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A modified NAD algorithm with minimum numerical dispersion for simulation of anisotropic wave propagation

DINGHUI YANG1 ,  GUOJIE SONG2 ,  JINHUA ZHANG3
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1 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P.R. China. dhyang@math.tsinghua.edu.cn,
2 College of Sciences, Southwest Petroleum University, Chengdu 610500, P.R. China.,
3 Kunming Vocational and Technical College of Industry, Yunnan, P.R. China.,
JSE 2010, 19(1), 21–42;
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

Yang, D., Song, G. and Zhang, J., 2010. A modified NAD algorithm with minimum numerical dispersion for simulation of anisotropic wave propagation. Journal of Seismic Exploration, 19: 21-42. Conventional explicit finite-difference methods for solving the elastic-wave equation suffer from numerical dispersion when too few samples per wavelength are used. A nearly analytic discrete method for suppressing the numerical dispersion was proposed recently by Yang et al. (2003a). In this paper, we present a modified algorithm of the nearly-analytic discrete method (NADM) for modelling seismic propagation in 2D anisotropic media. We also investigate the numerical dispersion of the modified algorithm using numerical examples and compare numerically the dispersion errors and the wavefield results computed using the modified algorithm against those of our previous method and other finite-difference (FD) methods. We show that, compared with the improved NADM, the modified algorithm for the 2D case can further minimize the numerical dispersion, while its computational cost and storage space are the same as those of our previous method. Wavefield snapshot for two-layer heterogeneous medium and three-component synthetic VSP seismograms in three-layer transversely isotropic media with a vertical symmetry axis, generated using the modified algorithm, are also reported. Numerical results demonstrate that the modified algorithm further reduces the numerical dispersion and source noise caused by the discretization of elastic-wave equations when too few samples per wavelength are used or when models have large velocity contrast and strong anisotropy.

Keywords
modified NAD algorithm
numerical dispersion
wavefield simulation
seismic anisotropy
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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