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To analyze seismic wave propagation in geological structures, it is possibleto consider various numerical approaches: the finite difference method, thespectral element method, the boundary element method, the finite elementmethod, the finite volume method, etc. All these methods have variousadvantages and drawbacks. The amplification of seismic waves in surface soillayers is mainly due to the velocity contrast between these layers and,possibly, to topographic effects around crests and hills. The influence of thegeometry of alluvial basins on the amplification process is also know to belarge. Nevertheless, strong heterogeneities and complex geometries are not easyto take into account with all numerical methods. 2D/3D models are needed inmany situations and the efficiency/accuracy of the numerical methods in suchcases is in question. Furthermore, the radiation conditions at infinity are noteasy to handle with finite differences or finite/spectral elements whereas itis explicitely accounted in the Boundary Element Method. Various absorbinglayer methods (e.g. F-PML, M-PML) were recently proposed to attenuate thespurious wave reflections especially in some difficult cases such as shallownumerical models or grazing incidences. Finally, strong earthquakes involvenonlinear effects in surficial soil layers. To model strong ground motion, itis thus necessary to consider the nonlinear dynamic behaviour of soils andsimultaneously investigate seismic wave propagation in complex 2D/3D geologicalstructures! Recent advances in numerical formulations and constitutive modelsin such complex situations are presented and discussed in this paper. A crucialissue is the availability of the field/laboratory data to feed and validatesuch models.

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