Elastic wave propagation in heterogeneous anisotropic media using the lumped finite‐element method

Abstract

A numerical technique for wave‐propagation simulation in 2‐D heterogeneous anisotropic structures is presented. The scheme is flexible in incorporating arbitrary surface topography, inner openings, liquid/solid boundaries, and irregular interfaces, and it naturally satisfies the free‐surface conditions of complex geometrical boundaries. The algorithm, based on a discretization mesh of triangles and quadrilaterals, solves the problem using integral equilibrium around each node instead of satisfying elastodynamic differential equations at each node as in the finite‐difference method. This study is an extension of previous work for the elastic‐isotropic case. Besides accounting for anisotropy, a simplified quadrilateral grid cell with low computational cost is introduced. The transversely isotropic medium with a symmetry axis on the horizontal or vertical plane, as typically caused by a system of parallel cracks or fine layers, is discussed in detail. A 2‐D algorithm is presented that can handle the situation where the symmetry axis of the anisotropy does not lie in the 2‐D plane. The proposed scheme is successfully tested against an analytical solution for Lamb's problem with a symmetry axis normal to the surface and agrees well with a numerical solution of the reflectivity method for a plane‐layered model in the isotropic case. Computed radiation patterns show characteristics such as shear‐wave splitting and triplications of quasi‐SV wavefronts, as predicted by the theory. Examples of surface‐wave propagation in an anisotropic half‐space with a semicylindrical pit on the surface and mixed liquid/(anisotropic) solid model with an inclined liquid/solid interface are presented. Moreover, seismograms are modeled for dome‐layered and plane‐layered anisotropic structures.