1887
  1. Home
  2. A-Z Publications
  3. Geophysical Prospecting
  4. Volume 42, Issue 4
  5. Article
Volume 42 Number 4
  • E-ISSN: 1365-2478

Abstract

Abstract

We present a discrete modelling scheme which solves the elastic wave equation on a grid with vertically varying grid spacings. Spatial derivatives are computed by finite‐difference operators on a staggered grid. The time integration is performed by the rapid expansion method. The use of variable grid spacings adds flexibility and improves the efficiency since different spatial sampling intervals can be used in regions with different material properties. In the case of large velocity contrasts, the use of a non‐uniform grid avoids spatial oversampling in regions with high velocities. The modelling scheme allows accurate modelling up to a spatial sampling rate of approximately 2.5 gridpoints per shortest wavelength. However, due to the staggering of the material parameters, a smoothing of the material parameters has to be applied at internal interfaces aligned with the numerical grid to avoid amplitude errors and timing inaccuracies. The best results are obtained by smoothing based on slowness averaging. To reduce errors in the implementation of the free‐surface boundary condition introduced by the staggering of the stress components, we reduce the grid spacing in the vertical direction in the vicinity of the free surface to approximately 10 gridpoints per shortest wavelength. Using this technique we obtain accurate results for surface waves in transversely isotropic media.

Loading

Article metrics loading...

/content/journals/10.1111/j.1365-2478.1994.tb00215.x
2006-04-27
2024-04-27

  • From This Site

    /content/journals/10.1111/j.1365-2478.1994.tb00215.x
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. HolbergO.1987. Computational aspects of the choice of operator and sampling interval for numerical differentiation in large‐scale simulation of wave phenomena. Geophysical Prospecting35, 625–655.
    [Google Scholar]
  2. JastramC. and BehleA.1992. Acoustic modelling on a grid of vertically varying spacing. Geophysical Prospecting40, 157–169.
    [Google Scholar]
  3. JastramC. and BehleA.1993. Accurate finite‐difference operators for modelling the elastic wave equation. Geophysical Prospecting41, 453–458.
    [Google Scholar]
  4. KosloffD., FilhoA.Q., TessmerE. and BehleA.1989. Numerical solution of the acoustic and elastic wave equations by a new rapid expansion method. Geophysical Prospecting37, 383–394.
    [Google Scholar]
  5. KosloffD., KesslerD., FilhoA.Q., TessmerE., BehleA. and StrahilevitzR.1990. Solution of the equations of dynamic elasticity by a Chebyshev spectral method. Geophysics55, 734–748.
    [Google Scholar]
  6. LevanderA.R.1988. Fourth‐order finite‐difference P‐SV seismograms. Geophysics53, 892–902.
    [Google Scholar]
  7. TsingasC., VafidisA. and KanasewichE.R.1990. Elastic wave propagation in transversely isotropic media using finite differences. Geophysical Prospecting38, 933–949.
    [Google Scholar]
  8. VirieuxJ.1986. P‐SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method. Geophysics51, 889–901.
    [Google Scholar]
  9. ZharadnikJ., MoczoP. and HronF.1993. Testing four elastic finite‐difference schemes for behaviour at discontinuities. Bulletin of the Seismological Society of America83, 107–129.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/j.1365-2478.1994.tb00215.x
Loading
  • Article Type: Research Article

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