant: $1849\ \mathrm{J\cdot K^{-1}}$
• The mass of water inside it: $1450\ \mathrm g$
• The change in temperature: $2.62\ \mathrm K$
• The end product is $\ce{K2O}$
The process should be: determining mol of $\ce{K(s)}$, which is $0.054\ \mathrm{mol}$. Then we obtain the amount of energy absorbed by the calorimeter/water. Here are the issues. I don't know which one changed its temperature by $2.62\ \mathrm K$ or if the calorimeter's constant already considers the water. Either way, the amount of energy released by each mol of potassium is extravagant; according to the result it is $322\ \mathrm{kJ}$ or $96.8\ \mathrm{kJ}$.
Continuing with this reasoning, the $\Delta U^\circ_\mathrm{f,m}$ should be $755\ \mathrm{kJ}$ or $193\ \mathrm{kJ}$, right? What do we need to obtain $\Delta H^\circ_\mathrm{f,m}$?
Now, when we say that the temperature rose by $\pu{2.62K}$, this is the temperature of the calorimeter and the water together. We are assuming that they have been given time to reach thermal equilibrium (and generally water and copper calorimeters take relatively less time to reach equilibrium, it's pretty safe to neglect the time). Calorimeters can be filled with varied amounts of water, so the calorimeter's constant is for just the calorimeter, not the water in it.
Note that if we were to assume that the specific heat of potassium/oxide were not negligible, we would have to know the specific heats of the two, as well as the temperature at the start of the reaction and the temperature at which they want $\Delta H^o$ to be calculated at. "Standard state" doesn't fix temperature, though when you say $\Delta H^o$, you generally mean $\Delta H^o_{\pu{298K}}$. Using these, you can form a reaction pathand calculate the answer (I can elaborate on this if you want, it's pretty interesting)
Finding the enthalpy change now is pretty easy. Since $\Delta H=\Delta U+ \Delta(PV)=\Delta U+\Delta(nRT)$. Using this and looking at the overall reaction, it shouldn't be too hard :) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9094560146331787, "perplexity": 348.64238407394663}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146186.62/warc/CC-MAIN-20200226023658-20200226053658-00485.warc.gz"} |
https://www.cut-the-knot.org/Probability/RoadToOne.shtml | # Waiting to Exceed 1
### Solution 2
Let $T_n=\sum_{k=0}^n S_n$.
(1)
$P(T_n\lt 1)=\int_{S_0=0}^1\int_{S_1=0}^{1-T_0}\int_{S_2=0}^{1-T_1}\ldots\int_{S_n=0}^{1-T_{n-1}}dS_ndS_{n-1}\ldots dS_0.$
Let us make an observation here. For some natural numbers $k$ and $j$,
\displaystyle \begin{align} \int_{S_k=0}^{1-T_{k-1}}\frac{(1-T_k)^j}{j!}dS_k &=\int_{S_k=0}^{1-T_{k-1}}\frac{(1-T_{k-1}-S_k)^j}{j!}dS_k \\ &=-\frac{(1-T_{k-1}-S_k)^{j+1}}{(j+1)!}\bigg\rvert_{0}^{1-T_{k-1}} =\frac{(1-T_{k-1})^{j+1}}{(j+1)!}. \end{align}
Note, this result is also valid if $j=0$.
The integrand for the right-most integral in (1) can we written as $\displaystyle \frac{(1-T_n)^j}{j!}$ with $j=0$. Thus, the integrand keeps propagating through the integrals from right to left with $k$ decrementing by $1$ and $j$ incrementing by $1$ with every integral. Thus, we are left with
$\displaystyle P(T_n\lt 1) =\int_{S_0=0}^1 \frac{(1-T_0)^n}{n!} dS_0=\int_{S_0=0}^1 \frac{(1-S_0)^n}{n!} dS_0=\frac{1}{(n+1)!}.$
The desired expected value is
\displaystyle \begin{align} &E(n) \\ &= \sum_{n=1}^\infty n\cdot P(T_{n-1}\lt 1\cap T_n\gt 1)=\sum_{n=1}^\infty n\cdot \left[P(T_n\gt 1)-P(T_{n-1}\gt 1\cap T_n\gt 1)\right] \\ &=\small{\sum_{n=1}^\infty n\cdot \left[P(T_n\gt 1)-P(T_{n-1}\gt 1)\right]=\sum_{n=1}^\infty n\cdot \left[\left(1-\frac{1}{(n+1)!}\right) -\left(1-\frac{1}{(n)!}\right)\right]}\\ &=\sum_{n=1}^\infty n\cdot \left[\frac{1}{n!}-\frac{1}{(n+1)!}\right] \\ &=1\cdot \left(\frac{1}{1!}-\frac{1}{2!}\right)+2\cdot \left(\frac{1}{2!}-\frac{1}{3!}\right)+\ldots=\frac{1}{1!}+(2-1)\cdot\frac{1}{2!}+(3-2)\cdot\frac{1}{3!}+\ldots \\ &=\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\ldots=e-1\sim 1.72. \end{align}
### Solution 3
Let $T_n=\sum_{k=0}^nS_n$ and $N$ be the first value of $n$ for which $T_n\gt 1:$
$P(N\gt n)=P(T_0\lt 1,T_1\lt 1,\ldots,T_n\lt 1)=P(T_n\lt 1).$
It follows that
\begin{align}P(N=n)&=P(N\gt n-1)-P(N\gt n)\\ &=P(T_{n-1}\lt 1)-P(T_n\lt 1). \end{align}
We also know that $P(N=0)=0.$ Thus,
\begin{align} E(N)&=\sum_{n=1}^{\infty}nP(N=n)=\sum_{n=1}^{\infty}n(P(T_{n-1}\lt 1)-P(T_n\lt 1))\\ &=\sum_{n=1}^{\infty}nP(T_{n-1}\lt 1)-\sum_{n=1}^{\infty}nP(T_n\lt 1))\\ &=\sum_{n=0}^{\infty}(n+1)P(T_{n}\lt 1)-\sum_{n=0}^{\infty}nP(T_n\lt 1))\\ &=\sum_{n=0}^{\infty}P(T_{n}\lt 1)\\ \end{align}
Now, $P(T_0\lt 1)=P(S_0\lt 1)=1.$ By induction, $P(T_n\lt 1)=\displaystyle\frac{1}{(n+1)!},$ so that
$\displaystyle E(N)=\sum_{n=0}^{\infty}P(T_{n}\lt 1)=\sum_{n=0}^{\infty}\frac{1}{(n+1)!}=e-1.$
### Remark
Note that above $T_n$ was defined as the sum of $n+1$ random variables. In a more common formulation, we would consider $T_n$ as the sum of $n$ random variables. In that case, the result would appear slightly different because then $P(T_n\lt 1)=\displaystyle\frac{1}{n!},$ so that we would have
$\displaystyle E(N)=\sum_{n=0}^{\infty}P(T_{n}\lt 1)=\sum_{n=0}^{\infty}\frac{1}{n!}=e.$
### Solution 4
Call $E(x)$ the expected number of number selections for the sum to exceed $x.$ Since the first number is unformly distributed on $[0,1],$
$\displaystyle E(x)=1+\int_0^1E(x-t)dt.$
But $E=0$ for $x\lt 0,$ so if $0\le x\le 1$ this relation can be converted into
$\displaystyle E(x)=1+\int_0^xE(x-t)dt=1+\int_0^uE(u)du.$
It follows that $E'(x)=E(x),$ $E(0)=1,$ and so $E(x)=e^x.$ In particular, $E(1)=e.$
### Acknowledgment
Solution 1 is by Marcos Carreira; Solution 2 is by Amit Itagi; Solution 3 is an adaptation from P. J. Nahin's Dueling Idiots and Other Probability Puzzles (Princeton University Press, 2000, 94-98); Solution 4 is an adaptation from D. Newman's A Problem Seminar (Springer-Verlag, 1982, problem 100). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 4, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999009370803833, "perplexity": 2683.42782513461}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655886865.30/warc/CC-MAIN-20200705023910-20200705053910-00014.warc.gz"} |
http://www.koreascience.or.kr/article/JAKO200532217923457.page | # ISOMORPHIC MODULAR GROUP ALGEBRAS OF SEMI-COMPLETE PRIMARY ABELIAN GROUPS
• DANCHEV, PETER V. (13 General Kutuzov Street)
• Published : 2005.02.01
#### Abstract
Suppose G is a semi-complete abelian p-group and FG ${\cong}$ FH as commutative unitary F-algebras of characteristic p for any fixed group H. Then, it is shown that, G ${\cong}$ H. This improves a result of the author proved in the Proceedings of the American Math. Society (2002) and also completely solves by an another method a long-standing problem of W. May posed in the same Proceedings (1979).
#### References
1. D. Beers, F. Richman, and E. Walker, Group algebras of abelian groups, Rend. Sem. Mat. Univ. Padova 69 (1983), 41-50
2. P. V. Danchev, Commutative group algebras of cardinality $N_1$, Southeast Asian Bull. Math. 25 (2002), no. 4, 589-598 https://doi.org/10.1007/s100120200003
3. P. V. Danchev, Commutative group algebras of direct sums of ${\sigma}-summable$ abelian p-groups, Math. J. Okayama Univ. 45 (2003), 1-15
4. P. V. Danchev, Invariances in commutative and noncommutative group algebras, Compt. rend. Acad. bulg. Sci. 54 (2001), no. 4, 5-8
5. P. V. Danchev, Isomorphism of commutative group algebras of closed p-groups and p-local algebraically compact groups, Proc. Amer. Math. Soc. 130 (2002), no. 7, 1937-1941
6. P. V. Danchev, Isomorphism of commutative group algebras of mixed splitting groups, Compt. rend. Acad. bulg. Sci. 51 (1998), no. 1-2, 13-16
7. P. V. Danchev, Isomorphism of modular group algebras of direct sums of torsion-complete abelian p-groups, Rend. Sem. Mat. Univ. Padova 101 (1999), 51-58
8. P. V. Danchev, The splitting problem and the direct factor problem in modular abelian group algebras, Math. Balkanica (N.S.) 15 (2000), no. 3-4, 217-226
9. P. V. Danchev, Units in abelian group rings of prime characteristic, Compt. rend. Acad. bulg. Sci. 48 (1995), no. 8, 5-8
10. J. Irwin, F. Richman, and E. Walker, Countable direct sums of torsion complete groups, Proc. Amer. Math. Soc. 17 (1966), no. 4, 763-766
11. G. Kolettis, Jr., Semi-complete primary abelian groups, Proc. Amer. Math. Soc. 11 (1960), no. 2, 200-205
12. W. May, Modular group algebras of totally projective p-primary groups, Proc. Amer. Math. Soc. 76 (1979), no. 1, 31-34
13. W. May, The direct factor problem for modular abelian group algebras, Contemp. Math. 93 (1989), 303-308 https://doi.org/10.1090/conm/093/1003359
#### Cited by
1. MODULAR ABELIAN GROUP ALGEBRAS vol.03, pp.02, 2010, https://doi.org/10.1142/S1793557110000192 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6094691157341003, "perplexity": 1555.092429022164}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487611641.26/warc/CC-MAIN-20210614074543-20210614104543-00488.warc.gz"} |
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https://fr.mathworks.com/help/ident/ug/online-armax-polynomial-model-estimation.html | # Online ARMAX Polynomial Model Estimation
This example shows how to implement an online polynomial model estimator. You estimate two ARMAX models for a nonlinear chemical reaction process. These models capture the behavior of the process at two operating conditions. The model behavior is identified online and used to adjust the gains of an adaptive PI controller during system operation.
### Continuously Stirred Tank Reactor
A Continuously Stirred Tank Reactor (CSTR) is a common chemical system in the process industry. A schematic of the CSTR system is:
This is a jacketed diabatic (i.e., nondiabatic) tank reactor described extensively in Bequette's book "Process Dynamics: Modeling, Analysis and Simulation", published by Prentice-Hall, 1998. The vessel is assumed to be perfectly mixed, and a single first-order exothermic and irreversible reaction, A --> B, takes place. The inlet stream of reagent A is fed to the tank at a constant rate. After stirring, the end product streams out of the vessel at the same rate as reagent A is fed into the tank (the volume in the reactor tank is constant). Details of the operation of the CSTR and its 2-state nonlinear model used in this example are explained in the example Non-Adiabatic Continuous Stirred Tank Reactor: MATLAB File Modeling with Simulations in Simulink®.
The inputs of the CSTR model are:
and the outputs (y(t)), which are also the states of the model (x(t)), are:
The control objective is to maintain the concentration of reagent A, at the desired level , which changes over time. The jacket temperature is manipulated by a PI controller in order to reject disturbances arising from the inlet feed stream temperature . The input of the PI controller is the tracking error signal, . The inlet feed stream concentration, , is assumed to be constant. The Simulink model iddemo_cstr implements the CSTR plant as the block CSTR.
open_system('iddemo_cstr');
The feed temperature input consists of a white noise disturbance on top of a constant offset. The noise power is 0.0075 [K^2]. This noise level causes up to 2% deviation from the desired .
The signal in this example contains a step change from 1.5 [kgmol/m^3] to 2 [kgmol/m^3] at time . In addition to this step change, also contains a white noise perturbation for t in the [0,200) and [400,600) ranges. The power of this white noise signal is 0.015. The noise power is adjusted empirically to approximately give a signal-to-noise ratio of 10. Not having sufficient excitation in the reference signal in closed-loop identification can lead to not having sufficient information to identify a unique model. The implementation of is in the iddemo_cstr/CA Reference block.
### Online Estimation for Adaptive Control
It is known from the nonlinear model that the CSTR output is more sensitive to the control input at higher levels. The Recursive Polynomial Model Estimator block is used to detect this change in sensitivity. This information is used to adjust the gains of the PI controller as varies. The aim is to avoid having a a high gain control loop which may lead to instability.
You estimate a discrete transfer-function from to online with the Recursive Polynomial Model Estimator block. The adaptive control algorithm uses the DC gain of this transfer function. The tracking error , is divided by the normalized DC gain of the estimated transfer function. This normalization is done to have a gain of 1 on the tracking error at the initial operating point, for which the PI controller is designed. For instance, the error signal is divided by 2 if the DC gain becomes 2 times its original value. This corresponds to dividing the PI controller gains by 2. This adaptive controller is implemented in iddemo_cstr/Adaptive PI Controller.
### Recursive Polynomial Model Estimator Block Inputs
The 'Recursive Polynomial Model Estimator' block is found under the System Identification Toolbox/Estimators library in Simulink. You use this block to estimate linear models with ARMAX structure. ARMAX models have the form:
• The Inputs and Output inport of the recursive polynomial model estimator block correspond to and respectively. For the CSTR model and are deviations from the jacket temperature and A concentration trim operating points: , . It is good to scale and to have a peak amplitude of 1 to improve the numerical condition of the estimation problem. The trim operating points, and , are not known exactly before system operation. They are estimated and extracted from the measured signals by using a first-order moving average filter. These preprocessing filters are implemented in the iddemo_cstr/Preprocess Tj and iddemo_cstr/Preprocess CA blocks.
open_system('iddemo_cstr/Preprocess Tj');
• The optional Enable inport of the Recursive Polynomial Model Estimator block controls the parameter estimation in the block. Parameter estimation is disabled when the Enable signal is zero. Parameter estimation is enabled for all other values of the Enable signal. In this example the estimation is disabled for the time intervals and . During these intervals the measured input does not contain sufficient excitation for closed-loop system identification.
### Recursive Polynomial Model Estimator Block Setup
Configure the block parameters to estimate a second-order ARMAX model. In the Model Parameters tab, specify:
• Model Structure: ARMAX. Choose ARMAX since the current and past values of the disturbances acting on the system, , are expected to impact the CSTR system output .
• Initial Estimate: None. By default, the software uses a value of 0 for all estimated parameters.
• Number of parameters in A(q) (na): 2. The nonlinear model has 2 states.
• Number of parameters in B(q) (nb): 2.
• Number of parameters in C(q) (nc): 2. The estimated model corresponds to a second order model since the maximum of na, nb, and nc are 2.
• Input Delay (nk): 1. Like most physical systems, the CSTR system does not have direct feedthrough. Also, there are no extra time delays between its I/Os.
• Parameter Covariance Matrix: 1e4. Specify a high covariance value because the initial guess values are highly uncertain.
• Sample Time: 0.1. The CSTR model is known to have a bandwidth of about 0.25Hz. chosen such that 1/0.1 is greater than 20 times this bandwidth (5Hz).
Click Algorithm and Block Options to set the estimation options:
• Estimation Method: Forgetting Factor
• Forgetting Factor: 1-5e-3. Since the estimated parameters are expected to change with the operating point, set the forgetting factor to a value less than 1. Choose which corresponds to a memory time constant of seconds. A 100 second memory time ensures that a significant amount data used for identification is coming from the 200 second identification period at each operating point.
• Select the Output estimation error check box. You use this block output to validate the estimation.
• Select the Add enable port check box. You only want to adapt the estimated model parameters when extra noise is injected in the reference port. The parameter estimation n is disabled through this port when the extra noise is no longer injected.
• External reset: None.
### Recursive Polynomial Model Estimator Block Outputs
At every time step, the recursive polynomial model estimator provides an estimate for , , , and the estimation error . The Error outport of the polynomial model estimator block contains and is also known as the one-step-ahead prediction error. The Parameters outport of the block contains the A(q), B(q), and C(q) polynomial coefficients in a bus signal. Given the chosen polynomial orders (, , , ) the Parameters bus elements contain:
The estimated parameters in the A(q), B(q), and C(q) polynomials change during simulation as follows:
sim('iddemo_cstr');
close_system('iddemo_cstr/Preprocess Tj');
open_system('iddemo_cstr/ABC');
The parameter estimates quickly change from their initial values of 0 due to the high value chosen for the initial parameter covariance matrix. The parameters in the and polynomials approach their values at rapidly. However, the parameters in the polynomial show some fluctuations. One reason behind these fluctuations is that the disturbance to CSTR output is not fully modelled by the ARMAX structure. The error model is not important for the control problem studied here since the to relationship is captured by the transfer function . Therefore, the fluctuation in is not a concern for this identification and control problem.
The parameter estimates are held constant for since the estimator block was disabled for this interval (0 signal to the Enable inport). The parameter estimation is enabled at when the CSTR tank starts switching to its new operating point. The parameters of and converge to their new values by , and then held constant by setting the Enable port to 0. The convergence of and is slower at this operating point. This slow convergence is because of the smaller eigenvalues of the parameter covariance matrix at t=400 compared to the initial 1e4 values set at t=0. The parameter covariance, which is a measure of confidence in the estimates, is updated with each time step. The algorithm quickly changed the parameter estimates when the confidence in estimates were low at t=0. The improved parameter estimates capture the system behavior better, resulting in smaller one-step-ahead prediction errors and smaller eigenvalues in the parameter covariance matrix (increased confidence). The system behavior changes in t=400. However, the block is slower to change the parameter estimates due to the increased confidence in the estimates. You can use the External Reset option of the Recursive Polynomial Model Estimator block to provide a new value for parameter covariance at t=400. To see the value of the parameter covariance, select the Output parameter covariance matrix check box in the Recursive Polynomial Model Estimator block.
### Validating the Estimated Model
The Error output of the Recursive Polynomial Model Estimator block gives the one-step-ahead error for the estimated model.
close_system('iddemo_cstr/ABC');
The one-step-ahead error is higher when there are no extra perturbations injected in the channel for system identification. These higher errors may be caused by the lack of sufficient information in the input channel that the estimator block relies on. However, even this higher error is low and bounded when compared to the measured fluctuations in . This gives confidence in the estimated parameter values.
A more rigorous check of the estimated model is to simulate the estimated model and compare with the actual model output. The iddemo_cstr/Time-Varying ARMAX block implements the time-varying ARMAX model estimated by the Online Polynomial Model Estimator block. The error between the output of the CSTR system and the estimated time-varying ARMAX model output is:
open_system('iddemo_cstr/Simulation Error');
The simulation error is again bounded and low when compared to the fluctuations in the . This further provides confidence that the estimated linear models are able to predict the nonlinear CSTR model behavior.
The identified models can be further analyzed in MATLAB. The model estimates for the operating points and can be obtained by looking at the estimated A(q), B(q), and C(q) polynomials at and respectively. Bode plots of these models are:
Ts = 0.1;
tidx = find(t>=200,1);
P200 = idpoly(AHat(:,:,tidx),BHat(:,:,tidx),CHat(:,:,tidx),1,1,[],Ts);
tidx = find(t>=600,1);
P600 = idpoly(AHat(:,:,tidx),BHat(:,:,tidx),CHat(:,:,tidx),1,1,[],Ts);
bodemag(P200,'b',P600,'r--',{10^-1,20});
legend('Estimated Model at C_A=1.5 [kgmol/m^3]', ...
'Estimated Model at C_A=2.0 [kgmol/m^3]', ...
'Location', 'Best');
The estimated model has a higher gain at higher concentration levels. This is in agreement with prior knowledge about the nonlinear CSTR plant. The transfer function at has a higher gain (double the amplitude) at low frequencies.
### Summary
You estimated two ARMAX models to capture the behavior of the nonlinear CSTR plant at two operating conditions. The estimation was done during closed-loop operation with an adaptive controller. You looked at two signals to validate the estimation results: One step ahead prediction errors and the errors between the CSTR plant output and the simulation of the estimation model. Both of these errors signals were bounded and small compared to the CSTR plant output. This provided confidence in the estimated ARMAX model parameters.
bdclose('iddemo_cstr');
Get trial now | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8294761180877686, "perplexity": 1252.6624665963238}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178381230.99/warc/CC-MAIN-20210307231028-20210308021028-00193.warc.gz"} |
https://wiki.sipeed.com/soft/maixpy/en/course/ai/image/1000_type_classifier.html | # 1000 object classification models
Can recognize 1000 objects
## Instructions
• Use minimum version firmware
• Download model file, download mobilenet_0x300000.kfpkg
• Use kflash_gui to burn this file to Flash, the default address is 0x300000
• Save the file labels.txt ([Alternate Link](https://en.bbs.sipeed.com /uploads/default/original/1X/d41ad9dfbe01f228abe726986fbf1baf4e288f2e.zip)) to the file system, see the introductory tutorial (use your ingenuity) for specific methods (reference answer: because there is too much content, if you use the REPL to copy and paste directly, data may be wrong. So use a tool to transfer. The easiest way is to put it on the SD card; if you want to put it in /flash, the minimum may not support IDE, you can use upyloader to send files)
• Because this model has 4.2MiB, which is relatively large, so the firmware of minimum is used, and the memory used by GC is not too large. You can set a smaller size in the following way and leave the memory for the model
from Maix import utils
import machine
utils.gc_heap_size(256*1024)
machine.reset()
• Import model
import KPU as kpu
f=open('/sd/labels.txt','r')
f.close()
• Initialize the camera, LCD
You can set whether the camera is mirrored and whether the LCD is rotated according to your own hardware installation
Slightly, please refer to the previous tutorial
• Identify objects
fmap = kpu.forward(task, img)
plist=fmap[:]
pmax=max(plist)
max_index=plist.index(pmax)
Here, the result of the operation is converted into a list object, and then the subscript of the maximum value is found. Through this subscript, we know what the label name is (labels[max_index])
• show result
img = img.draw_string(0, 0, "%.2f: %s" %(pmax, labels[max_index].strip()), color=(255, 0, 0))
lcd.display(img, oft=(0,0))
print(fps)
See the complete example maixpy_scripts | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20464669167995453, "perplexity": 3834.9875337364488}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950247.65/warc/CC-MAIN-20230401191131-20230401221131-00488.warc.gz"} |
http://clay6.com/qa/24574/which-of-the-following-is-not-a-false-statement- | Browse Questions
# Which of the following is not a false statement?
$\begin {array} {1 1} (A)\;\ni \: n\: \in \: N\: such\: that\: n+5\: > \: 4 \\ (B)\;\forall \: n\: \in \: N,\: n+6\: >\: 9 \\ (C)\;All \: of\: these \\ (D)\;Each\: prime\: number \: has\: exactly\: two\: factors \end {array}$
Ans : (D) Each prime number has exactly two factors. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23224182426929474, "perplexity": 1045.8326691982072}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719079.39/warc/CC-MAIN-20161020183839-00540-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://collegephysicsanswers.com/openstax-solutions/250-kg-steel-gasoline-can-holds-200-l-gasoline-when-full-what-average-density-0 | Change the chapter
Question
A 2.50-kg steel gasoline can holds 20.0 L of gasoline when full. What is the average density of the full gas can, taking into account the volume occupied by steel as well as by gasoline?
$0.79 \textrm{ g/mL}$
Solution Video
OpenStax College Physics for AP® Courses Solution, Chapter 11, Problem 8 (Problems & Exercises) (2:57)
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Video Transcript
This is College Physics Answers with Shaun Dychko. A steel can with a mass of 2.50 kilograms is holding 20.0 liters of gasoline and we have to figure out what the average density of this can-gasoline combination is. So we need to know what the total mass of the can plus gasoline is and then divide that by the total volume of the can plus the gasoline. So we need to know the densities of the can material and the gasoline in order to figure out some of the unknowns here. We don't know the volume of the can like how much metal is used... like what volume of metal is used to make it and we don't know the mass of the gasoline either. So we look up in table [11.1] for the density of steel which is 7.8 grams per milliliter and the density of gasoline, which is petrol, is 0.68 grams per milliliter so that's where these numbers came from. So we need to find the mass of gasoline and so we know the density of gasoline is its mass divided by its volume and we are given the volume so we can use the density to figure out the mass. So we'll multiply both sides by the volume of gasoline here and we get that the mass of the gasoline is the density multiplied by the volume. Also we want to find the volume of steel used to make up the can so that's gonna be the mass of the steel divided by the density of steel. And so we make substitutions for these two unknowns: the mass of the gas is substituted with density of gasoline times volume of gasoline; and the volume of the can is substituted with mass of the can divided by the density of the can. So now when you are plugging in numbers, you have to be careful with units so the important thing is that you choose an unit system be it grams per milliliter or kilograms per cubic meter and pick one or the other and stick with those units throughout every number in your calculation. So I have chosen grams per milliliter and so whenever there's a mass, I need grams and whenever there's a volume, I need milliliters. So the mass of the can is 2.50 kilograms but the prefix 'kilo-' means times 10 to the 3 so I have written times 10 to the 3 grams and then add to that the 0.68 grams per milliliter—density of gasoline— multiplied by 20.0 liters but liters doesn't belong here—we want milliliters— so we multiply by 1000 milliliters for every liter. Then in the denominator, we have 2.50 times 10 to the 3 grams again divided by 7.8 grams per milliliter— density of steel— plus 20.0 liters but this has to be converted into milliliters and we end up with 0.79 grams per milliliter is the average density of the can-gasoline combination. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8614964485168457, "perplexity": 496.0891393377804}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991693.14/warc/CC-MAIN-20210512004850-20210512034850-00613.warc.gz"} |
https://koreauniv.pure.elsevier.com/en/publications/reduction-kinetics-of-electric-arc-furnace-oxidizing-slag-by-al-f | # Reduction Kinetics of Electric Arc Furnace Oxidizing Slag by Al-Fe Alloy
Jaehong Lee, Joon Seok Oh, Joonho Lee
Research output: Contribution to journalArticlepeer-review
2 Citations (Scopus)
## Abstract
Effects of temperature and slag basicity on the reduction rate of iron oxide in molten synthetic electric arc furnace oxidizing slag by Al-40 wt.%Fe alloy was investigated. An alloy sample was dropped into molten slag in an MgO crucible. When the initial slag temperature was 1723 K, there was no reduction. However, when the initial slag temperature was 1773 K and the slag basicity was 1.1, the reduction was initiated and the temperature of the slag rapidly increased. When the slag basicity was 1.1, increasing the initial slag temperature from 1773 K to 1823 K increases the reaction rate. As the slag basicity increased from 1.1 to 1.4 at 1773 K, the reaction rate increased. From SEM analysis, it was found that an Al2O3 or a spinel phase at the slag-metal interface inhibited the reaction at a lower temperature and a lower slag basicity.
Original language English 2359-2364 6 JOM 68 9 https://doi.org/10.1007/s11837-016-2022-y Published - 2016 Sept 1
## ASJC Scopus subject areas
• Materials Science(all)
• Engineering(all)
## Fingerprint
Dive into the research topics of 'Reduction Kinetics of Electric Arc Furnace Oxidizing Slag by Al-Fe Alloy'. Together they form a unique fingerprint. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8245540857315063, "perplexity": 13174.431538903891}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945381.91/warc/CC-MAIN-20230326013652-20230326043652-00274.warc.gz"} |
http://math.stackexchange.com/questions/728280/interesting-mathematical-problems-for-1st-year-university-students | Interesting mathematical problems for 1st year university students [closed]
Can you explain some mathematical problems that you find the most interesting (NB: the problem must be accessible to a 1st year university student: that is, a problem for which there is an elegant solution that a student can find). Also, why do they interest you?
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closed as too broad by Jack M, studiosus, Claude Leibovici, Sasha, Jyrki LahtonenMay 3 at 4:43
There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.
Do you mean problems that a first year undergrad can solve, or problems that a first year student can understand and drive further education? – Thomas Andrews Mar 26 at 22:30
Also, top 3 is really an artificial constraint - is it really necessary for this to be a useful question? Perhaps just ask about problems in general... – Thomas Andrews Mar 26 at 22:31
As a general rule, it is best to be very specific about what you are looking for in this sort of soft question. Are you looking for yourself, as a teacher, etc? – Thomas Andrews Mar 26 at 22:32
Different people find different things interesting. In the past when I've taught problem-solving courses and presented the students with a large menu of problems to work on, almost none of the students picked the same problems. Instead of trying to find three problems that will appeal to everyone, I think a better strategy is to assemble a large list of interesting problems and let students decide for themselves what is interesting. – MJD Mar 26 at 22:33
Are you looking for solvable problems? I work on problems which are very interesting to me, and you can relatively easily explain them to a freshman student that know the statement of the axiom of choice, and the term "equivalent" (in the context of logic). But I don't think mathematics have the tools to solve many of these problems nowadays, and we need to come up with better ways to understand the universes of set theory before we can truly solve these problems. – Asaf Karagila Mar 26 at 22:41
I think if you take the three-course calculus sequence and differential equations and an intro physics course, then you might find the calculus of variations very interesting. Consider the following question: What is the brachistochrone curve, i.e., the curve of fastest descent? In other words, what is the path that will carry a particle from one place to another in the least amount of time? A related question is what is the tautochrone, namely, the curve for which the time taken by a particle sliding without friction, under the influence of gravity, to its lowest point, is independent of its starting point? Another related curve is known as the catenary. This curve appears everywhere in nature. The calculus of variations allows one to answer such questions. Personally, I found this problems very interesting when I was an undergrad. Richard Feynman also found this intriguing. He used the principles of the calculus of variations in quantum mechanics to develop something known as quantum electrodynamics (QED).
Another memorable problem I found interesting is known as the Basel problem: Find the value of $$\sum_{n = 1}^\infty \frac{1}{n^2} = 1 + \frac{1}{2^2} + \frac{1}{3^2} + \cdots$$
It is hard to find a mathematician who did not find this problem and the answer fascinating as an undergrad.
It is hard to come up with the top three. It varies from person to person. Some people like applied math, while others like pure math.
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If you find number patterns interesting you may like the following problem. It amazed me when I first learned about it because I did not expect odd numbers and square numbers to be so closely connected.
What is the sum of the first $n$ odd numbers? Prove it.
I'll concede that this problem is really simple -- the answer is "square numbers" -- but it generalizes quite nicely. Here are a few directions you can generalize it in:
1. Prove that your solution is correct in as many different ways as you can. (There are seven proofs in Knuth's book Concrete Math, for instance. This could be a good segue into any number of topics in discrete mathematics.)
2. Which sequence has the property that the sum of its first $n$ terms is $n^k$, for $k\geq1$ an integer?
3. What is the sum of the first $n$ numbers of the form $k(k+1)\dots(k+l-1)$?
These problems are trivial to most mathematicians but are probably not trivial to many first-years. They would be particularly accessible to first-years because they rely on little mathematical background and are easy to tackle with experimentation.
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the ~¾ century old Collatz conjecture is a great problem to experiment/study on esp with CS based approaches (writing code, visualizing results); its possible/ultimate/eventual(?) solution is regarded as very hard by experts. however there are many basic variants of exercises on it that have "correct solutions" that are accessible to undergraduates. (example: create a Finite state transducer to calculate iterates.) it has remarkable/amazing aspects of/connections to many areas of active mathematical & CS research:
see eg this Collatz conjecture experiments page for some basic starting leads & many links to standard/recent references
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I like this question because it is easy to understand yet incredibly hard to solve. Students may come up with a short proof but that often has a logical flaw.
We allow for equality in the definition of increasing and decreasing and call a function monotonic if it is increasing or decreasing. If $f:\mathbb R\to \mathbb R$ is not monotonic, are there three points $x<y<z$ such that $f(y)<f(x),f(z)$ or $f(y)>f(x),f(z)$?
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Note that $f$ need not be continuous - that tripped me up when I first saw this! – Mike Miller Mar 26 at 22:35
Since when does trivial case analysis count as "incredibly hard to solve"? It may not be the most elegant solution and may take some work, but it's definitely not hard. – user2345215 Mar 26 at 23:07
@user2345215 Now you're just being a mean, mean person. – Pedro Tamaroff Mar 27 at 3:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8176247477531433, "perplexity": 435.7339215530261}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414637900031.50/warc/CC-MAIN-20141030025820-00181-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/the-string-theory-and-im-new.16227/ | # The String Theory-and im new
1. Mar 14, 2004
### ninja nemesi$hi-im new here.....im 15, from london, and i like physics...lots! lol String Theory i found this site that has a whole load of info about it, and even 3 one hour clips explaining it and the theory behind it- apparantly, all particles are made up of little strings that vibrate, and that's how energy is made...these strings are so small, that in comparison to an atom, they would be the size of a tree, where the atom would be the size of the universe....! here's the site- http://www.pbs.org/wgbh/nova/elegant/ sorry if this has already been discussed....im still new-and 15-lol 2. Mar 14, 2004 ### cookiemonster 3. Mar 14, 2004 ### ninja nemesi$
lol----i dont particularly see myself as a geek of any sort, but usually when i tell people that im 15 and im into astrophysics.....lol-u know hehe
4. Mar 14, 2004
Blah, the prejudices we're subjected to.
What's the difference between being 15 and wanting to be an astronaut and being 15 and being into astrophysics? One of 'em actually knows what he's doing!
5. Apr 1, 2004
### Javier
6. Apr 14, 2004
### garytse86
can someone explain supersymmetry to me please?
7. Apr 14, 2004
### chroot
Staff Emeritus
garytse86: Please create a new thread in the Strings forum for this topic.
- Warren | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3296349346637726, "perplexity": 15663.296158522955}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221219109.94/warc/CC-MAIN-20180821210655-20180821230655-00534.warc.gz"} |
https://mdtpmodules.org/polq-3-lesson-4-solutions-quadratic-word-problems/ | # POLQ 3 | Lesson 4 | Practice (Quadratic Word Problems) Solutions
Solutions:
1. $$h(t) = 0.5 at^2+vt+s$$ → $$h(t) = 0.5(-32)t^2+160(t)+4$$ → $$h(t) = -16t^2+160t+4$$
2. $$h(3) = 0.5 at^2+vt +s$$ → $$h(3) = 0.5(-32)3^2+160(3)+4$$ → (h(3)=-144+480\) → $$h(3) = 360ft$$
3. Ball’s highest point can be found with $$x= \dfrac{-b}{2a}$$ which will give the $$x$$ value for the line of symmetry and the max of minimum of any quadratic.
$$h(t) = -16t^2+160t+4$$
$$t = -\dfrac{160}{2(-16)}$$
$$t = 5$$; $$h(t) =-16\cdot5^2+160(5)+4$$ →$$h(t) = 404$$
So, the highest point is (5, 404)
4. The answer is the larger answer as we want the $$x$$-coordinate of when the ball lands.
$$-16t^2+160t+4 = 0$$
Divide both sides by 4: $$-4t^2+40t+1= 0$$
To solve by quadratic formula: $$x = \dfrac{-b±\sqrt{b^2-4ac}}{2a}$$
$$a = -4, b = 40, c = 1$$
$$x = \dfrac{-40 \pm\sqrt{40^2-4(-4)(1)}}{2\cdot(-4)}$$
$$x = \dfrac{-40\pm\sqrt{1616}}{-8}$$
simplifying the radical $$x =\dfrac{-40±16\sqrt{101}}{-8}$$
simplifying and taking the largest value:
$$x = 5+2\sqrt{101}$$ this is approximately 25 sec.
You could also find this by completing the square.
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