This article documents a comparative exercise for numerical simulation of ground motion, addressing the seismic response of the Grenoble site, a typical Alpine valley with complex 3D geometry and large velocity contrasts. Predictions up to 2 Hz were asked for four different structure wave-field configurations (point source and extended source, with and without surface topography). This effort is part of a larger exercise organized for the third international symposium on the effects of surface geology (ESG 2006), the complete results of which are reported elsewhere (Tsuno et al., 2009).

While initial, blind computations significantly differed from one another, a remarkable fit was obtained after correcting for some nonmethodological errors for four 3D methods: the arbitrary high-order derivative discontinuous Galerkin method (ADER-DGM), the velocity-stress finite-difference scheme on an arbitrary discontinuous staggered grid (FDM), and two implementations of the spectral-element method (SEM1 and SEM2). Their basic formulation is briefly recalled, and their implementation for the Grenoble Valley and the corresponding requirements in terms of computer resources are detailed.

Besides a visual inspection of PGV maps, more refined, quantitative comparisons based on time-frequency analysis greatly help in understanding the origin of differences, with a special emphasis on phase misfit. The match is found excellent below 1 Hz, and gradually deteriorates for increasing frequency, reflecting differences in meshing strategy, numerical dispersion, and implementation of damping properties.

While the numerical prediction of ground motion cannot yet be considered a mature, push-button approach, the good agreement reached by four participants indicates that, when used properly, numerical simulation is actually able to handle correctly wave radiation from extended sources in complex 3D media. The main recommendation to obtain reliable numerical predictions of earthquake ground motion is to use at least two different but comparably accurate methods, for instance the present formulations and implementations of the FDM, SEM, and ADER-DGM.

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