A second-order, perfectly matched layer formulation to model 3D transient wave propagation in anisotropic elastic media
This work provides a physically motivated PML formulation for anisotropic media, enabling accurate time-domain simulation of unbounded wave propagation for geophysics and engineering applications.
The authors propose a second-order PML formulation for 3D transient wave propagation in anisotropic elastic media, using three second-order displacement equations and nine auxiliary equations. Numerical results with FEM demonstrate near-perfect absorption in a highly anisotropic medium, with extension to viscoelastic media.
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.