ARTICLE

Simulation of microseismic wave propagation using high-order finite difference velocity implementation on both source and media

YI YAO1,2,3 YIBO WANG1,2,* QINGFENG XUE1,2,3 XU CHANG1,2
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1 Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, P.R. China.,
2 Institution of Earth Science, Chinese Academy of Sciences, Beijing 100029, P.R.China.,
3 University of Chinese Academy of Sciences, Beijing 100049, P.R. China.,
JSE 2021, 30(1), 45–64;
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/ )
Abstract

Yao, Y., Wang, Y., Xue, Q.F. and Chang, X., 2021. Simulation of microseismic wave propagation using high-order finite difference velocity implementation on both source and media. Journal of Seismic Exploration, 30: 45-64. The characteristics of micro-seismic wave propagation of different source types have raised the interest of seismologists in the past few decades. When using staggered grid finite difference method as simulator, we need to establish a computational staggered grid which has N-th order accuracy and then do source implementation on this grid. There are two kinds of source implementations. One is the stress implementation, which applies the body force onto stress grid directly, and the other is the velocity implementation, which needs to convert body force into velocity component first and then applies the converted velocity component onto velocity grid. The existing velocity implementations mostly do the force-to-velocity conversion based on second-order accuracy, and this kind of implementation is fine when the wave propagation simulator also has second-order accuracy. However, with the increasing accuracy of finite difference simulator, there will be increasing errors due to the calculation order difference between wave propagation simulator and force-to-velocity conversion. We propose a N-th order staggered grid finite difference simulation formula which also has N-th order accuracy of force-to-velocity conversion. We make comparisons with analytical solutions in 3D homogeneous medium, and the results show the effectiveness and high accuracy of proposed approach.

Keywords
microseismic propagation simulation
moment tensor
high-order velocity implementation
staggered grid finite difference
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing