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An effective method to suppress numerical dispersion in 3D elastic modeling using a high-order Padé approximation

YANJIE ZHOU1 ,  XUEYUAN HUANG1 ,  XIJUN HE1 ,  YONGCHANG ZHENG2
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1 Department of Mathematics, School of Mathematics and Statistics, Beijing Technology and Business University (BTBU), Beijing 100048, P.R. China.,
2 Department of Liver Surgery, Peking Union Medical College Hospital, Chinese Academy of Medical Sciences, Beijing 100730, P.R. China.,
JSE 2020, 29(5), 425–454;
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

Zhou, Y.J., Huang, X.Y., He, X.J. and Zheng, Y.C., 2020. An effective method to suppress numerical dispersion in 3D elastic modeling using a high-order Padé approximation. Journal of Seismic Exploration, 29: 425-454. We proposed a numerical method for solving seismic wave equations called the fourth-order Padé approximation method (PAM). This work was an extension of the 2D PAM to the 3D case. We used the PAM for time discretization to obtain an implicit scheme, in which the time difference operator has a rational function form. To avoid solving large linear systems with a block tridiagonal coefficient matrix, we proposed an algorithm to transform the implicit scheme into an explicit method. For the spatial discretization, we adapted the nearly analytic discrete (NAD) operator, which uses a linear combination of wavefield displacements and their gradients to discretize higher-order spatial derivatives. In addition, for the fourth- and fifth-order mixed partial differential terms, we used operator splitting to reduce the order of the differential operators in the scheme and decrease the calculation time. The proposed scheme had higher precision with eighth-order accuracy in space, lower dispersion, and higher computational efficiency than the other Padé approximation-based approaches, which were fourth-order compact finite difference schemes that required solving a large tridiagonal system at each time step. The stability condition, relative error, and dispersion relation of the 3D PAM were analyzed. Comparisons of the theoretical and numerical results of the proposed method, the 3D Lax-Wendroff correction (LWC) method, and the staggered grid (SG) finite difference method demonstrated the superiority of the PAM for solving 3D seismic wave equations and its advantages of lower dispersion and higher computational efficiency. The results indicated that the 3D high-order PAM was an efficient and accurate forward modeling tool for solving large-scale wave propagation problems related to reverse time migration or full-waveform inversion.

Keywords
Padé approximation
forward method
wavefield modeling
numerical dispersion
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