A second-order, perfectly matched layer formulation to model 3D transient wave propagation in anisotropic elastic media

TL;DR

This paper introduces a second-order 3D PML formulation for simulating transient wave propagation in anisotropic elastic media, enhancing accuracy and implementation in numerical schemes.

Contribution

It presents a novel second-order PML formulation for 3D anisotropic elastic wave modeling, including extensions to viscoelastic media, improving simulation fidelity.

Findings

PML acts as a near-perfect absorber for anisotropic media.

Finite element simulations validate the formulation's effectiveness.

Extension to viscoelastic media broadens application scope.

Abstract

Numerical simulation of wave propagation in an infinite medium is made possible by surrounding a finite region by a perfectly matched layer (PML). Using this approach a generalized three-dimensional (3D) formulation is proposed for time-domain modeling of elastic wave propagation in an unbounded lossless anisotropic medium. The formulation is based on a second-order approach that has the advantages of, physical relationship to the underlying equations, and amenability to be implemented in common numerical schemes. Specifically, our formulation uses three second-order equations of the displacement field and nine auxiliary equations, along with the three time histories of the displacement field. The properties of the PML, which are controlled by a complex two-parameter stretch function, are such that it acts as near perfect absorber. Using finite element method (FEM) 3D numerical results are presented for a highly anisotropic medium. An extension of the formulation to the particular case of a Kelvin-Vogit viscoelastic medium is also presented.