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Time-domain formulation of a perfectly matched layer for the second-order elastic wave equation with VTI media

JAEJOON LEE1 ,  CHANGSOO SHIN2
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1 Computational Science and Technology Program, Seoul National University, Seoul, South Korea.,
2 Department of Energy System Engineering, Seoul National University, Seoul, South Korea.,
JSE 2015, 24(3), 231–257;
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/ )
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Abstract

Lee, J. and Shin, C.S., 2015. Time-domain formulation of a perfectly matched layer for the second-order elastic wave equation with VTI media. Journal of Seismic Exploration, 24: 231-257. In this study, we introduce the unsplit Perfectly Matched Layer (PML) for the 2D and 3D second-order elastic wave equations with isotropic and transversely isotropic vertical axis of symmetry (VTI) media in the time domain. The introduced PML formulations are successfully applied to practical applications in terms of efficiency and stability. The PML formulations require less than or an equal number of auxiliary variables than other formulations, thereby decreasing the computational power necessary to calculate the solution in the PML zone. Derived directly from the second-order wave form, the PML formulation demonstrates an improved stability compared to first-order PMLs or second-order PMLs that are derived from first-order systems. Numerical examples demonstrate that the bulk waves and strong surface waves are perfectly damped out without introducing instability for an isotropic material in both 2D and 3D. The derived formulation also provides effective absorption with strong VTI materials, including zinc and apatite, that cause instability problems in other PML formulations.

Keywords
perfectly matched layer
time-domain seismic wave modeling
second-order elastic wave equation
VTI media
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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