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Modeling seismic wave propagation in 1D/2D/3D linear and nonlinear media

To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the finite volume method, etc. All these methods have various advantages and drawbacks. The amplification of seismic waves in surface soil layers is mainly due to the velocity contrast between these layers and, possibly, to topographic effects around crests and hills. The influence of the geometry of alluvial basins on the amplification process is also know to be large. Nevertheless, strong heterogeneities and complex geometries are not easy to take into account with all numerical methods. 2D/3D models are needed in many situations and the efficiency/accuracy of the numerical methods in such cases is in question. Furthermore, strong earthquakes implies nonlinear effects in surficial soil layers. To model strong ground motion, it is then necessary to consider the nonlinear dynamic behaviour of soils and simultaneously investigate seismic wave propagation in complex 2D/3D geometries ! Recent advances in numerical formulations and constitutive models in such complex situations are presented and discussed in this paper. Finally, a crucial point concerns the availability of the field/laboratory data to feed such models.