1887
Volume 53, Issue 6
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

Compared with the standard staggered-grid finite-difference (FD) methods, equivalent staggered-grid (ESG) ones can significantly reduce the computational memory for acoustic wave modelling in the variable-density media. To further enhance the simulation efficiency and accuracy, one way is to optimize the FD coefficients, another way is to design new FD stencils. In this paper, we propose a modified ESG (M-ESG) scheme which can significantly accelerate the wavefield simulation process while preserving or even improving the modelling accuracy. We calculate the FD coefficients by approximating the temporal and spatial derivatives simultaneously based on time–space domain (TS-D) dispersion relation of the discrete wave equation. Our M-ESG scheme in the TS-D can maintain basically the same accuracy as the conventional ESG (C-ESG) one when the FD coefficients are derived by the Taylor-series expansion (TE) approach. Note that the TS-D dispersion relation is nonlinear with respect to the FD coefficients of the C-ESG scheme, so it is difficult to obtain the optimized FD coefficients for the discrete wave equation. However, we can minimize the L2-norm error of the dispersion relation based on our M-ESG scheme to implement a linear FD coefficients optimization strategy, which is easy and efficient. Comparisons with TE- and optimization-based C-ESG schemes demonstrate the accuracy, stability, and efficiency superiorities of our TE- and optimization-based M-ESG ones.

© 2022 Australian Society of Exploration Geophysicists
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2022-11-02
2026-01-13

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References

  1. Chen, H., H.Zhou, and S.Sheng. 2016. General rectangular grid based time-space domain high-order finite-difference methods for modeling scalar wave propagation. Journal of Applied Geophysics133: 141–156.
     [Google Scholar]
  2. Chu, C., and P.L.Stoffa. 2012. Determination of finite-difference weights using scaled binomial windows. Geophysics77: W17–W26.
     [Google Scholar]
  3. Claerbout, J.F.1985. Imaging the Earth’s interior. Oxford: Blackwell Scientific Publications1: 47–49.
     [Google Scholar]
  4. Crase, E.1990. High-order (space and time) finite-difference modeling of the elastic wave equation. 60th Annual International Meeting, SEG, Expanded Abstracts, 987–991.
     [Google Scholar]
  5. Dablain, M.A.1986. The application of high-order differencing to the scalar wave equation. Geophysics51: 54–66.
     [Google Scholar]
  6. Di Bartolo, L., C.Dors, and W.J.Mansur. 2012. A new family of finite difference schemes to solve the heterogeneous acoustic wave equation. Geophysics77: T187–T199.
     [Google Scholar]
  7. Di Bartolo, L., C.Dors, and W.J.Mansur. 2015. Theory of equivalent staggered-grid schemes: application to rotated and standard grids in anisotropic media. Geophysical Prospecting63: 1097–1125.
     [Google Scholar]
  8. Di Bartolo, L., L.Lopes, and L.J.R.Lemos. 2017. High-order finite-difference approximations to solve pseudoacoustic equations in 3D VTI media. Geophysics82: T225–T235.
     [Google Scholar]
  9. Dong, L., Z.Ma, J.Cao, H.Wang, J.Geng, B.Lei, and S.Xu. 2000. A staggered-grid high-order difference method of one-order elastic wave equation. Chinese Journal of Geophysics-Chinese43: 411–419.
     [Google Scholar]
  10. Du, Q., B.Li, and B.Hou. 2009. Numerical modeling of seismic wavefields in transversely isotropic media with a compact staggered-grid finite difference scheme. Applied Geophysics6: 42–49.
     [Google Scholar]
  11. Koene, E.F.M., J.O.A.Robertsson, and F.Andersson. 2021. Anisotropic elastic finite-difference modeling of sources and receivers on lebedev grids. Geophysics86: A21–A25.
     [Google Scholar]
  12. Etemadsaeed, L., P.Moczo, J.Kristek, A.Ansari, and M.Kristekova. 2016. A no-cost improved velocity–stress staggered-grid finite-difference scheme for modelling seismic wave propagation. Geophysical Journal International207: 481–511.
     [Google Scholar]
  13. Etgen, J.T.2007. A tutorial on optimizing time domain finite difference schemes: “Beyond Holberg”. Stanford Exploration Project Report129: 33–43.
     [Google Scholar]
  14. Etgen, J.T., and M.J.O’Brien. 2007. Computational methods for large-scale 3D acoustic finite-difference modeling: a tutorial. Geophysics72: SM223–SM230.
     [Google Scholar]
  15. Faria, E.L., and P.L.Stoffa. 1994. Finite-difference modeling in transversely isotropic media. Geophysics59: 282–289.
     [Google Scholar]
  16. Fang, G., S.Fomel, Q.Du, and J.Hu. 2014. Lowrank seismic-wave extrapolation on a staggered grid. Geophysics79: T157–T168.
     [Google Scholar]
  17. Finkelstein, B., and R.Kastner. 2007. Finite difference time domain dispersion reduction schemes. Journal of Computational Physics221: 422–438.
     [Google Scholar]
  18. Finkelstein, B., and R.Kastner. 2008. A comprehensive new methodology for formulating FDTD schemes with controlled order of accuracy and dispersion. IEEE Antennas and Wireless Propagation Letters56: 3516–3525.
     [Google Scholar]
  19. Fornberg, B.1998. Calculation of weights in finite difference formulas. SIAM Review40: 685–691.
     [Google Scholar]
  20. Gao, L., and D.Keyes. 2020. Explicit coupling of acoustic and elastic wave propagation in finite-difference simulations. Geophysics85: T293–T308.
     [Google Scholar]
  21. Graves, R.W.1996. Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences. Bulletin of the Seismological Society of America86: 1091–1106.
     [Google Scholar]
  22. Hestholm, S.2009. Acoustic VTI modeling using high-order finite differences. Geophysics74: T67–T73.
     [Google Scholar]
  23. Itzá, R., U.Iturrarán-Viveros, and J.O.Parra. 2016. Optimal implicit 2-D finite differences to model wave propagation in poroelastic media. Geophysical Journal International206: 1111–1125.
     [Google Scholar]
  24. Kindelan, M., A.Kamel, and P.Sguazzero. 1990. On the construction and efficiency of staggered numerical differentiators for the wave equation. Geophysics55: 107–110.
     [Google Scholar]
  25. Levander, A.R., and D.E.James. 1989. Finite-difference forward modeling in seismology. In The encyclopedia of solid earth Geophysics, ed. D. E. James, 410–31. New York: Van Nostrand Reinhold.
  26. Liang, W., C.Wu, Y.Wang, and C.Yang. 2018. A simplified staggered-grid finite-difference scheme and its linear solution for the first-order acoustic wave-equation modeling. Journal of Computational Physics374: 863–872.
     [Google Scholar]
  27. Liu, Y.2013. Globally optimal finite-difference schemes based on least squares. Geophysics78: T113–T132.
     [Google Scholar]
  28. Liu, Y., and M.K.Sen. 2009a. An implicit staggered-grid finite-difference method for seismic modelling. Geophysical Journal International179: 459–474.
     [Google Scholar]
  29. Liu, Y., and M.K.Sen. 2009b. Numerical modeling of wave equation by truncated high-order finite difference method. Earthquake Science22: 205–213.
     [Google Scholar]
  30. Liu, Y., and M.K.Sen. 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]
  31. Liu, Y., and M.K.Sen. 2013. Time-space domain dispersion-relation-based finite-difference method with arbitrary even-order accuracy for the 2D acoustic wave equation. Journal of Computational Physics232: 327–345.
     [Google Scholar]
  32. Masson, Y., S.Pride, and K.Nihei. 2006. Finite difference modeling of Biot’s poroelastic equations at seismic frequencies. Journal of Geophysical Research: Solid Earth111: 1–12.
     [Google Scholar]
  33. Moczo, P., J.Kristek, and M.Galis. 2014. The finite-difference modelling of earthquake motions: waves and ruptures. Cambridge: Cambridge University Press.
  34. Moczo, P., J.Kristek, and L.Halada. 2000. 3D fourth-order staggered-grid finite-difference schemes: stability and grid dispersion. Bulletin of the Seismological Society of America90: 587–603.
     [Google Scholar]
  35. Moczo, P., J.Kristek, V.Vavrycuk, R.Archuleta, and L.Halada. 2002. Heterogeneous staggered-grid finite-difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli and densities. Bulletin of the Seismological Society of America92: 3042–3066.
     [Google Scholar]
  36. Ren, Z., and Y.Liu. 2015. Acoustic and elastic modeling by optimal time-space-domain staggered-grid finite-difference schemes. Geophysics80: T17–T40.
     [Google Scholar]
  37. Ren, Z., and Z.Li. 2017. Temporal high-order staggered-grid finite-difference schemes for elastic wave propagation. Geophysics82: T207–T224.
     [Google Scholar]
  38. Ren, Z., and Z.Li. 2019. High-order temporal and implicit spatial staggered-grid finite-difference operators for modelling seismic wave propagation. Geophysical Journal International217: 844–865.
     [Google Scholar]
  39. Ren, Z., Z.Li, Y.Liu, and M.K.Sen. 2017. Modeling of the acoustic wave equation by staggered-grid finite-difference schemes with high-order temporal and spatial accuracy. Bulletin of the Seismological Society of America107: 2160–2182.
     [Google Scholar]
  40. Robertsson, J.O.A.1996. A numerical free-surface condition for elastic/viscoelastic finite-difference modeling in the presence of topography. Geophysics61: 1921–1934.
     [Google Scholar]
  41. Robertsson, J.O.A., J.Blanch, and W.Symes. 1994. Viscoelastic finite-difference modeling. Geophysics59: 1444–1456.
     [Google Scholar]
  42. Sethi, H., J.Shragge, and I.Tsvankin. 2020. Finite-difference modeling for coupled acoustic-elastic anisotropic media using mimetic operators. 80th Annual International Meeting, SEG, Expanded Abstracts, 2658–2662.
     [Google Scholar]
  43. Tan, S., and L.Huang. 2014. An efficient finite-difference method with high-order accuracy in both time and space domains for modelling scalar-wave propagation. Geophysical Journal International197: 1250–1267.
     [Google Scholar]
  44. Virreux, J.1984. SH-wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics49: 1933–1957.
     [Google Scholar]
  45. Virieux, J.1986. P-SV wave propagation in heterogeneous media: velocity stress finite-difference method. Geophysics51: 889–901.
     [Google Scholar]
  46. Wang, E., Y.Liu, and M.K.Sen. 2016. Effective finite-difference modelling methods with 2D acoustic wave equation using a combination of cross and rhombus schemes. Geophysical Journal International206: 1933–1958.
     [Google Scholar]
  47. Wang, J., Y.Liu, and H.Zhou. 2021. Acoustic wave propagation with new spatial implicit and temporal high-order staggered-grid finite-difference schemes. Journal of Geophysics and Engineering18: 808–823.
     [Google Scholar]
  48. Yee, K.1966. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Antennas and Wireless Propagation Letters14: 302–307.
     [Google Scholar]
  49. Zhang, J., and Z.Yao. 2013. Optimized explicit finite-difference schemes for spatial derivatives using maximum norm. Geophysical Journal International250: 511–526.
     [Google Scholar]
  50. Zhou, H., Y.Liu, and J.Wang. 2021. Elastic wave modeling with high-order temporal and spatial accuracies by a selectively modified and linearly optimized staggered-grid finite-difference scheme. IEEE Transactions on Geoscience and Remote Sensing, online.
     [Google Scholar]
/content/journals/10.1080/08123985.2022.2034477
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A novel equivalent staggered-grid finite-difference scheme and its optimization strategy for variable-density acoustic wave modelling
Exploration Geophysics 53, 669 (2022); https://doi.org/10.1080/08123985.2022.2034477
/content/journals/10.1080/08123985.2022.2034477
/content/journals/10.1080/08123985.2022.2034477
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  • Article Type: Research Article
Keyword(s): Acoustic wave equation; equivalent staggered-grid; finite-difference; linear optimization; time–space domain

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