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A weak dispersion 3D wave field simulation method: A predictor-corrector method of the implicit Runge-Kutta scheme

NIAN WANG1 ,  YANJIE ZHOU1,2
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1 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P.R. China. happyxiaoxi114@163.com,
2 Department of Mathematics, School of Science, Beijing Technology and Business University (BTBU), Beijing 100048, P.R. China.,
JSE 2014, 23(5), 431–462;
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

Wang, N. and Zhou, Y., 2014. A weak dispersion 3D wave field simulation method: A predictor-corrector method of the implicit Runge-Kutta scheme. Journal of Seismic Exploration, 23: 431-462. We propose a numerical method for solving the acoustic- and elastic-wave equations, which is called the predictor-corrector method of the implicit Runge-Kutta scheme (IRK-PCM). This work is an extension of the corresponding 2D IRK-PCM to the 3D case. To solve wave equations, we first transform them into a system of semi-discrete ordinary differential equations (ODEs). And then we use the local interpolation theory for spatial discretization, and use the 2-step predictor-corrector method based on an implicit Runge-Kutta method for the temporal discretization. In this paper, we investigate the theoretical property of the 3D IRK-PCM including stability criteria, approximation error, numerical dispersion, and computational efficiency when solving the acoustic wave equation. Seismic wave field simulations for both acoustic and elastic models show that the 3D IRK-PCM can suppress effectively the numerical dispersion caused by the discretization of wave equations when coarse grids are used, high frequency bands are chosen, or models have large velocity contrasts between adjacent layers. Whereas other high-order schemes such as the fourth-order LWC and the staggered-grid (SG) method suffer from serious numerical dispersion for the same cases. It suggests that to achieve the same accuracy, the 3D IRK-PCM can increase greatly the computational speed and save significantly the storage space. We conclude that the IRK-PCM provides us an useful tool for the 3D large-scale wave field simulation, reverse time migration and full waveform inversion.

Keywords
wave equation
wave-field simulation
numerical dispersion
implicit Runge-Kutta method
predictor-corrector method
anisotropy
shear wave splitting.
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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