AccScience Publishing / JSE / Article
Submit to JSE
Cite this article
44
Views
Journal Browser
Volume | Year
Issue
Search
Forthcoming Issue
Current Issue
View All
News and Announcements
View All
ARTICLE

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

DINGHUI YANG1 ,  GUOJIE SONG2 ,  JINHUA ZHANG3
Show Less
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: 8 March 2009 | Accepted: 8 August 2009 | Published: 1 January 2010
© 2010 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/ )
Download PDF
Cite
XML
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
References
  1. Alford, R.M., Kelly, K.R. and Boore, D.M., 1974. Accuracy of finite-difference modeling of theacoustic wave equation. Geophysics, 39: 834-842.
  2. Blanch, J.O. and Robertsson, J.O.A., 1997. A modified Lax-Wendroff correction for wavepropagation in media described by Zener elements. Geophys. J. Int., 131: 381-386.
  3. Dablain, M.A., 1986. The application of high-order differencing to the scalar wave equation.Geophysics, 51: 54-66.
  4. Faria, E.L. and Stoffa, P.L., 1994. Finite-difference modelling in transversely isotropic media.Geophysics 59: 282-289.
  5. Fei, T. and Larner, K., 1995. Elimination of numerical dispersion in finite-difference modeling andmigration by flux-corrected transport. Geophysics, 60: 1830-1842.
  6. Fornberg, B., 1990. High-order finite differences and pseudo-spectral method on staggered grids.SIAM J. Numeric. Analys., 27: 904-918.
  7. Holberg, O., 1987. Computational aspects of the choice of operator and sampling interval fornumerical differentiation in large-scale simulation of wave phenomena. Geophys. Prosp., 35:629-655.
  8. Huang, B.S., 1992. A program for two-dimensional seismic wave propagation by thepseudospectrum method. Comput. Geosci., 18: 289-307.
  9. Igel, H., Mora, P. and Riollet, B., 1995. Anisotropic wave propagation through finite-differencegrids. Geophysics, 60: 1203-1216.
  10. Kelly, K., Ward, R., Treitel, S. and Alford, R., 1976. Synthetic seismograms: a finite-differenceapproach. Geophysics, 41: 2-27.
  11. Komatitsch, D., Barnes, C. and Tromp, J., 2000. Wave propagation near a fluid-solid interface: Aspectral-element approach. Geophysics, 65: 623-631.
  12. Kosloff, D. and Baysal, E., 1982. Forward modeling by a Fourier method. Geophysics, 47:1402-1412.
  13. Kosloff, D., Reshef, M. and Loewenthal, D., 1984. Elastic wave calculations by the Fouriermethod. Bull. Seismol. Soc. Am., 74: 875-891.
  14. Mizutani, H., Geller, R.J. and Takeuchi, N., 2000. Comparison of accuracy and efficiency oftime-domain schemes for calculating synthetic seismograms. Phys. Earth Planet. Inter., 119:75-97.
  15. Sei, A. and Symes, W., 1994. Dispersion analysis of numerical wave propagation and itscomputational consequences. J. Scient. Comput., 10: 1-27.
  16. Vichnevetsky, R., 1979. Stability charts in the numerical approximation of partial differentialequations: a review. Math. Comput. Simul., 21: 170-177.
  17. Virieux, J., 1986. P-SV wave propagation in heterogeneous media: Velocity-stress finite-differencemethod. Geophysics, 51: 889-901.
  18. Wang, S.Q., Yang, D.H. and Yang, K.D., 2002. Compact finite difference scheme for elasticequations. J. Tsinghua Univ. (Sci. & Tech.), 42: 1128-1131 (in Chinese).
  19. Yang, D.H., Liu, E., Zhang, Z.J. and Teng, J., 2002a. Finite-difference modelling intwo-dimensional anisotropic media using a flux-corrected transport technique. Geophys. J.Internat., 148: 320-328.MODIFIED NAD ALGORITHM 41
  20. Yang, D.H., Teng, J.W., Zhang, Z.J. and Liu, E., 2003a. A nearly-analytic discrete method foracoustic and elastic wave equations in anisotropic media. Bull. Seismol. Soc. Am., 93:882-890.
  21. Yang, D.H., Wang, S.Q., Zhang, Z.J. and Teng, J.W., 2003b. n-times absorbing boundaryconditions for compact finite difference modeling of acoustic and elastic wave propagationin the 2-D TI Medium. Bull. Seismol. Soc. Am., 93: 2389-2401.
  22. Yang, D.H., Peng, J.M., Lu, M. and Terlaky, T., 2006. Optimal nearly analytic discreteapproximation to the scalar wave equation. Bull. Seismol. Soc. Am., 96: 1114-1130.
  23. Yang, D.H., Song, G.J., Chen, S. and. Hou, B.Y., 2007a. An improved nearly analytical discretemethod: An efficient tool to simulate the seismic response of 2-D porous structures. J.Geophys. Engin., 4: 70-82.
  24. Yang, D.H., Chen, S. and Li, J.Z., 2007b. A Runge-Kutta method using high-order interpolationapproximation for solving 2D acoustic and elastic wave equations. J. Seismic Explor., 16:331-353.
  25. Yang, K.D., Yang, D.H. and Wang, S.Q., 2002b. Numerical simulation by the staggered gridmethod for the high frequency limited BISQ equation. Oil Geophys. Prosp., 37: 463-468 (inChinese).
  26. Zhang, Z.J., Wang, G.J. and Harris, J.M., 1999. Multi-component wavefield simulation in viscousextensively dilatancy anisotropic media. Phys. Earth Planet. Inter., 114: 25-38.
  27. Zheng, H.S. and Zhang, Z.J., 2005. Synthetic seismograms of nonlinear seismic waves inanisotropic media. Chinese J. Geophys., 48: 660-671 (in Chinese).
  28. Zheng, H.S., Zhang, Z.J. and Liu, E.R., 2006. Non-linear seismic wave propagation in anisotropicmedia using the flux-corrected transport technique. Geophys. J. Int., 165: 943-956.
Share
Back to top
Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here
Accept