Parallel 3-D simulation of seismic wave propagation in heterogeneous anisotropic media: a grid method approach

Abstract

SUMMARY This paper presents a parallel numerical technique for modelling wave propagation in 3-D heterogeneous anisotropic media. The scheme is developed by following a so-called 3-D grid method of the elastic-isotropic case. The proposed parallel algorithm needs small data exchanges between subdomains in contrast to that developed based on other numerical techniques; therefore, it is more suitable for a PC-Cluster. The algorithm is implemented on a mesh of mixed tetrahedrons and parallelepipedons, thus providing an accurate description of arbitrary 3-D surface and interface topographies and an easy generation of a non-uniform, unstructured mesh. The unstructured mesh means that the proposed algorithm can reduce the memory requirement by flexibly assigning small grid spacing in regions with low velocities and larger grid spacing in regions with higher velocities. Like the 3-D grid method, the resulting anisotropic scheme naturally satisfies the free-surface boundary conditions of arbitrary surface topography. As a result, the near-surface scattering effects can be more accurately modelled. The proposed scheme can handle a general anisotropy without any interpolations. In this paper, the transversely isotropic medium with a tilted symmetry axis, as typically caused by a system of parallel cracks or fine layers, is discussed in detail. A paraxial absorbing boundary condition in a 3-D general anisotropic case is also proposed. Comparisons with analytical solutions demonstrate the accuracy of the parallel algorithm. Computed 3-D radiation patterns illustrate shear-wave splitting, as predicted by the theory. We show the generality and flexibility of the algorithm by modelling wave propagation in an anisotropic half-space with a hemispherical crater on the surface and in mixed isotropic/anisotropic models with horizontal and inclined interfaces.