The 2014/04/01 Iquique earthquake struck off the coast of Chile at 20:46 local time (23:46 UTC), with a moment magnitude of 8.1. The epicenter of the earthquake was approximately 95 kilometers (59 mi) northwest of Iquique, as shown in Fig. 7.
We have carried out simulations of the tsunami induced by the earthquake using
a topography obtained from the National Oceanic and Atmospheric Administration (NOAA, [47]) using the ETOPO1 data (1-arc minute global relief model),
an unstructured mesh whose dimensions – a square of 2224.2 km² – correspond to the domain covered by Fig. 7,
a source corresponding to the seafloor displacement induced by the earthquake (Fig. 7). This source is obtained by computing the 3D final displacements of the seafloor generated by the earthquake coseismic slip. This coseismic slip has been itself retrieved by inversion of numerous geodetic and seismic data, according to the model determined by [51]. The source is activated at time $t_0$, just after the earthquake occurrence ($t_0$ is here 2014/04/01,23h47mn25s)
We did not consider here the Coriolis force, the tides and the ocean currents. The results shown in Fig. 8 have been obtained with a mesh containing 545821 nodes and 5 layers (computation time was 35 minutes with a Mac book air 1.7 GHz Intel core i7). We compare the numerical solutions – provided by the first order scheme (space and time) and the second order scheme (space and time) – with the DART measurements (obtained from the NOAA website http://www.ndbc.noaa.gov/dart.shtml). A series of simulations have been performed using several meshes and we present “converged” results in the sense that a finer mesh would give the same results. This is illustrated in Fig. 8-(d), where we plot the simulation results obtained with three meshes having respectively 311687 nodes (coarse mesh), 545821 nodes (fine mesh), and 985327 nodes (very fine mesh): the curves corresponding to the fine (cyan) and very fine (blue) curves are very similar.
Fig. 8-(a),(b),(c) shows that the second order scheme significantly improves the results both for the amplitude and phase of the water waves. The second order scheme is able to very accurately reproduce the shape of the first wave at the closest DART buoy 32401, located at 287 km from the epicenter. The two following peaks in the waveform are quite well reproduced up to about $1.755 \times 10^5$ s. This is also the case at the DART buoy 32402, located 853 km from the epicenter. The arrival time of the first wave is very well reproduced at the three DART buoys, slightly better with the second order scheme. At the most distant buoy 32412 (1650 km from the source), the first order scheme is not able to reproduce the recorded wave. The second order scheme reproduces the first wave quite well but not the rest of the waveform, possibly due to Earth curvature effects that are not taken into account here. Globally, the low frequency content of the signals is better explained by the model than the high frequency fluctuations. These high frequency fluctuations may be related to effects not accounted for here, such as spatio-temporal heterogeneity of the real source, small wavelength fluctuation of the topography, and possibly non-hydrostatic effects [26, 1].
6.4 Monai valley benchmark
In 2004, as part of a workshop organized by the US National Science Foundation, an experiment has been set up, reproducing the impact of a tsunami wave on the shore of the Okushiri island, in the Monai village area. The objective of the experiment was to provide a set of well organized data, reproducing the 1993 tsunami event, to validate numerical codes for Tsunami simulation [42, 39].
This test case has been simulated by various numerical tools, it is well suited to test the numerical treatment of wet/dry interfaces. We reproduce hereafter the results obtained with Freshkiss3d [49].
The geometrical domain of 5.448 m × 3.402 m is depicted over Fig. 9 where the bathymetry and the free surface elevation at time $t = 16$ s are presented. The topography, the input wave