A new Implementation of CPML for the Second-Order Wave Equation

Abstract

Summary The perfectly matched layer (PML) boundary condition has been widely used as a very effective absorbing boundary condition for seismic wavefield simulations. Convolutional PML (CPML) achieved by using a complex frequency-shifted stretch function was the latest development to further improve PML’s absorption performance for near-grazing angle incident waves as well as for low-frequency incident waves. However, the mathematical theory of most PML methods are derived from the first-order equation system; When implementing the PML technique to second-order wave equations, all the existing methods involve adding auxiliary terms and rewriting the CPML wave equations into the original coordinate, which will lead to the increase of calculation, more auxiliary variables, and complicate the implementation more than is necessary. We propose a new implementation of CPML for the second-order wave equation system. It does not need to introduce auxiliary variables or auxiliary equations for transforming the second-order CPML equations into the original coordinate, and furthermore, the implementation is simple and efficient.