1887
Volume 65, Issue S1
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

The classical finite‐difference methods for seismic wave modelling are very accurate at low wavenumbers but suffer from inaccuracies at high wavenumbers, particularly at Nyquist wavenumber. In contrast, the optimisation finite‐difference methods reduce inaccuracies at high wavenumbers but suffer from inaccuracies at low wavenumbers, particularly at zero wavenumber when the operator length is not long and the whole range of wavenumbers is considered. Inaccuracy at zero wavenumber means that the optimisation methods only have a zeroth‐order accuracy of truncation and thus are not rigorously convergent. To guarantee the rigorous convergence of the optimisation methods, we have developed accuracy‐constrained optimisation methods. Different‐order accuracy‐constrained optimisation methods are presented. These methods not only guarantee the rigorous convergence but also reduce inaccuracies at low wavenumbers. Accuracy‐constrained optimisation methods are applied to staggered‐grid elastic wave modelling.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12571
2017-12-26
2024-04-20
Loading full text...

Full text loading...

References

  1. AlfordR.M., KellyK.R. and BooreD.M.1974. Accuracy of finite‐difference modeling of the acoustic wave equation. Geophysics39, 834–842.
    [Google Scholar]
  2. AltermanZ. and KaralF.1968. Propagation of elastic waves in layered median by finite differences methods. Bulletin of the Seismological Society of America58, 367–398.
    [Google Scholar]
  3. CerjanC., KosloffD., KosloffR. and ReshefM.1985. A nonreflecting boundary condition for discrete acoustic and elastic wave equations. Geophysics50, 705–708.
    [Google Scholar]
  4. ChenJ.‐B.2011. A stability formula for Lax‐Wendroff methods with fourthorder in time and general‐order in space for the scalar wave equation. Geophysics, 76(2), T37–T42.
    [Google Scholar]
  5. DablainM.A.1986. The application of high‐order differencing to the scalar wave equation. Geophysics51, 54–66.
    [Google Scholar]
  6. FornbergB.1987. The pseudospectral method: comparisons with finite differences for the elastic wave equation. Geophysics52, 483–501.
    [Google Scholar]
  7. FornbergB.1988. Generation of finite difference formulas on arbitrarily spaced grids. Mathematics of Computation51, 699–706.
    [Google Scholar]
  8. FornbergB.1990. High‐order finite difference and the pseudospectral method on staggered grids. SIAM Journal on Numerical Analysis27, 904–918.
    [Google Scholar]
  9. FornbergB.1996. A Practical Guide to Pseudospectral Method. Cambridge, UK: Cambridge University Press.
    [Google Scholar]
  10. GolubG.H. and Van LoanC.F.1996. Matrix Computations. The Johns Hopkins University Press.
    [Google Scholar]
  11. HolbergO.1987. Computational aspects of the choice of operator and sampling interval for numerical differentiation in large‐scale simulation of wave phenomena. Gophysical Prospecting35, 629–655.
    [Google Scholar]
  12. HouseB., LarsenS. and BednarJ.B.2000. 3‐D elastic numerical modeling of a complex salt structure. 70th annual meeting, SEG, Expanded Abstracts, 2201–2204.
  13. KellyK.R., TreitelS. and AlfordR.M.1976. Synthetic seismograms: a finite difference approach. Geophysics41, 12–27.
    [Google Scholar]
  14. LevanderA.R.1988. Fourth‐order finite‐difference P‐SV seismograms. Geophysics53, 1425–1436.
    [Google Scholar]
  15. LinesL.R., SlawinskiR.S. and BordingR.P.1999. A recipe for stability of finite‐difference wave‐equation computations. Geophysics64, 967–969.
    [Google Scholar]
  16. LiuY.2014. Optimal staggered‐grid finite‐difference schemes based on leastsquares for wave equation modelling. Geophysical Journal International197, 1033–1047.
    [Google Scholar]
  17. LiuY. and SenM.K.2009. An implicit staggered‐grid finite‐difference for seismic modelling. Geophysical Journal International179, 459–474.
    [Google Scholar]
  18. MittetR.2002. Free‐surface boundary conditions for elastic staggered modeling schemes. Geophysics67, 1616–1623.
    [Google Scholar]
  19. TamC.K.W. and WebbJ.C.1993. Dispersion‐relation‐preserving finite difference schemes for computational acoustics. Journal of Computational Physics107, 262–281.
    [Google Scholar]
  20. VirieuxJ.1986. P‐SV wave propagation in heterogeneous media: velocity stress finite difference method. Geophysics51, 889–901.
    [Google Scholar]
  21. XuY.X., XiaJ.H. and MillerR.D.2007. Numerical investigation of implementation of air‐earth boundary by acoustic‐elastic boundary approach. Geophysics72, SM147–SM153.
    [Google Scholar]
  22. YangL., YanH.Y. and LiuH.2014. Least squares staggered‐grid finitedifference for elastic wave modeling. Exploration Geophysics45, 255–260.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12571
Loading
/content/journals/10.1111/1365-2478.12571
Loading

Data & Media 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