Modeling seismic wave propagation and amplification in 1D/2D/3D linear and nonlinear unbounded 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, and so on. All these methods have various advantages and drawbacks to analyze the propagation of seismic waves. In surficial soil layers, seismic waves may be strongly amplified because of 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. Two-dimensional/three dimensional (2D/3D) models are needed in many situations, and the efficiency/accuracy of the numerical methods in such cases is in question. Furthermore, the radiation conditions at infinity are not easy to handle with finite differences or finite/spectral elements, whereas it is explicitly accounted for in the boundary element method. Various absorbing layer methods (e.g., F-PML, M-PML, CALM) were recently proposed to attenuate the spurious wave reflections, especially in some difficult cases, such as shallow numerical models or grazing incidences. Finally, strong earthquakes may involve nonlinear effects in surficial soil layers. To model strong ground motion, it is thus necessary to consider the nonlinear dynamic behavior of soils and simultaneously investigate seismic wave propagation in complex 2D/3D geological structures. Recent advances in numerical formulations and constitutive models in such complex situations are presented and discussed in this paper. A crucial issue is the availability of the field/laboratory data to feed and validate such models.