A non-split perfectly matched layer absorbing boundary condition for the second-order wave equation modeling

The perfectly matched layer (PML) absorbing boundary conditions (ABC) have been well studied for seismic wavefield modeling. However, existing approaches are either based on a wavefield variable-split or are only applicable to first-order wave equations. In this paper, we present a non-split PML ABC for the second order wave equations in displacement. The principle of the proposed method lies in introducing a series of auxiliary variables to represent the partial derivatives associated with the stretching axis. We derive the non-split PML formula by using basic tensor algebra. The derived equations are in a compact form which makes the ABC condition easier for implementation in practice. Furthermore, as no extra splitting wavefield variables are introduced, the computer memory usage of wave equation modeling can be reduced accordingly. Numerical results for both acoustic and elastic examples show the quality of the performance of the proposed new method.