1887
Volume 52, Issue 3
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

Using orthogonal-octahedron finite-difference (FD) stencils, even-order accuracy for temporal and spatial derivatives can be reached for 3D acoustic wave equation modelling. However, the required length of FD operator is still long for high accuracy modelling. To tackle this issue, we have developed an optimization method using a combination of Taylor-series expansion plus Remez exchange methods. The Taylor-series expansion for the octahedron-shaped operator ensures high temporal accuracy and the Remez exchange for axial operator further improves the spatial accuracy. The comparison between our method, exisiting 3D temporal high order method and space domain least-square opimization method validates the efficiency and accuracy superiority of the new method.

© 2020 Australian Society of Exploration Geophysicists
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2021-05-04
2026-01-21

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References

  1. Alford, R., K.Kelly, and D.M.Boore. 1974. Accuracy of finite-difference modeling of the acoustic wave equation. Geophysics39: 834–42. doi: 10.1190/1.1440470
     https://doi.org/10.1190/1.1440470 [Google Scholar]
  2. Alterman, Z., and F.Karal. 1968. Propagation of elastic waves in layered media by finite difference methods. Bulletin of the Seismological Society of America58: 367–98.
     [Google Scholar]
  3. An, Y.2017. Uniform dispersion reduction schemes for the one dimensional wave equation in isotropic media. Journal of Computational Physics341: 13–21. doi: 10.1016/j.jcp.2017.04.015
     https://doi.org/10.1016/j.jcp.2017.04.015 [Google Scholar]
  4. Anderson, J.E., V.Brytik, and G.Ayeni. 2015. Numerical temporal dispersion corrections for broadband temporal simulation, RTM and FWI. SEG technical program expanded abstracts 2015. Society of Exploration Geophysicists, 1096–1100.
  5. Chen, H., H.Zhou, Q.Zhang, and Y.Chen. 2016. Modeling elastic wave propagation using k-space operator-based temporal high-order staggered-grid finite-difference method. IEEE Transactions on Geoscience and Remote Sensing55: 801–15. doi: 10.1109/TGRS.2016.2615330
     https://doi.org/10.1109/TGRS.2016.2615330 [Google Scholar]
  6. Chen, H., H.Zhou, Q.Zhang, M.Xia, and Q.Li. 2016. A k-space operator-based least-squares staggered-grid finite-difference method for modeling scalar wave propagation. Geophysics81: T45–T61. doi: 10.1190/geo2015‑0090.1
     https://doi.org/10.1190/geo2015-0090.1 [Google Scholar]
  7. Chu, C., and P.L.Stoffa. 2012a. An implicit finite-difference operator for the helmholtz equation. Geophysics77: T97–T107. doi: 10.1190/geo2011‑0314.1
     https://doi.org/10.1190/geo2011-0314.1 [Google Scholar]
  8. Chu, C., and P.L.Stoffa. 2012b. Determination of finite-difference weights using scaled binomial windows. Geophysics77: W17–W26. doi: 10.1190/geo2011‑0336.1
     https://doi.org/10.1190/geo2011-0336.1 [Google Scholar]
  9. Dablain, M.1986. The application of high-order differencing to the scalar wave equation. Geophysics51: 54–66. doi: 10.1190/1.1442040
     https://doi.org/10.1190/1.1442040 [Google Scholar]
  10. Dai, N., A.Vafidis, and E.Kanasewich. 1995. Wave propagation in heterogeneous, porous media: A velocity-stress, finite-difference method. Geophysics60: 327–40. doi: 10.1190/1.1443769
     https://doi.org/10.1190/1.1443769 [Google Scholar]
  11. Emerman, S.H., W.Schmidt, and R.Stephen. 1982. An implicit finite-difference formulation of the elastic wave equation. Geophysics47: 1521–26. doi: 10.1190/1.1441302
     https://doi.org/10.1190/1.1441302 [Google Scholar]
  12. Forsythe, G.E., and W.R.Wasow. 1960. Finite difference methods for partial differential equations. New York: John Wiley and Sons.
  13. Geller, R.J., and N.Takeuchi. 1998. Optimally accurate second-order time-domain finite difference scheme for the elastic equation of motion: One-dimensional cases. Geophysical Journal International135: 48–62. doi: 10.1046/j.1365‑246X.1998.00596.x
     https://doi.org/10.1046/j.1365-246X.1998.00596.x [Google Scholar]
  14. Hayashi, K., and D.R.Burns. 1999. Variable grid finite-difference modeling including surface topography. SEG technical program expanded abstracts.
  15. He, Z., J.Zhang, and Z.Yao. 2019. Determining the optimal coefficients of the explicit finite-difference scheme using the remez exchange algorithm. Geophysics84: S137–S147. doi: 10.1190/geo2018‑0446.1
     https://doi.org/10.1190/geo2018-0446.1 [Google Scholar]
  16. Holberg, O.1987. Computational aspects of the choice of operator and sampling interval for numerical differentiation in large-scale simulation of wave phenomena. Geophysical Prospecting35: 629–55. doi: 10.1111/j.1365‑2478.1987.tb00841.x
     https://doi.org/10.1111/j.1365-2478.1987.tb00841.x [Google Scholar]
  17. Igel, H., P.Mora, and B.Riollet. 1995. Anisotropic wave propagation through finite-difference grids. Geophysics60: 1203–16. doi: 10.1190/1.1443849
     https://doi.org/10.1190/1.1443849 [Google Scholar]
  18. Kelly, K., R.Ward, S.Treitel, and R.Alford. 1976. Synthetic seismograms: A finite-difference approach. Geophysics41: 2–27. doi: 10.1190/1.1440605
     https://doi.org/10.1190/1.1440605 [Google Scholar]
  19. Kindelan, M., A.Kamel, and P.Sguazzero. 1990. On the construction and efficiency of staggered numerical differentiators for the wave equation. Geophysics55: 107–10. doi: 10.1190/1.1442763
     https://doi.org/10.1190/1.1442763 [Google Scholar]
  20. Koene, E.F., J.O.Robertsson, F.Broggini, and F.Andersson. 2017. Eliminating time dispersion from seismic wave modeling. Geophysical Journal International213: 169–80. doi: 10.1093/gji/ggx563
     https://doi.org/10.1093/gji/ggx563 [Google Scholar]
  21. Kosloff, D., R.C.Pestana, and H.Talezer. 2010. Acoustic and elastic numerical wave simulations by recursive spatial derivative operators. Geophysics75.
     [Google Scholar]
  22. Lax, P., and B.Wendroff. 1960. Systems of conservation laws. Communications on Pure and Applied Mathematics13: 217–37. doi: 10.1002/cpa.3160130205
     https://doi.org/10.1002/cpa.3160130205 [Google Scholar]
  23. Lele, S.K.1992. Compact finite difference schemes with spectral-like resolution. Journal of Computational Physics103: 16–42. doi: 10.1016/0021‑9991(92)90324‑R
     https://doi.org/10.1016/0021-9991(92)90324-R [Google Scholar]
  24. Li, B., Y.Liu, M.K.Sen, and Z.Ren. 2017. Time-space-domain mesh-free finite difference based on least squares for 2D acoustic-wave modeling. Geophysics82.
     [Google Scholar]
  25. Liu, H., N.Dai, F.Niu, and W.Wu. 2014. An explicit time evolution method for acoustic wave propagation. Geophysics79: T117–T124. doi: 10.1190/geo2013‑0073.1
     https://doi.org/10.1190/geo2013-0073.1 [Google Scholar]
  26. Liu, Y.2013. Globally optimal finite-difference schemes based on least squares. Geophysics78: T113–T132. doi: 10.1190/geo2012‑0480.1
     https://doi.org/10.1190/geo2012-0480.1 [Google Scholar]
  27. Liu, Y., and M.K.Sen. 2009. A new time–space domain high-order finite-difference method for the acoustic wave equation. Journal of Computational Physics228: 8779–806. doi: 10.1016/j.jcp.2009.08.027
     https://doi.org/10.1016/j.jcp.2009.08.027 [Google Scholar]
  28. Liu, Y., and M.K.Sen. 2010. Acoustic VTI modeling with a time-space domain dispersion-relation-based finite-difference scheme. Geophysics75: A11–A17. doi: 10.1190/1.3374477
     https://doi.org/10.1190/1.3374477 [Google Scholar]
  29. Liu, Y., and M.K.Sen. 2011a. Finite-difference modeling with adaptive variable-length spatial operators. Geophysics76: T79–T89. doi: 10.1190/1.3587223
     https://doi.org/10.1190/1.3587223 [Google Scholar]
  30. Liu, Y., and M.K.Sen. 2011b. Scalar wave equation modeling with time–space domain dispersion-relation-based staggered-grid finite-difference schemes. Bulletin of the Seismological Society of America101: 141–59. doi: 10.1785/0120100041
     https://doi.org/10.1785/0120100041 [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: 327–45. doi: 10.1016/j.jcp.2012.08.025
     https://doi.org/10.1016/j.jcp.2012.08.025 [Google Scholar]
  32. Long, G., Y.Zhao, and J.Zou. 2013. A temporal fourth-order scheme for the first-order acoustic wave equations. Geophysical Journal International194: 1473–85. doi: 10.1093/gji/ggt168
     https://doi.org/10.1093/gji/ggt168 [Google Scholar]
  33. McClellan, J., and T.Parks. 1972. Equiripple approximation of fan filters. Geophysics37: 573–83. doi: 10.1190/1.1440284
     https://doi.org/10.1190/1.1440284 [Google Scholar]
  34. McMechan, G.A.1983. Migration by extrapolation of time-dependent boundary values. Geophysical Prospecting31: 413–20. doi: 10.1111/j.1365‑2478.1983.tb01060.x
     https://doi.org/10.1111/j.1365-2478.1983.tb01060.x [Google Scholar]
  35. Moczo, P.1989. Finite-difference technique for sh-waves in 2-D media using irregular grids-application to the seismic response problem. Geophysical Journal International99: 321–29. doi: 10.1111/j.1365‑246X.1989.tb01691.x
     https://doi.org/10.1111/j.1365-246X.1989.tb01691.x [Google Scholar]
  36. Oprsal, I., and J.Zahradnik. 1999. Elastic finite-difference method for irregular grids. Geophysics64: 240–50. doi: 10.1190/1.1444520
     https://doi.org/10.1190/1.1444520 [Google Scholar]
  37. Parks, T., and J.Mcclellan. 1972. Chebyshev approximation for nonrecursive digital filters with linear phase. IEEE Transactions on Circuit Theory19: 189–94. doi: 10.1109/TCT.1972.1083419
     https://doi.org/10.1109/TCT.1972.1083419 [Google Scholar]
  38. Remez, E.Y.1934. Sur la détermination des polynômes d'approximation de degré donnée. Comm. Soc. Math. Kharkov10: 41–63.
     [Google Scholar]
  39. Ren, Z., and Z.Li. 2017. Temporal high-order staggered-grid finite-difference schemes for elastic wave propagation. Geophysics82: T207–T224. doi: 10.1190/geo2017‑0005.1
     https://doi.org/10.1190/geo2017-0005.1 [Google Scholar]
  40. Ren, Z., and Y.Liu. 2015. Acoustic and elastic modeling by optimal time-space-domain staggered-grid finite-difference schemes. Geophysics80: T17–T40. doi: 10.1190/geo2014‑0269.1
     https://doi.org/10.1190/geo2014-0269.1 [Google Scholar]
  41. Saenger, E.H., N.Gold, and S.A.Shapiro. 2000. Modeling the propagation of elastic waves using a modified finite-difference grid. Wave Motion31: 77–92. doi: 10.1016/S0165‑2125(99)00023‑2
     https://doi.org/10.1016/S0165-2125(99)00023-2 [Google Scholar]
  42. Shan, G.2009. Optimized implicit finite-difference and fourier finite-difference migration for VTI media. Geophysics74: WCA189–WCA197. doi: 10.1190/1.3202306
     https://doi.org/10.1190/1.3202306 [Google Scholar]
  43. Song, X., S.Fomel, and L.Ying. 2013. Lowrank finite-differences and lowrank fourier finite-differences for seismic wave extrapolation in the acoustic approximation. Geophysical Journal International193: 960–9. doi: 10.1093/gji/ggt017
     https://doi.org/10.1093/gji/ggt017 [Google Scholar]
  44. Tan, S., and L.Huang. 2014a. A staggered-grid finite-difference scheme optimized in the time-space domain for modeling scalar-wave propagation. In SEG technical program expanded abstracts 2014. Society of Exploration Geophysicists, 3292–3296.
  45. Tan, S., and L.Huang. 2014b. An efficient finite-difference method with high-order accuracy in both time and space domains for modelling scalar-wave propagation. Geophysical Journal International197: 1250–67. doi: 10.1093/gji/ggu077
     https://doi.org/10.1093/gji/ggu077 [Google Scholar]
  46. Tarantola, A.1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics49: 1259–66. doi: 10.1190/1.1441754
     https://doi.org/10.1190/1.1441754 [Google Scholar]
  47. Virieux, J.1986. P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method. Geophysics51: 889–901. doi: 10.1190/1.1442147
     https://doi.org/10.1190/1.1442147 [Google Scholar]
  48. Virieux, J., and S.Operto. 2009. An overview of full-waveform inversion in exploration geophysics. Geophysics74: WCC1–WCC26. doi: 10.1190/1.3238367
     https://doi.org/10.1190/1.3238367 [Google Scholar]
  49. Wang, E., J.Ba, and Y.Liu. 2018. Time-space-domain implicit finite-difference methods for modeling acoustic wave equations. Geophysics83: T175–T193. doi: 10.1190/geo2017‑0546.1
     https://doi.org/10.1190/geo2017-0546.1 [Google Scholar]
  50. Wang, E., J.Ba, and Y.Liu. 2019. Temporal high-order time–space domain finite-difference methods for modeling 3D acoustic wave equations on general cuboid grids. Pure and Applied Geophysics176: 5391–414. doi: 10.1007/s00024‑019‑02277‑2
     https://doi.org/10.1007/s00024-019-02277-2 [Google Scholar]
  51. Wang, E., Y.Liu, and M.K.Sen. 2016. Effective finite-difference modelling methods with 2-D acoustic wave equation using a combination of cross and rhombus stencils. Geophysical Journal International206: 1933–58. doi: 10.1093/gji/ggw250
     https://doi.org/10.1093/gji/ggw250 [Google Scholar]
  52. Wang, M., and S.Xu. 2015. Finite-difference time dispersion transforms for wave propagation. Geophysics80: WD19–WD25. doi: 10.1190/geo2015‑0059.1
     https://doi.org/10.1190/geo2015-0059.1 [Google Scholar]
  53. Wang, Y., W.Liang, Z.Nashed, X.Li, G.Liang, and C.Yang. 2014. Seismic modeling by optimizing regularized staggered-grid finite-difference operators using a time-space-domain dispersion-relationship-preserving method. Geophysics79: T277–T285. doi: 10.1190/geo2014‑0078.1
     https://doi.org/10.1190/geo2014-0078.1 [Google Scholar]
  54. Xu, S., and Y.Liu. 2018. 3D acoustic wave modeling with a time-space-domain temporal high-order finite-difference scheme. Journal of Geophysics and Engineering15: 1963–76. doi: 10.1088/1742‑2140/aac131
     https://doi.org/10.1088/1742-2140/aac131 [Google Scholar]
  55. Yang, L., H.Yan, and H.Liu. 2016. Optimal implicit staggered-grid finite-difference schemes based on the sampling approximation method for seismic modelling. Geophysical Prospecting64: 595–610. doi: 10.1111/1365‑2478.12325
     https://doi.org/10.1111/1365-2478.12325 [Google Scholar]
  56. Yang, L., H.Yan, and H.Liu. 2017. Optimal staggered-grid finite-difference schemes based on the minimax approximation method with the remez algorithm. Geophysics82: T27–T42. doi: 10.1190/geo2016‑0171.1
     https://doi.org/10.1190/geo2016-0171.1 [Google Scholar]
  57. Zhang, J., and Z.Yao. 2012. Optimized finite-difference operator for broadband seismic wave modeling. Geophysics78: A13–A18. doi: 10.1190/geo2012‑0277.1
     https://doi.org/10.1190/geo2012-0277.1 [Google Scholar]
  58. Zhang, J., and Z.Yao. 2013. Optimized explicit finite-difference schemes for spatial derivatives using maximum norm. Journal of Computational Physics250: 511–26. doi: 10.1016/j.jcp.2013.04.029
     https://doi.org/10.1016/j.jcp.2013.04.029 [Google Scholar]
  59. Zhou, H., Y.Liu, and J.Wang. 2018. Finite-difference modeling with adaptive variable-length temporal and spatial operators. 88th annual international meeting. SEG, Expanded Abstracts, 4015–4019.
  60. Zhou, H., and G.Zhang. 2011. Prefactored optimized compact finite-difference schemes for second spatial derivatives. Geophysics76: WB87–WB95. doi: 10.1190/geo2011‑0048.1
     https://doi.org/10.1190/geo2011-0048.1 [Google Scholar]
/content/journals/10.1080/08123985.2020.1826890
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Optimizing orthogonal-octahedron finite-difference scheme for 3D acoustic wave modeling by combination of Taylor-series expansion and Remez exchange method
Exploration Geophysics 52, 335 (2021); https://doi.org/10.1080/08123985.2020.1826890
/content/journals/10.1080/08123985.2020.1826890
/content/journals/10.1080/08123985.2020.1826890
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  • Article Type: Research Article
Keyword(s): 3D modelling; acoustic; finite difference; optimization; wave equation

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