International audienceWe present a discontinuous Galerkin finite-element method (DG-FEM) formulation with Convolutional Perfectly Matched Layer (CPML) absorbing boundary condition for 3-D elastic seismic wave modelling. This method makes use of unstructured tetrahedral meshes locally refined according to the medium properties (h-adaptivity), and of approximation orders that can change from one element to another according to an adequate criterion (p-adaptivity). These two features allow us to significantly reduce the computational cost of the simulations. Moreover, we have designed an efficient CPML absorbing boundary condition, both in terms of absorption and computational cost, by combining approximation orders in the numerical domain. A quadratic interpolation is typically used in the medium to obtain the required accuracy, while lower approximation orders are used in the CPMLs to reduce the total computational cost and to obtain a well-balanced workload over the processors. While the efficiency of DG-FEMs have been largely demonstrated for high approximation orders, we favour the use of low approximation orders as they are more appropriate to the applications we are interested in. In particular, we address the issues of seismic modelling and seismic imaging in cases of complex geological structures that require a fine discretization of the medium. We illustrate the efficiency of our approach within the framework of the EUROSEISTEST verification and validation project, which is designed to compare high-frequency (up to 4 Hz) numerical predictions of ground motion in the Volvi basin (Greece). Through the tetrahedral meshing, we have achieved fine discretization of the basin, which appears to be a sine qua non condition for accurate computation of surface waves diffracted at the basin edges. We compare our results with predictions computed with the spectral element method (SEM), and demonstrate that our method yields the same level of accuracy with computation times of the same order of magnitude

Built-up on top of ancient lake deposits, Mexico City experiences some of the largest seismic site effects worldwide. Besides the extreme amplification of seismic waves, duration of intense ground motion from large subduction earthquakes exceeds three minutes in the lake-bed zone of the basin, where hundreds of buildings collapsed or were seriously damaged during the magnitude 8.0 Michoacán earthquake in 1985. Different mechanisms contribute to the long lasting motions, such as the regional dispersion and multiple-scattering of the incoming wavefield from the coast, more than 300 km away the city. By means of high performance computational modeling we show that, despite the highly dissipative basin deposits, seismic energy can propagate long distances in the deep structure of the valley, promoting also a large elongation of motion. Our simulations reveal that the seismic response of the basin is dominated by surface-waves overtones, and that this mechanism increases the duration of ground motion by more than 170% and 290% of the incoming wavefield duration at 0.5 and 0.3 Hz, respectively, which are two frequencies with the largest observed amplification. This conclusion contradicts what has been previously stated from observational and modeling investigations, where the basin itself has been discarded as a preponderant factor promoting long and devastating shaking in Mexico City.

International audiencen a low‐seismicity context, the use of numerical simulations becomes essential due to the lack of representative earthquakes for empirical approaches. The goals of the EUROSEISTEST Verification and Validation Project (E2VP) are to provide (1) a quantitative analysis of accuracy of the current, most advanced numerical methods applied to realistic 3D models of sedimentary basins (verification) and (2) a quantitative comparison of the recorded ground motions with their numerical predictions (validation). The target is the EUROSEISTEST site located within the Mygdonian basin, Greece. The site is instrumented with surface and borehole accelerometers, and a 3D model of the medium is available. The simulations are performed up to 4 Hz, beyond the 0.7 Hz fundamental frequency, thus covering a frequency range at which ground motion undergoes significant amplification. The discrete representation of material heterogeneities, the attenuation model, the approximation of the free surface, and nonreflecting boundaries are identified as the main sources of differences among the numerical predictions. The predictions well reproduce some, but not all, features of the actual site effect. The differences between real and predicted ground motions have multiple origins: the accuracy of source parameters (location, hypocentral depth, and focal mechanism), the uncertainties in the description of the geological medium (damping, internal sediment layering structure, and shape of the sediment‐basement interface). Overall, the agreement reached among synthetics up to 4 Hz despite the complexity of the basin model, with code‐to‐code differences much smaller than predictions‐to‐observations differences, makes it possible to include the numerical simulations in site‐specific analysis in the 3D linear case and low‐to‐intermediate frequency range

[1] We introduce a novel scheme, DGCrack, to simulate dynamic rupture of earthquakes in three dimensions based on an hp-adaptive discontinuous Galerkin method. We solve the velocity-stress weak formulation of elastodynamic equations on an unstructured tetrahedral mesh with arbitrary mesh refinements (h-adaptivity) and local approximation orders (p-adaptivity). Our scheme considers second-order fault elements (P2) where dynamic-rupture boundary conditions are enforced through ad hoc fluxes across the fault. To model the Coulomb slip-dependent friction law, we introduce a predictor-corrector scheme for estimating shear fault tractions, in addition to a special treatment of the normal tractions that guarantees the continuity of fault normal velocities. We verify the DGCrack by comparison with several methods for two spontaneous rupture tests and find excellent agreement (i.e., rupture times RMS errors smaller than 1.0%) provided that one or more fault elements resolve the fault cohesive zone. For a quantitative comparison, we introduce a methodology based on cross-correlation measurements that provide a simple way to quantify the similarity between solutions. Our verification tests include a 60 dipping normal fault reaching the free surface. The DGCrack method reveals convergence rates close to those of well-established methods and a numerical efficiency significantly higher than that of similar discontinuous Galerkin approaches. We apply the method to the 1992 Landers-earthquake fault system in a layered medium, considering heterogeneous initial stress conditions and mesh adaptivities. Our results show that previously proposed dynamic models for the Landers earthquake require a reevaluation in terms of the initial stress conditions that take account of the intricate fault geometry.Citation: Tago, J., V. M. Cruz-Atienza, J. Virieux, V. Etienne, and F. J. Sánchez-Sesma (2012), A 3D hp-adaptive discontinuous Galerkin method for modeling earthquake dynamics,

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