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A generalized 17-point scheme based on the directional derivative method for highly accurate finite-difference simulation

WEI LIU1,2 ,  YANMIN HE1,2 ,  SHU LI1,3 ,  HAO WU1,2 ,  LIFENG YANG1,2 ,  ZHENMING PENG1,2
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1 School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 610054, P.R. China.,
2 Information Geoscience Research Center, University of Electronic Science and Technology of China, Chengdu 610054, P.R. China.,
3 School of Information Science and Engineering, Jishou University, Jishou 416000, P.R. China.,
JSE 2019, 28(1), 4–34;
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

Liu, W., He, Y.M., Li, S, Wu, H., Yang, L.F. and Peng, Z.M., 2019. A generalized 17- point scheme based on the directional derivative method for highly accurate finite- difference simulation of the frequency-domain 2D scalar wave equation. Journal of Seismic Exploration, 28: 41-71. Forward modeling of the frequency-domain wave equation represents an essential foundation for full waveform inversion in the frequency domain, the accuracy and efficiency of which rely heavily on the forward modeling method employed. To reduce the numerical dispersion, anisotropy, and number of grids per the shortest wavelength in forward modeling methods, rotating coordinate systems have been successfully applied to establish finite-difference (FD) schemes for the forward modeling of the frequency- domain wave equation. However, rotated optimal FD schemes are incapable of handling rectangular sampling grids, which are ubiquitous in practice. Fortunately, optimal FD schemes based on the average-derivative method (ADM) overcome this restriction on different directional sampling intervals. However, the ADM itself is merely an algebraic approach and therefore does not inherit the geometrical properties of the rotating coordinate system. Based on the principle of a rotating coordinate system, a novel optimal directional derivative method (DDM)-based 4th-order, 17-point FD scheme is developed in this paper for the forward modeling of the frequency-domain, two- dimension scalar wave equation to approximate the spatial derivatives. The conventional 0963-065 1/19/$5.00 © 2019 Geophysical Press Ltd. 42 4th-order, 9-point scheme and rotated optimal 17-point FD scheme can be derived as special cases of the proposed scheme. Compared with the rotated optimal 17-point FD scheme, the proposed scheme is capable of addressing arbitrary rectangular sampling grids, including equal and unequal directional sampling intervals; moreover, the optimized weighted coefficients can reduce the number of grids per the shortest wavelength from 2.56 to less than 2.4 with maximum phase velocity errors of 1%. Furthermore, the proposed scheme is superior to the ADM-based optimal 17-point FD scheme in suppressing numerical dispersion due to the inherited geometrical properties of the rotating coordinate system. A perfectly matched layer boundary condition is applied to the final FD equation to attenuate boundary reflections. Numerical examples demonstrate the validity and adaptability of our 17-point FD scheme.

Keywords
seismic forward modeling
acoustic wave equation
frequency domain
finite difference
numerical dispersion analysis
directional derivative
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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