1887
Volume 63, Issue 2
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Migration velocity analysis aims at determining the background velocity model. Classical artefacts, such as migration smiles, are observed on subsurface offset common image gathers, due to spatial and frequency data limitations. We analyse their impact on the differential semblance functional and on its gradient with respect to the model. In particular, the differential semblance functional is not necessarily minimum at the expected value. Tapers are classically applied on common image gathers to partly reduce these artefacts. Here, we first observe that the migrated image can be defined as the first gradient of an objective function formulated in the data‐domain. For an automatic and more robust formulation, we introduce a weight in the original data‐domain objective function. The weight is determined such that the Hessian resembles a Dirac function. In that way, we extend quantitative migration to the subsurface‐offset domain. This is an automatic way to compensate for illumination. We analyse the modified scheme on a very simple 2D case and on a more complex velocity model to show how migration velocity analysis becomes more robust.

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2014-12-01
2024-03-28
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References

  1. AlkhalifahT.2013. Prestack wavefield approximations. Geophysics78, T141–T149.
    [Google Scholar]
  2. BeylkinG.1985. Imaging of discontinuities in the inverse scattering problem by inversion of a causal generalized Radon transform. Journal of Mathematical Physics26, 99–108.
    [Google Scholar]
  3. ChaurisH. and NobleM.2001. Two‐dimensional velocity macro model estimation from seismic reflection data by local differential semblance optimization: Applications to synthetic and real data sets. Geophysical Journal International144, 14–26.
    [Google Scholar]
  4. ChaurisH., LameloiseC.A. and DonnoD.2013. Migration velocity analysis with reflected and transmitted waves. 75th EAGE meeting, London, UK, Expanded Abstracts.
  5. ChaventG.1974. Identification of function parameters in partial differential equations. In: Identification of parameter distributed systems, (eds R.E. GoodsonPolis , New‐York). ASME 1974.
    [Google Scholar]
  6. de HoopM. and StolkC.2005. Modeling of seismic data in the downward continuation approach. SIAM Journal on Applied Mathematics65, 1388–1406.
    [Google Scholar]
  7. FarraV. and MadariagaR.1987. Seismic waveform modeling in heterogeneous media by ray perturbation theory. Journal of Geophysical Research: Solid Earth92, 2697–2712.
    [Google Scholar]
  8. FarraV.1990. Amplitude computation in heterogeneous media by ray perturbation theory: A finite element approach. Geophysical Journal International103, 341–354.
    [Google Scholar]
  9. FeiW. and WilliamsonP.2010. On the gradient artifacts in migration velocity analysis based on differential semblance optimization. 80th SEG meeting, Denver, Colorado, USA, Expanded Abstracts, 4071–4076.
  10. ForguesE.1996. Inversion linéarisée multi‐paramètres via la théorie des rais (applications aux données de sismique réflexion de surface) . PhD thesis, Institut Français du pétrole ‐ University Paris VII.
  11. GauthierO., VirieuxJ. and TarantolaA.1986. Two‐dimensional nonlinear inversion of seismic waveforms: Numerical results. Geophysics51, 1387–1403.
    [Google Scholar]
  12. JinS., MadariagaR., VirieuxJ. and LambaréG.1992. Two‐dimensional asymptotic iterative elastic inversion. Geophysical Journal International108, 575–588.
    [Google Scholar]
  13. LaillyP.1983. The seismic inverse problem as a sequence of before stack migrations. In: Conference on Inverse Scattering: Theory and Application (ed. J.Bednar ), pp. 206–220. Society for Industrial and Applied Mathematics, Philadelphia.
    [Google Scholar]
  14. LambaréG., VirieuxJ., MadariagaR. and JinS.1992. Iterative asymptotic inversion in the acoustic approximation. Geophysics57, 1138–1154.
    [Google Scholar]
  15. LambaréG., OpertoS., PodvinP. and ThierryP.2003. 3D ray+Born migration/inversion ‐Part 1: Theory. Geophysics68, 1348–1356.
    [Google Scholar]
  16. MulderW.A. and tenKroode A.P.E.2002. Automatic velocity analysis by differential semblance optimization. Geophysics67, 1184–1191.
    [Google Scholar]
  17. MulderW.A.2014. Subsurface offset behaviour in velocity analysis with extended reflectivity images. Geophysical Prospecting62, 17–33.
    [Google Scholar]
  18. PlessixR.‐E., MulderW.A. and tenKroode A.P.E.2000. Automatic crosswell tomography by semblance and differential semblance optimization: Theory and gradient computation. Geophysical Prospecting48, 913–935.
    [Google Scholar]
  19. 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]
  20. RibodettiA., VirieuxJ. and DurandS.1995. Asymptotic theory for viscoacoustic seismic imaging. 65th SEG meeting, Houston, Texas, USA, Expanded Abstracts.
  21. RibodettiA. and VirieuxJ.1998. Asymptotic theory for imaging the attenuation factor Q. Geophysics63, 1767–1778.
    [Google Scholar]
  22. RickettJ. and SavaP.C.2002. Offset and angle‐domain common image‐point gathers for shot‐profile migration. Geophysics67, 883–889.
    [Google Scholar]
  23. SavaP. and FomelS.2003. Angle‐domain common‐image gathers by wavefield continuation methods. Geophysics68, 1065–1074.
    [Google Scholar]
  24. SavaP. and VasconcelosI.2011. Extended imaging conditions for wave‐equation migration. Geophysical Prospecting59, 35–55.
    [Google Scholar]
  25. ShenH., MothiS. and AlbertinU.2011. Improving subsalt imaging with illumination‐based weighting of RTM 3D angle gathers. 81st SEG meeting, San Antonio, Texas, USA, Expanded Abstracts, 3206–3211.
  26. ShenP. and SymesW.W.2008. Automatic velocity analysis via shot profile migration. Geophysics73, VE49–VE59.
    [Google Scholar]
  27. ShenP. and SymesW.W.2013. Subsurface domain image warping by horizontal contraction and its application to wave‐equation migration velocity analysis. 83rd SEG meeting, Houston, Texas, USA, Expanded Abstracts, 4715–4719.
  28. SymesW.W. and CarazzoneJ.1991. Velocity inversion by differential semblance optimization. Geophysics56, 2061–2073.
    [Google Scholar]
  29. SymesW.W.2008. Migration velocity analysis and waveform inversion. Geophysical Prospecting56, 765–790.
    [Google Scholar]
  30. TarantolaA.1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics49, 1259–1266.
    [Google Scholar]
  31. ThierryP., OpertoS. and LambaréG.1999. Fast 2‐D ray+Born migration/inversion in complex media. Geophysics64, 162–181.
    [Google Scholar]
  32. VyasM. and TangY.2010. Gradients for wave‐equation migration velocity analysis. 80th SEG meeting, Denver, Colorado, USA, Expanded Abstracts, 4077–4081.
  33. YangT., ShraggeJ. and SavaP.C.2013. Illumination compensation for image‐domain wavefield tomography. Geophysics78, U65–U76.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): Imaging; Seismic; Velocity analysis

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