1887
Volume 64, Issue 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

We propose new implicit staggered‐grid finite‐difference schemes with optimal coefficients based on the sampling approximation method to improve the numerical solution accuracy for seismic modelling. We first derive the optimized implicit staggered‐grid finite‐difference coefficients of arbitrary even‐order accuracy for the first‐order spatial derivatives using the plane‐wave theory and the direct sampling approximation method. Then, the implicit staggered‐grid finite‐difference coefficients based on sampling approximation, which can widen the range of wavenumber with great accuracy, are used to solve the first‐order spatial derivatives. By comparing the numerical dispersion of the implicit staggered‐grid finite‐difference schemes based on sampling approximation, Taylor series expansion, and least squares, we find that the optimal implicit staggered‐grid finite‐difference scheme based on sampling approximation achieves greater precision than that based on Taylor series expansion over a wider range of wavenumbers, although it has similar accuracy to that based on least squares. Finally, we apply the implicit staggered‐grid finite difference based on sampling approximation to numerical modelling. The modelling results demonstrate that the new optimal method can efficiently suppress numerical dispersion and lead to greater accuracy compared with the implicit staggered‐grid finite difference based on Taylor series expansion. In addition, the results also indicate the computational cost of the implicit staggered‐grid finite difference based on sampling approximation is almost the same as the implicit staggered‐grid finite difference based on Taylor series expansion.

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/content/journals/10.1111/1365-2478.12325
2015-10-01
2024-04-23
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References

  1. AbokhodairA.A.2009. Complex differentiation tools for geophysical inversion. Geophysics74, H1–H11.
    [Google Scholar]
  2. BansalR. and SenM.K.2008. Finite‐difference modelling of S‐wave splitting in anisotropic media. Geophysical Prospecting56, 293–312.
    [Google Scholar]
  3. ChangS. and LiuY.2013. A truncated implicit high‐order finite‐difference scheme combined with boundary conditions. Applied Geophysics10, 53–62.
    [Google Scholar]
  4. ChuC.2009. Seismic modeling and imaging with the Fourier method: numerical analyses and parallel implementation strategies. PhD dissertation, The University of Texas at Austin, USA.
    [Google Scholar]
  5. ChuC. and StoffaP.L.2010. Frequency domain modeling using implicit spatial finite difference operators. 80thSEG Annual International Meeting, Denver, USA, Expanded Abstracts, 3076–3080.
    [Google Scholar]
  6. ChuC. and StoffaP.L.2012a. Implicit finite‐difference simulations of seismic wave propagation. Geophysics77, T57–T67.
    [Google Scholar]
  7. ChuC. and StoffaP.L.2012b. Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media. Journal of Applied Geophysics76, 44–49.
    [Google Scholar]
  8. ClaerboutJ.F.1985. Imaging the Earth's Interior. Blackwell Scientific Publications.
    [Google Scholar]
  9. DongL., MaZ. and CaoJ.2000. A study on stability of the staggered‐grid high‐order difference method of first‐order elastic wave equation. Chinese Journal of Geophysics (in Chinese) 43, 856–864.
    [Google Scholar]
  10. EmermanS., SchmidtW. and StephenR.1982. An implicit finite‐difference formulation of the elastic wave equation. Geophysics47, 1521–1526.
    [Google Scholar]
  11. FornbergB.1998. Calculation of weights in finite difference formulas. SIAM Review40, 685–691.
    [Google Scholar]
  12. KomatitschD. and VilotteJ.1998. The spectral element method: An efficient tool to simulate the seismic response of 2D and 3D geological structures. Bulletin of the Seismological Society of America88, 368–392.
    [Google Scholar]
  13. KosloffD. and BaysalE.1982. Forward modeling by a Fourier method. Geophysics47, 1402–1412.
    [Google Scholar]
  14. KosloffD., PestanaR. and Tal‐EzerH.2008. Numerical solution of the constant density acoustic wave equation by implicit spatial derivative operators. SEG 78th Annual International Meeting, Las Vegas, USA, Expanded Abstracts, 2057–2061.
    [Google Scholar]
  15. KosloffD., PestanaR. and Tal‐EzerH.2010. Acoustic and elastic numerical wave simulations by recursive spatial derivative operators. Geophysics75, T167–T174.
    [Google Scholar]
  16. LisitsaV. and VishnevskiyD.2010. Lebedev scheme for the numerical simulation of wave propagation in 3D anisotropic elasticity. Geophysical Prospecting58, 619–635.
    [Google Scholar]
  17. LiuY.2014. Optimal staggered‐grid finite‐difference schemes based on least‐squares for wave equation modelling. Geophysical Journal International197, 1033–1047.
    [Google Scholar]
  18. LiuY. and SenM.K.2009a. A practical implicit finite‐difference method: examples from seismic modeling. Journal of Geophysics and Engineering6, 231–249.
    [Google Scholar]
  19. LiuY. and SenM.K.2009b. An implicit staggered‐grid finite‐difference method for seismic modeling. Geophysical Journal International179, 459–474.
    [Google Scholar]
  20. LiuY. and SenM.K.2011. Scalar wave equation modeling with time‐space domain dispersion‐relation‐based staggered‐grid finite‐difference schemes. Bulletin of the Seismological Society of America101, 141–159.
    [Google Scholar]
  21. McClellanJ.H. and ParksT.W.1972. Equiripple approximation of fan filters. Geophysics37, 573–583.
    [Google Scholar]
  22. VirieuxJ.1984. SH‐wave propagation in heterogeneous media: velocity stress finite‐difference method. Geophysics49, 1933–1957.
    [Google Scholar]
  23. VirieuxJ.1986. P‐SV wave propagation in heterogeneous media: velocity stress finite difference method. Geophysics51, 889–901.
    [Google Scholar]
  24. VirieuxJ., CalandraH. and PlessixR.2011. A review of the spectral, pseudo‐spectral, finite‐difference and finite‐element modeling techniques for geophysical imaging. Geophysical Prospecting59, 794–813.
    [Google Scholar]
  25. VishnevskyD., LisitsaV., TcheverdaV. and ReshetovaG.2014. Numerical study of the interface errors of finite‐difference simulations of seismic waves. Geophysics79, T219–T232.
    [Google Scholar]
  26. WuW., LinesL.R. and LuH.1996. Analysis of higher‐order, finite‐difference schemes in 3‐D reverse time migration. Geophysics61, 845–856.
    [Google Scholar]
  27. YanH. and LiuY.2013. Visco‐acoustic pre‐stack reverse‐time migration based on the time‐space domain adaptive high‐order finite‐difference method. Geophysical Prospecting61, 941–954.
    [Google Scholar]
  28. YangL., YanH. and LiuH.2014. Least squares staggered‐grid finite‐difference for elastic wave modeling. Exploration Geophysics45(4), 255–260.
    [Google Scholar]
  29. ZhangH., ZhangY. and SunJ.2007. Implicit splitting finite difference scheme for multi‐dimensional wave simulation. SEG 77th Annual International Meeting, San Antonio, USA, Expanded Abstracts, 2011–2015.
    [Google Scholar]
  30. ZhouH. and ZhangG.2011. Prefactored optimized compact finite difference schemes for second spatial derivatives. Geophysics76, WB87–WB95.
    [Google Scholar]
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