一维/二维/三维线性和非线性无界介质中地震波传播和放大的数值模拟
Modeling seismic wave propagation and amplification in 1D/2D/3D linear and nonlinear unbounded media
摘要：
分析地震波在地质构造中的传播，可以考虑各种数值方法：有限差分法、谱元法、边界元法、有限单元法、有限体积法等。地震波在地表土层中的放大主要是由于这些土层之间的速度差异，也可能是由于波峰和丘陵周围的地形影响。冲积盆地的几何形状对放大过程的影响也很大。然而，强不均匀性和复杂的几何形状是不容易考虑到所有的数值方法。在许多情况下需要2D/3D模型，并且在这种情况下数值方法的效率/精度是有问题的。此外，在无穷远的辐射条件是不容易处理的有限差分或有限/谱元素，而它是显式地考虑在边界元法。最近提出了各种吸收层方法（如F-PML，M-PML），特别是在一些困难的情况下，如浅的数值模型或掠入射衰减虚假波的反射。最后，强震涉及到表层土壤的非线性效应。为了模拟强地面运动，有必要考虑土壤的非线性动力特性，同时研究地震波在复杂的2D/3D地质结构中的传播。本文介绍和讨论了在这种复杂情况下的数值公式和本构模型的最新进展。一个关键问题是是否有实地/实验室数据来支持和验证这些模型。
英文摘要：
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, the radiation conditions at infinity are not easy to handle with finite differences or finite/spectral elements whereas it is explicitely accounted in the Boundary Element Method. Various absorbing layer methods (e.g. F-PML, M-PML) 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 involve nonlinear effects in surficial soil layers. To model strong ground motion, it is thus necessary to consider the nonlinear dynamic behaviour 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.
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