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Optimization of staggered grid finite-difference coefficients based on conjugate gradient method

KEJIE JIN1,2 ,  JIANPING HUANG1,2 ,  QIANG ZOU3 ,  ZIYING WANG1,2 ,  SIYOU TONG4 ,  BIN LIU5 ,  ZIDUO HU6
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1 School of Geosciences, China University of Petroleum (East China), Qingdao 266580, P.R. China.,
2 Laboratory for Marine Mineral Resources, Pilot National Laboratory for Marine Science and Technology (Qingdao), Qingdao 266071, P.R. China.,
3 Tarim Oilfield Branch, CNPC, Korla 841000, P.R. China.,
4 College of Marine Geosciences, Ocean University of China, Qingdao 266100, P.R. China.,
5 Research and Development Center Sinopec Geophysical Corp, Nanjing 210009, P.R. China.,
6 Northwest Branch, Research Institute of Petroleum Exploration & Development， PetroChina, Lanzhou 730020, P.R. China.,
JSE 2022, 31(1), 33–52;
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

The implementation of difference coefficients optimization strategy can effectively suppress numerical dispersion and improve the modeling accuracy. The conventional difference coefficients calculation method based on Taylor-series Expansion exists serious numerical dispersion. In this paper, we derive a new dispersion error function from the dispersion relation, and the optimal difference coefficients are obtained iteratively by using the conjugate gradient method, thus a staggered-grid difference coefficients optimization method based on the conjugate gradient is developed. We compare dispersion curves, snapshots and single shot records using low-velocity model, high-velocity model and Marmousi model, the results show that the new method can effectively reduce the numerical dispersion compared with the difference coefficients of the conventional Taylor-series Expansion method. The 8th-order optimized difference operators can achieve the modeling precision of 12th-order Taylor-series Expansion difference operators, which can effectively save calculation time and internal storage. The optimization method performs well for both simple model and complex model forward modeling.

Keywords
finite-difference
staggered grid
numerical dispersion
difference coefficients
conjugate gradient
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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