1887
Volume 56, Issue 6
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Several methods exist to automatically obtain a velocity model from seismic data via optimization. Migration velocity analysis relies on an imaging condition and seeks the velocity model that optimally focuses the migrated image. This approach has been proven to be very successful. However, most migration methods use simplified physics to make them computationally feasible and herein lies the restriction of migration velocity analysis. Waveform inversion methods use the full wave equation to model the observed data and more complicated physics can be incorporated. Unfortunately, due to the band‐limited nature of the data, the resulting inverse problem is highly nonlinear. Simply fitting the data in a least‐squares sense by using a gradient‐based optimization method is sometimes problematic. In this paper, we propose a novel method that measures the amount of focusing in the data domain rather than the image domain. As a first test of the method, we include some examples for 1D velocity models and the convolutional model.

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2008-10-06
2020-03-30
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References

  1. BrownM.P. and GuittonA.2005. Least‐squares joint imaging of multiples and primaries. Geophysics70, S79–S89.
    [Google Scholar]
  2. ChaventG. and ClémentF.1993. Waveform inversion through MBTT formulation. Technical Report 1893 INRIA.
    [Google Scholar]
  3. ClémentF., ChaventG. and GómezS.2001. Migration‐based traveltime waveform inversion of 2‐D simple structures: A synthetic example. Geophysics66, 845–860.
    [Google Scholar]
  4. DohertyS.M. and ClaerboutJ.F.1974. Velocity analysis based on the wave equation. Technical Report 1, Stanford Exploration Project. http://sepwww.stanford.edu/oldreports/sep01/01_12.pdf.
    [Google Scholar]
  5. DussaudE.A. and SymesW.W.2005. Velocity analysis from interferometric data. 75thSEG meeting, Houston, Texax , USA , Expanded Abstracts, pp. 2237–2241.
    [Google Scholar]
  6. JiangZ., ShengJ., YuJ., SchusterG.T. and HornbyB.E.2007. Migration methods for imaging different‐order multiples. Geophysical Prospecting51, 1–19.
    [Google Scholar]
  7. LaillyP.1983. The seismic inverse problem as a sequence of before stack migrations. In: Conference on Inverse Scattering: Theory and Application (eds J.B.Bednar , R.Redner , E.Robinson and A.Weglein ). Society for Industrial and Applied Mathematics, Philadelphia .
    [Google Scholar]
  8. LiJ. and SymesW.W.2007. Interval velocity estimation via NMO‐based differential semblance. Geophysics72, U75–U88.
    [Google Scholar]
  9. LuoY. and SchusterG.T.1989. Wave‐equation traveltime inversion. Geophysics56, 645–653.
    [Google Scholar]
  10. MacKayS. and AbmaR.1992. Imaging and velocity analysis with depth‐focussing analysis. Geophysics57, 1608–1622.
    [Google Scholar]
  11. MoraP.1988. Elastic wave‐field inversion of reflection and transmission data. Geophysics53, 750–759.
    [Google Scholar]
  12. MulderW.A. and Ten KroodeA.P.E.2002. Automatic velocity analysis by differential semblance optimization. Geophysics67, 1184–1191.
    [Google Scholar]
  13. PlessixR.‐E.2006. A review of the adjoint‐state method for computing the gradient of a functional with geophysical applications. Geophysical Journal International167, 495–503.
    [Google Scholar]
  14. PlessixR.‐E., ChaventG. and RoeckY.‐H. De1999. Waveform inversion of reflection seismic data for kinematic parameters by local inversion. SIAM Journal of Scientific Computing20, 1033–1052.
    [Google Scholar]
  15. PrattR.G., SongZ.M., WilliamsonP. and WarnerM.1996. Two‐dimensional velocity models from wide‐angle seismic data by wavefield inversion. Geophysical Journal International124, 232–340.
    [Google Scholar]
  16. PrattR.G. and HicksG.J.1998. Gauss‐Newton and full‐Newton methods in frequency space seismic waveform inversion. Geophysical Journal International133, 341–362.
    [Google Scholar]
  17. RickettJ.E. and SavaP.C.2002. Offset and angle‐domain common image‐point gathers for shot‐profile migration. Geophysics67, 883–889.
    [Google Scholar]
  18. SavaP.C. and BiondiB.2004. Wave‐equation migration velocity analysis. I. Theory. Geophysical Prospecting52, 593–606.
    [Google Scholar]
  19. SavaP.C. and FomelS.2006. Time‐shift imaging condition in seismic migration. Geophysics71, S209–S217.
    [Google Scholar]
  20. ShenP., SymesW.W. and StolkC.C.2003. Differential semblance velocity analysis by wave‐equation migration. 73th SEG meeting, Dallas, Texas , USA , Expanded Abstracts, pp. 2132–2135.
  21. StorkC.1992. Reflection tomography in the postmigrated domain. Geophysics57, 680–692.
    [Google Scholar]
  22. SymesW.W.1999. All stationary points of differential semblance are global minimizers: Layered acoustics. Technical Report 100, Stanford Exlorayion Project.
    [Google Scholar]
  23. SymesW.W. and CarazzoneJ.J.1991. Velocity inversion by differential semblance optimization. Geophysics56, 654–663.
    [Google Scholar]
  24. TarantolaA.1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics49, 1259–1266.
    [Google Scholar]
  25. TarantolaA. and ValetteA.1982. Generalized nonlinear inverse problems solved using the least squares criterion. Reviews of Geophysics and Space Physics20, 129–232.
    [Google Scholar]
  26. VogelC. R.2002. Computational Methods for Inverse Problems , vol. 23. SIAM , Philadelphia .
    [Google Scholar]
  27. YilmazO. and ChambersR.1984. Migration velocity analysis by wavefield extrapolation. Geophysics32, 1664–1674.
    [Google Scholar]
  28. YounO.K. and ZhouH.2001. Depth imaging with multiples. Geophysics66, 246–255.
    [Google Scholar]
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