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The application of the nearly optimal sponge boundary conditions for seismic wave propagation in poroelastic media

JINGYI CHEN1* ,  RALPH PHILLIP BORDING1 ,  ENRU LIU2 ,  ZHONGJIE ZHANG3 ,  JOSÉ BADAL4
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1 Department of Earth Sciences, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1B 3X5,
2 ExxonMobil Upstream Research Company, Geophysics Division, Houston, TX 77252-2189, U.S.A.,
3 State Key Laboratory of Lithosphere Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China,
4 Physics of the Earth, Sciences B, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain,
JSE 2010, 19(1), 1–19;
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

Chen, J., Bording, J.P., Liu, E., Zhang, Z. and Badal, J., 2010. The application of the nearly optimal sponge boundary conditions for seismic wave propagation in poroelastic media. Journal of Seismic Exploration, 19: 1-19. Absorbing boundary conditions (ABC) play an important role in eliminating artificial reflections from the edges of the seismic model. In this paper, we present a modified nearly optimal sponge boundary condition. Utilizing the measure of reflected wave energy it is possible to construct a contour map for a range of sponge absorption coefficients and numbers of grid points at tapered zone, and determine the best set of parameters to minimize this energy metric. We apply this optimal scheme to the numerical simulation of seismic wave propagation in 2D transversely isotropic poroelastic media using staggered-grid finite-difference operator. We consider a first-order hyperbolic system that is equivalent to Biot/squirt equation. The vector of unknowns in this system consists of the solid and fluid particle velocity components, the solid stress components and the fluid pressure. Eighth-order accuracy in space and second-order accuracy in time are used in our numerical computation. Modeling studies indicate remarkably good results, the nearly optimal sponge boundary conditions is simple and effective enough to eliminate the artificial reflections from the boundaries of the model.

Keywords
boundary conditions
numerical modeling
poroelastic media
Biot/squirt mechanism
staggered-grid finite-difference
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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