Application of the perfectly matched layer (PML) absorbing boundary condition to elastic wave propagation

Abstract

A method is presented for application of the perfectly matched layer (PML) absorbing boundary condition (ABC) to the P-SV velocity–stress finite-difference method. The PML consists of a nonphysical material, containing both passive loss and dependent sources, that provides ‘‘active’’ absorption of fields. It has been used in electromagnetic applications where it has provided excellent results for a wide range of angles and frequencies. In this work, numerical simulations are used to compare the PML and an ‘‘optimal’’ second-order elastic ABC [Peng and Toksöz, J. Acoust. Soc. Am. 95, 733–745 (1994)]. Reflection factors are used to compare angular performance for continuous wave illumination; snapshots of potentials are used to compare performance for broadband illumination. These comparisons clearly demonstrate the superiority of the PML formulation. Within the PML there is a 60% increase in the number of unknowns per grid cell relative to the velocity–stress formulation. However, the high quality of the PML ABC allows the use of a smaller grid, which can result in a lower overall computational cost.