PERFECTLY MATCHED LAYERS FOR THE SIMULATION OF ELASTIC WAVES IN ANISOTROPIC MEDIA

Abstract

This paper introduces perfectly matched layers (PMLs) for the simulation of elastic waves in heterogeneous anisotropic media. The PMLs are used as wave-absorbing boundaries to sur-round a finite computational domain of interest truncated from the originally semi-infinite ex-tent. In the formulation, standard Navier equations governing the wave motion in the regular domain are combined with mixed unsplit-field equations which yield the solution of attenuated waves within the PML. For the modeling of anisotropic material properties, the strain-stress relationship of the anisotropic material is incorporated into the constitutive relation of the mixed unsplit-field wave equations in PML-truncated domains. In this work, a transversely iso-tropic material is considered for elastic waves in a semi-infinite domain truncated by PML. The second-order semi-discrete form of the problem is constructed by using a mixed finite element method and integrated in time for the solution of displacements and stresses by using the New-mark time integration method. Numerical results are presented for elastic waves propagating in the transversely isotropic PML-truncated domain. The wave motion in the anisotropic me-dium is compared with that in the corresponding isotropic medium, and the effect of wave at-tenuation enforced by the developed anisotropic PML is shown by a series of numerical examples.