Application of the Reflectionless Discrete Perfectly Matched Layer for Acoustic Wave Simulation

The perfectly matched layer (PML) is one of the most popular absorbing boundary conditions for simulating seismic waves. In theory, the PML can absorb incident waves at any incident angle and any frequency in a medium. However, numerical reflections will be generated after the PML has been discretized. Therefore, how to reduce the reflections of discrete PML has been a research topic for more than 2 decades. In this paper, we adopt the reflectionless discrete PML (RD-PML) for seismic wave and implement the RD-PML based on the acoustic wave equation, and then compare its absorbing performance with that of the conventional discrete PML. Our numerical experiments show that the RD-PML has advantages over the conventional discrete PML. In homogeneous model, a thick enough RD-PML can effectively eliminate reflections. In heterogeneous model, a thin-layer RD-PML can obtain better absorbing performance even than the thick-layer conventional discrete PML. The absorbing performance of the RD-PML can be improved by using the periodic boundary without increasing the amount of computation and memory. RD-PML provides a new perspective to understand the discretization of PML, and may play an important role in promoting the development of PML technology.