1887
  1. Home
  2. A-Z Publications
  3. Geophysical Prospecting
  4. Volume 70, Issue 4
  5. Article
Volume 70, Issue 4
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Frequency‐domain finite‐difference modelling is widely used in exploration geophysics. However, it involves solving a large system of linear algebraic equations, which may cause huge computational costs, especially for large‐scale models. To address this issue, we have proposed an improved 25‐point finite‐difference scheme for wavefield modelling of two‐dimensional frequency‐domain elastic wave equations. The biggest difference between the improved 25‐point scheme with other 25‐point schemes is the finite‐difference formulas for spatial derivatives. The proposed 25‐point scheme applies to equal and unequal grid intervals, and its optimization coefficients depend on the grid‐spacing ratio and Poisson's ratio. The dispersion analysis indicates that within the phase velocity errors of 1% and 2%, the improved 25‐point scheme only requires approximately 2.3 and 2.2 grid points per shear wavelength, which has greater accuracy than the existing schemes. To eliminate artificial boundary reflections, we apply the perfectly matched layer boundary conditions to the model edges. Several numerical examples are presented to prove the validity of the improved 25‐point scheme.

© 2022 European Association of Geoscientists & Engineers © 2022 European Association of Geoscientists & Engineers
Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.13188
2022-04-14
2024-04-23

  • From This Site

    /content/journals/10.1111/1365-2478.13188
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Belonosov, M., Dmitriev, M., Kostin, V., Neklyudov, D. and Tcheverda, V. (2017) An iterative solver for the 3D Helmholtz equation. Journal of Computational Physics, 345, 330–344.
     [Google Scholar]
  2. Belonosov, M., Kostin, V., Neklyudov, D. and Tcheverda, V. (2018) 3D numerical simulation of elastic waves with a frequency‐domain iterative solver. Geophysics, 83(6), T333–T344.
     [Google Scholar]
  3. Cao, S.‐H. and Chen, J.‐B. (2012) A 17‐point scheme and its numerical implementation for high‐accuracy modelling of frequency‐domain acoustic equation (in Chinese). Chinese Journal of Geophysics, 55(10), 3440–3449.
     [Google Scholar]
  4. Chen, J.‐B. (2012) An average‐derivative optimal scheme for frequency‐domain scalar wave equation. Geophysics, 77(6), T201–T210.
     [Google Scholar]
  5. Chen, J.‐B. (2014) A 27‐point scheme for a 3D frequency‐domain scalar wave equation based on an average‐derivative method. Geophysical Prospecting, 62, 258–277.
     [Google Scholar]
  6. Chen, J.‐B. and Cao, J. (2016) Modelling of frequency‐domain elastic wave equation with an average‐derivative optimal method. Geophysics, 81(6), T339–T356.
     [Google Scholar]
  7. Chen, J.‐B. and Cao, J. (2018) An average‐derivative optimal scheme for modelling of the frequency‐domain 3D elastic wave equation. Geophysics, 83(4), T209–T234.
     [Google Scholar]
  8. Chen, Z., Cheng, D., Feng, W. and Wu, T. (2013) An optimal 9‐point finite difference scheme for the Helmholtz equation with PML. International Journal of Numerical Analysis and Modelling, 10(2), 389–410.
     [Google Scholar]
  9. Chu, C. and Stoffa, P.L. (2012) Implicit finite‐difference simulations of seismic wave propagation. Geophysics, 77(2), T57–T67.
     [Google Scholar]
  10. Dablain, M.A. (1986) The application of high‐order differencing to the scalar wave equation. Geophysics, 51, 54–66.
     [Google Scholar]
  11. Ernst, O.G. and Gander, M.J. (2012) Why it is difficult to solve Helmholtz problems with classical iterative methods. Numerical Analysis of Multiscale Problems, 83, 325–363.
     [Google Scholar]
  12. Fan, N., Zhao, L.‐F., Xie, X.‐B., Tang, X.‐G. and Yao, Z.‐X. (2017) A general optimal method for 2D frequency‐domain finite‐difference solution of scalar wave equation. Geophysics, 82(3), T121–T132.
     [Google Scholar]
  13. Fan, N., Zhao, L.‐F., Xie, X.‐B. and Yao, Z.‐X. (2018) A discontinuous‐grid finite‐difference scheme for frequency‐domain 2D scalar wave modelling. Geophysics, 83(4), T235–T244.
     [Google Scholar]
  14. Gossenlin‐Cliche, B. and Giroux, B. (2014) 3D frequency‐domain finite‐difference viscoelastic‐wave modelling using weighted average 27‐point operators with optimal coefficients. Geophysics, 79(3), T169–T188.
     [Google Scholar]
  15. Gu, B., Liang, G. and Li, Z. (2013) A 21‐point finite difference scheme for 2D frequency‐domain elastic wave modelling. Exploration Geophysics, 44, 156–166.
     [Google Scholar]
  16. Hustedt, B., Operto, S. and Virieux, J. (2004) Mixed‐grid and staggered‐grid finite‐difference methods for frequency‐domain acoustic wave modelling. Geophysical Journal International, 157, 1269–1296.
     [Google Scholar]
  17. Jo, C.‐H., Shin, C. and Suh, J.H. (1996) An optimal 9‐point, finite‐difference, frequency‐space, 2‐D scalar wave extrapolator. Geophysics, 61, 529–537.
     [Google Scholar]
  18. Li, A., Liu, H., Yuan, Y., Hu, T. and Cui, X. (2019) The numerical modelling of frequency domain scalar wave equation based on the rhombus stencil. Journal of Applied Geophysics, 166, 42–56.
     [Google Scholar]
  19. Li, A., Liu, H., Yuan, Y., Hu, T. and Guo, X. (2018a) Modelling of frequency‐domain elastic‐wave equation with a general optimal scheme. Journal of Applied Geophysics, 159, 1–15.
     [Google Scholar]
  20. Li, H., Wang, S., Wang, D., Cui, M. and Su, K. (2018b) 2‐D elastic wave forward modeling with frequency‐space 25‐point finite‐difference operators. In: International Geophysical Conference, SEG, Expanded Abstracts. SEG, pp. 890–893.
     [Google Scholar]
  21. Li, Q. and Jia, X. (2018) A generalized average‐derivative optimal finite‐difference scheme for 2D frequency‐domain acoustic‐wave modelling on continuous nonuniform grids. Geophysics, 83(5), T265–T279.
     [Google Scholar]
  22. Li, S., Sun, C., Wu, H., Cai, R. and Xu, N. (2021) An optimal finite‐difference method based on the elongated stencil for 2D frequency‐domain acoustic‐wave modeling. Geophysics, 86(6), T523–T541.
     [Google Scholar]
  23. Li, Y., Métivier, L., Brossier, R., Han, B. and Virieux, J. (2015) 2D and 3D frequency‐domain elastic wave modeling in complex media with a parallel iterative solver. Geophysics, 80(3), T101–T118.
     [Google Scholar]
  24. Liu, L., Liu, H. and Liu, H.‐W. (2013) Optimal 15‐point finite difference forward modelling in frequency‐space domain (in Chinese). Chinese Journal of Geophysics, 56(2), 644–652.
     [Google Scholar]
  25. Lysmer, J. and Drake, L.A. (1972) A finite element method for seismology. Methods in Computational Physics: Advances in Research and Applications, 11, 181–216.
     [Google Scholar]
  26. Marfurt, K.J. (1984) Accuracy of finite‐difference and finite‐element modelling of the scalar and elastic wave equations. Geophysics, 49, 533–549.
     [Google Scholar]
  27. Min, D.‐J., Shin, C., Kwon, B.‐D. and Chung, S. (2000) Improved frequency‐domain elastic wave modelling using weighted‐averaging difference operators. Geophysics, 65(3), 884–895.
     [Google Scholar]
  28. Operto, S., Virieux, J., Amestoy, P., L'Excellent, J.‐Y., Giraud, L. and Ali, H.B.H. (2007) 3D finite‐difference frequency‐domain modeling of visco‐acoustic wave propagation using a massively parallel direct solver: A feasibility study. Geophysics, 72(5), SM195–SM211.
     [Google Scholar]
  29. Pratt, R.G. (1990) Frequency‐domain elastic wave modelling by finite differences: A tool for crosshole seismic imaging. Geophysics, 55, 626–632.
     [Google Scholar]
  30. Pratt, R.G. and Worthington, M.H. (1990) Inverse theory applied to multi‐source cross‐hole tomography, Part I: Acoustic wave‐equation method. Geophysical Prospecting, 38, 287–310.
     [Google Scholar]
  31. Saenger, E.H., Gold, N. and Shapiro, S.A. (2000) Modelling the propagation of elastic waves using a modified finite‐difference grid. Wave Motion, 31, 77–92.
     [Google Scholar]
  32. Shin, C. and Sohn, H. (1998) A frequency‐space 2‐D scalar wave extrapolator using extended 25‐point finite‐difference operator. Geophysics, 63, 289–296.
     [Google Scholar]
  33. Štekl, I. and Pratt, R.G. (1998) Accurate viscoelastic modelling by frequency‐domain finite differences using rotated operators. Geophysics, 63, 1779–1794.
     [Google Scholar]
  34. Takekawa, J. and Mikada, H. (2019) An elongated finite‐difference scheme for 2D acoustic and elastic wave simulations in the frequency domain. Geophysics, 84(2), T29–T45.
     [Google Scholar]
  35. Tang, X., Liu, H., Zhang, H., Liu, L. and Wang, Z. (2015) An adaptable 17‐point scheme for high‐accuracy frequency‐domain acoustic wave modelling in 2D constant density media. Geophysics, 80(6), T211–T221.
     [Google Scholar]
  36. Virieux, J. (1986) P‐SV wave propagation in heterogeneous media: Velocity stress finite difference method. Geophysics, 51, 889–901.
     [Google Scholar]
  37. Xu, W.H. and Gao, J.H. (2018) Adaptive 9‐point frequency‐domain finite difference scheme for wavefield modelling of 2D acoustic wave equation. Journal of Geophysics and Engineering, 15(4), 1432–1445.
     [Google Scholar]
  38. Zhang, H., Zhang, B., Liu, B., Liu, H. and Shi, X. (2015) Frequency‐space domain high‐order modelling based on an average‐derivative optimal method. In: 85th Annual International Meeting, SEG, Expanded Abstracts. SEG, pp. 3749–3753.
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.13188
Loading
An improved 25‐point finite‐difference scheme for frequency‐domain elastic wave modelling
Geophysical Prospecting 70, 702 (2022); https://doi.org/10.1111/1365-2478.13188
/content/journals/10.1111/1365-2478.13188
/content/journals/10.1111/1365-2478.13188
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Elastics; modelling; Seismics

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error