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A non-split perfectly matched layer absorbing boundary condition for the second-order wave equation modeling
C. ZHANG1,3 ,
B. SUN1 ,
H. YANG1 ,
J. MA2
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1
School of Aerospace, Tsinghua University, Beijing, P.R. China. bbsunok@126.com,
2
Department of Mathematics, Harbin Institute of Technology, Harbin, P.R. China.,
3
Department of Geophysics, Research Institute of Petroleum Exploration & Development, Beijing, P.R. China.,
JSE 2016, 25(6), 513–525;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract
Zhang, C., Sun, B., Yang, H. and Ma, J., 2016. A non-split perfectly matched layer absorbing boundary condition for the second-order wave equation modeling. Journal of Seismic Exploration, 25: 513-525. 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.
Keywords
perfectly matched layer
absorbing boundary condition
second-order
wave equation
seismic modeling
finite difference
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