1887
Volume 62, Issue 2
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Based on an average‐derivative method and optimization techniques, a 27‐point scheme for a 3D frequency‐domain scalar wave equation is developed. Compared to the rotated‐coordinate approach, the average‐derivative optimal method is not only concise but also applies to equal and unequal directional sampling intervals. The resulting 27‐point scheme uses a 27‐point operator to approximate spatial derivatives and the mass acceleration term. The coefficients are determined by minimizing phase velocity dispersion errors and the resultant optimal coefficients depend on ratios of directional sampling intervals. Compared to the classical 7‐point scheme, the number of grid points per shortest wavelength is reduced from approximately 13 to approximately 4 by this 27‐point optimal scheme for equal directional sampling intervals and unequal directional sampling intervals as well. Two numerical examples are presented to demonstrate the theoretical analysis. The average‐derivative algorithm is also extended to a 3D frequency‐domain viscous scalar wave equation.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12090
2013-12-27
2024-04-28
Loading full text...

Full text loading...

References

  1. Boonyasiriwat, C., P.Valasek, P.Routh, W.Cao, G. T.Schuster, and B.Macy, 2009, An efficient multiscale method for time‐domain waveform tomography: Geophysics, 74(6), WCC59‐WCC68.
    [Google Scholar]
  2. Chen, J.‐B., 2001, New schemes for the nonlinear Schrödinger equation: Applied Mathematics and Computation, 124, 371‐379.
    [Google Scholar]
  3. Chen, J.‐B., 2008, Variational integrators and the finite element method: Applied Mathematics and Computation, 196, 941‐958.
    [Google Scholar]
  4. Chen, J.‐B., 2009, Lax‐Wendroff and Nyström methods for seismic modelling: Geophysical Prospecting, 57, 931‐941.
    [Google Scholar]
  5. Chen, J.‐B., 2012, An average‐derivative optimal scheme for frequency‐domain scalar wave equation: Geophysics, 77 (6), T201‐T210.
    [Google Scholar]
  6. Clapp, R. G., 2009, Reverse time migration with random boundaries: 79th Annual International Meeting, SEG, Expanded Abstracts, 2809‐2813.
    [Google Scholar]
  7. Clayton, R., and B.Engqusit, 1977, Absorbing boundary conditions for scalar and elastic wave equations: Bulletin of the Seismological Society of America, 67, 1529‐1540.
    [Google Scholar]
  8. Gauthier, O., J.Virieux, and A.Tarantola, 1986, Two‐dimensional nonlinear inversion of seismic waveforms: Numerical results: Geophysics, 51, 1387‐1403.
    [Google Scholar]
  9. Hustedt,B., S.Operto, and J.Virieux, 2004, Mix‐grid and staggered‐grid finite‐difference methods for frquency‐domain acoustic wave modelling: Geophysical Journal International, 157, 1269‐1296.
    [Google Scholar]
  10. Jo, C.‐H., C.Shin, and J. H.Suh, 1996, An optimal 9‐point, finite‐difference, frequency‐space, 2‐D scalar wave extrapolator: Geophysics, 61, 529‐537.
    [Google Scholar]
  11. Operto, S., J.Virieux, P.Amestoy, J.‐Y.L'Excellent, L.Giraud, and H. B. H.Ali, 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]
  12. Operto, S., J.Virieux, and F.Sourbier, 2007, Documentation of FWT2D program (version 4.8): Frequency‐domain full‐waveform modeling/inversion of wide‐aperture seismic data for imaging 2D scalar media: Technical report No007‐SEISCOPE project.
  13. Pratt, R. G., C.Shin, and G. J.Hicks, 1998, Gauss‐Newton and full Newton methods in frequency‐space seismic waveform inversion: Geophysical Journal International, 133, 341‐362.
    [Google Scholar]
  14. Pratt, R. G., and M.‐H.Worthington, 1990, Inverse theory applied to multi‐source cross‐hole tomography, Part I: acoustic wave‐equation method: Geophysical Prospecting, 38, 287‐310.
    [Google Scholar]
  15. Symes, W. M., 2007, Reverse‐time migration with optimal checkpointing: Geophysics, 72(5), SM213‐SM221.
    [Google Scholar]
  16. Tarantola, A., 1984, Inversion of seismic reflection data in the acoustic approximation: Geophysics, 49, 1259‐1266.
    [Google Scholar]
  17. Virieux, J., and S.Operto, 2009, An overview of full‐waveform inversion in exploration geophysics: Geophysics, 74(6), WCC1‐WCC26.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12090
Loading
/content/journals/10.1111/1365-2478.12090
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Average‐derivative method; Scalar wave equation

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