ORIGINAL RESEARCH article
Front. Earth Sci.
Sec. Solid Earth Geophysics
This article is part of the Research TopicThe State-of-Art Techniques of Seismic Imaging for the Deep and Ultra-deep Hydrocarbon Reservoirs - Volume IIIView all 8 articles
Elastic wave equation numerical simulation with time-space domain dispersion-relation-based staggered-grid finite-difference method
Provisionally accepted
Xuewen Shi1,2Chang Wang1,2,3
Wei Liu4,5*Dongjun Zhang1,2
Hu ZiDuo5,6Yanwen Feng1,2Yang Gao1,2Zhiwen Zhou1,2- 1Shale Gas Research Institute, PetroChina Southwest Oil & Gas Field Company, Chengdu, China
- 2Sichuan Provincial Key Laboratory of Shale Gas Evaluation and Exploitation, Chengdu, China
- 3BGP Inc., China National Petroleum Corporation, Zhuozhou, China
- 4Research Institute of Petroleum Exploration & Development-Northwest, PetroChina, Lanzhou, China
- 5PetroChina Key Laboratory of Reservoir Description, Lanzhou, China
- 6PetroChina Research Institute of Petroleum Exploration & Development-Northwest, Lanzhou, China
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Compared to the conventional high-order staggered-grid finite-difference method (C-SFD), the 3 time-space domain dispersion-relation-based high-order staggered-grid finite-difference method 4 (TS-SFD) is able to suppress the numerical dispersion more efficiently to achieve higher modelling 5 accuracy when applied to numerically solving the velocity-stress acoustic equation. The enhanced 6 modelling accuracy of TS-SFD is attributed to the difference coefficients calculating approach 7 based on the time-space domain dispersion-relation, which makes the difference coefficients 8 change adaptively with the propagation velocity of seismic wave in the medium. However, when 9 numerical simulation of the velocity-stress elastic wave equation is conducted with TS-SFD, if the 10 difference coefficients are calculated based on the time-space domain P-wave dispersion-relation, 11 the modelling accuracy of P-wave is high while the modelling accuracy of S-wave is low, and 12 vice versa. In order to address the limitation of TS-SFD in ensuring high modelling accuracy 13 for both Pand S-wave, in this paper we propose a novel strategy to conduct elastic wave 14 numerical simulation with TS-SFD, in which the decoupled Pand S-wave elastic wave equation 15 are numerically solved with TS-SFD, and the difference coefficients are calculated based on the 16 time-space domain Pand S-wave dispersion-relation respectively. Numerical dispersion analysis 17 and numerical simulation examples show that the simulation strategy proposed in this paper 18 can ensure high simulation accuracy for both Pand S-wave. Stability analysis shows that this 19 simulation strategy can effectively improve the stability of elastic wave numerical simulation with 20 TS-SFD. In addition, the simulation strategy has the added advantage of automatically separating 21 the Pand S-wave, which provides a solid foundation for the subsequent analysis of Pand 22 S-wave propagation characteristics in elastic media and elastic wave reverse time migration.
Keywords: Elastic wave, numerical modelling, numerical dispersion, Time-space domain, Difference coefficient calculation
Received: 29 Jul 2025; Accepted: 30 Nov 2025.
Copyright: © 2025 Shi, Wang, Liu, Zhang, ZiDuo, Feng, Gao and Zhou. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Wei Liu
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