1887
Volume 45, Issue 4
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

[

Staggered-grid finite-difference (SFD) methods have been used widely in seismic wave numerical modelling and migration. The conventional way to calculate the high-order SFD coefficients on spatial derivatives is the Taylor-series expansion method, which generally leads to great accuracy on just a small frequency zone. In this paper, we first derive the SFD coefficients of arbitrary even-order accuracy for the first-order spatial derivatives by the dispersion relation and the least-squares method, which can satisfy the specific numerical solution accuracy of the derivative on a wide frequency zone. Then we use the SFD coefficients based on the least-squares to solve the first-order spatial derivatives and analyse the accuracy of the numerical solution. Finally, we perform elastic wave numerical modelling with the least-squares staggered-grid finite-difference (LSSFD) method. Meanwhile, the numerical dispersion, the modelling accuracy and the computing costs of the new method are compared with that of the Taylor-series expansion staggered-grid finite-difference (TESFD) method. The numerical dispersion analysis and elastic wavefield modelling results demonstrate that the LSSFD method can efficiently suppress the numerical dispersion and has greater modelling accuracy than the conventional TESFD method under the same discretisations and without extra computing costs.

,

In this paper, we derive the staggered-grid finite-difference coefficients of arbitrary even-order accuracy for the first-order spatial derivatives by the dispersion relation and the least squares method, which can satisfy the specific numerical solution accuracy of the derivative on a wide frequency zone for elastic wave numerical modelling.

]
© 2014 ASEG
Loading

Article metrics loading...

/content/journals/10.1071/EG13087
2014-12-01
2026-01-15

  • From This Site

    /content/journals/10.1071/EG13087
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Bérenger J. P. 1994 A perfectly matched layer for the absorption of electromagnetic waves: Journal of Computational Physics 114 185 200 10.1006/jcph.1994.1159
    https://doi.org/10.1006/jcph.1994.1159 [Google Scholar]
  2. Chu C. Stoffa P. L. 2012 a Implicit finite-difference simulations of seismic wave propagation: Geophysics 77 T57 T67 10.1190/geo2011‑0180.1
    https://doi.org/10.1190/geo2011-0180.1 [Google Scholar]
  3. Chu C. Stoffa P. L. 2012 b Determination of finite-difference weights using scaled binomial windows: Geophysics 77 W17 W26 10.1190/geo2011‑0336.1
    https://doi.org/10.1190/geo2011-0336.1 [Google Scholar]
  4. Dong L. G. Ma Z. T. Cao J. Z. Wang H. Z. Gao J. H. Lei B. Xu S. Y. 2000 a A staggered-grid high-order difference method of one-order elastic wave equation: Chinese Journal of Geophysics 43 411 419 [in Chinese]
    [Google Scholar]
  5. Dong L. G. Ma Z. T. Cao J. Z. 2000 b A study on stability of the staggered-grid high-order difference method of first-order elastic wave equation: Chinese Journal of Geophysics 43 856 864 [in Chinese]
    [Google Scholar]
  6. Etgen, J. T., 2007, A tutorial on optimizing time domain finite-difference schemes: ‘Beyond Holberg’: Stanford Exploration Project Report, 129, 33–43.
  7. Graves R. W. 1996 Simulating seismic wave propagation in 3D elastic media using staggered-grid finite difference: Bulletin of the Seismological Society of America 86 1091 1106
    [Google Scholar]
  8. Holberg O. 1987 Computational aspects of the choice of operator and sampling interval for numerical differentiation in large-scale simulation of wave phenomena: Geophysical Prospecting 35 629 655 10.1111/j.1365‑2478.1987.tb00841.x
    https://doi.org/10.1111/j.1365-2478.1987.tb00841.x [Google Scholar]
  9. Igel, H., Riollet, B., and Mora, P., 1992, Accuracy of staggered 3-D finite-difference grids for anisotropic wave propagation: 62nd Annual International Meeting, SEG, Expanded Abstracts, 1244–1246.
  10. Kim J. W. Lee D. J. 1996 Optimized compact finite difference schemes with maximum resolution: AIAA Journal 34 887 893 10.2514/3.13164
    https://doi.org/10.2514/3.13164 [Google Scholar]
  11. Kindelan M. Kamel A. Sguazzero P. 1990 On the construction and efficiency of staggered numerical differentiators for the wave equation: Geophysics 55 107 110 10.1190/1.1442763
    https://doi.org/10.1190/1.1442763 [Google Scholar]
  12. Lee C. Seo Y. 2002 A new compact spectral scheme for turbulence simulations: Journal of Computational Physics 183 438 469 10.1006/jcph.2002.7201
    https://doi.org/10.1006/jcph.2002.7201 [Google Scholar]
  13. Liu Y. 2013 Globally optimal finite-difference schemes based on least squares: Geophysics 78 T113 T132 10.1190/geo2012‑0480.1
    https://doi.org/10.1190/geo2012-0480.1 [Google Scholar]
  14. Liu Y. Sen M. K. 2009 a A practical implicit finite-difference method: examples from seismic modeling: Journal of Geophysics and Engineering 6 231 249 10.1088/1742‑2132/6/3/003
    https://doi.org/10.1088/1742-2132/6/3/003 [Google Scholar]
  15. Liu Y. Sen M. K. 2009 b An implicit staggered-grid finite-difference method for seismic modeling: Geophysical Journal International 179 459 474 10.1111/j.1365‑246X.2009.04305.x
    https://doi.org/10.1111/j.1365-246X.2009.04305.x [Google Scholar]
  16. Liu Y. Sen M. K. 2011 Scalar wave equation modeling with time-space domain dispersion-relation-based staggered-grid finite-difference schemes: Bulletin of the Seismological Society of America 101 141 159 10.1785/0120100041
    https://doi.org/10.1785/0120100041 [Google Scholar]
  17. Madariaga R. 1976 Dynamics of an expanding circular fault: Bulletin of the Seismological Society of America 66 639 666
    [Google Scholar]
  18. Nakata N. Tsuji T. Matsuoka T. 2011 Acceleration of computation speed for elastic wave simulation using a Graphic Processing Unit: Exploration Geophysics 42 98 104 10.1071/EG10039
    https://doi.org/10.1071/EG10039 [Google Scholar]
  19. Pei Z. 2004 Numerical modeling using staggered-grid high order finite difference of elastic wave equation on arbitrary relief surface: Oil Geophysical Prospecting 39 629 634 [in Chinese]
    [Google Scholar]
  20. Tam C. K. W. Webb J. C. 1993 Dispersion-relation-preserving finite difference schemes for computational acoustics: Journal of Computational Physics 107 262 281 10.1006/jcph.1993.1142
    https://doi.org/10.1006/jcph.1993.1142 [Google Scholar]
  21. Tessmer E. 2011 Using the rapid expansion method for accurate time-stepping in modeling and reverse-time migration: Geophysics 76 S177 S185 10.1190/1.3587217
    https://doi.org/10.1190/1.3587217 [Google Scholar]
  22. Virieux J. 1984 SH-wave propagation in heterogeneous media: velocity stress finite-difference method: Geophysics 49 1933 1942 10.1190/1.1441605
    https://doi.org/10.1190/1.1441605 [Google Scholar]
  23. Virieux J. 1986 P-SV wave propagation in heterogeneous media: velocity stress finite difference method: Geophysics 51 889 901 10.1190/1.1442147
    https://doi.org/10.1190/1.1442147 [Google Scholar]
  24. Yan H. Liu Y. 2012 High-order finite-difference numerical modeling of wave propagation in viscoelastic TTI media using rotated staggered grid: Chinese Journal of Geophysics 55 252 265 [in Chinese] 10.1002/cjg2.1719
    https://doi.org/10.1002/cjg2.1719 [Google Scholar]
  25. Yan H. Liu Y. Zhang H. 2013 Prestack reverse-time migration with a time-space domain adaptive high-order staggered-grid finite-difference method: Exploration Geophysics 44 77 86 10.1071/EG12047
    https://doi.org/10.1071/EG12047 [Google Scholar]
  26. Zhang J. Yao Z. 2013 Optimized finite-difference operator for broadband seismic wave modeling: Geophysics 78 A13 A18 10.1190/geo2012‑0277.1
    https://doi.org/10.1190/geo2012-0277.1 [Google Scholar]
  27. Zhou H. Zhang G. 2011 Prefactored optimized compact finite-difference schemes for second spatial derivatives: Geophysics 76 WB87 WB95 10.1190/geo2011‑0048.1
    https://doi.org/10.1190/geo2011-0048.1 [Google Scholar]
/content/journals/10.1071/EG13087
Loading
Least squares staggered-grid finite-difference for elastic wave modelling
Exploration Geophysics 45, 255 (2014); https://doi.org/10.1071/EG13087
/content/journals/10.1071/EG13087
/content/journals/10.1071/EG13087
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): dispersion, elastic wave, least squares, numerical modelling, staggered-grid finite-difference (SFD).

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