1887
Volume 52, Issue 2
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

The finite difference method is widely used in seismic wave numerical simulation, reverse time migration and full waveform inversion. However, the numerical dispersion problem seriously affects the results of seismic imaging and inversion. Based on this, we introduced cosine-combined window function (CCWF) used in harmonic analysis of the power system and compared the amplitude response and error properties with other window functions. Then, an optimised CCWF and a new weighting method are proposed, which results in finite-difference operators with not only large spectral coverage but also small precision error fluctuation. In this paper, the analysis shows the good stability of using finite difference operators. Finally, we perform numerical forward modelling, which denotes that our method is superior than other optimum methods. From an economic point of view, this method will effectively reduce the computation cost and improve efficiency.

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2021-03-04
2026-01-16
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References

  1. Alterman, Z., and F.C.KaralJr. 1968. Propagation of elastic waves in layered media by finite difference methods. Bulletin of the Seismological Society of America58, no. 1: 367–98.
    [Google Scholar]
  2. Bashir, Y., and D.Prasad Ghosh. 2019. Advance wave modeling and diffractions for high-resolution subsurface seismic imaging. In Applied geophysics with case studies on environmental, exploration and engineering geophysics, ed. Ali Ismet Kanlı. IntechOpen.
    [Google Scholar]
  3. Baysal, E., D.D.Kosloff, and J.W.C.Sherwood. 1983. Reverse time migration. Geophysics48, no. 11: 1514–24. doi:10.1190/1.441434.
    [Google Scholar]
  4. Cheng, B.J., L.I.Xiao-Fan, and G.H.Long. 2008. Seismic waves modeling by convolutional Forsyte polynomial differentiator method. Chinese Journal of Geophysics51, no. 2: 378–85.
    [Google Scholar]
  5. Chu, C.L., and P.L.Stoffa. 2012. Determination of finite-difference weights using scaled binomial windows. Geophysics77: W17–W26. doi:10.1190/GEO2011-0336.1.
    [Google Scholar]
  6. Diniz, P.S.R., E.A.B.D.Silva, and S.L.Netto, 2012. Digital signal processing system analysis and design. Beijing: China Machine Press.
  7. Fornberg, B.1987. The pseudospectral method: Comparisons with finite differences for the elastic wave equation. Geophysics52: 483–501. doi:10.1190/1.1442319.
    [Google Scholar]
  8. Huang, S., X.Fan, S.Liu, and S.Yang. 2010. Optimized combined cosine window functions with maximum side lobe decay speed for harmonic analysis. Information & Control39, no. 4: 435–40.
    [Google Scholar]
  9. Kelly, K.R., R.W.Ward, S.Treitel, and R. M.Alford. 2012. Synthetic seismograms – a finite-difference approach. Numerical Modeling of Seicmic Wave Propagation41: 2–27.
    [Google Scholar]
  10. Lee, C., and Y.Seo. 2002. A new compact spectral scheme for turbulence simulations. Journal of Computational Physics183, no. 2: 438–69. doi:10.1006/jcph.2002.7201.
    [Google Scholar]
  11. Liu, Y.2013. Globally optimal finite-difference schemes based on least squares. Geophysics78: T113–T132. doi:10.1190/geo2012-0480.1.
    [Google Scholar]
  12. Liu, Y., and M.K.Sen. 2009a. A new time–space domain high-order finite-difference method for the acoustic wave equation. Journal of Computational Physics228, no. 23: 8779–806. doi:10.1016/j.jcp.2009.08.027.
    [Google Scholar]
  13. Liu, Y., and M.K.Sen. 2009b. Numerical modeling of wave equation by a truncated high-order finite-difference method. Earthquake Science22, no. 2: 205–13. doi:10.1007/s11589-009-0205-0.
    [Google Scholar]
  14. Madariaga, R.1976. Dynamics of an expanding circular fault. Bulletin of the Seismological Society of America66, no. 3: 639–66.
    [Google Scholar]
  15. Rao, Y., and Y.Wang. 2018. Seismic waveform simulation for models with fluctuating interfaces. Scientific Reports8, no. 1: 3098.
    [Google Scholar]
  16. Wang, J., X.H.Meng, H.Liu, W.Q.Zheng, and S.Gui. 2017. Cosine-modulated window function-based staggered-grid finite-difference forward modeling. Applied Geophysics14, no. 1: 115–24.
    [Google Scholar]
  17. Wang, Z.Y., H.Liu, X.D.Tang, and Y.Wang. 2014. Optimized finite-difference operators based on Chebyshev auto-convolution combined window function. Chinese Journal of Geophysics(in Chinese)58, no. 2: 628–42.
    [Google Scholar]
  18. Yang, L., H.Yan, and H.Liu. 2014. Elastic wave modeling with staggered-grid finite-difference based on least squares. Global Meeting. Society of Exploration Geophysicists and Chinese Petroleum Society.
  19. Yang, L., H.Yan, and H.Liu. 2017. An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling. Journal of Applied Geophysics138: 161–71.
    [Google Scholar]
  20. Zhou, B.Z., and S.Greenhalgh. 1992. Seismic scalar wave equation modeling by a convolutional differentiator. Bulletin of the Seismological Society of America82, no. 1: 289–303.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): 2D modelling; finite difference; optimisation; Seismic exploration; wave equation

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