1887
Volume 65 Number 1
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

In anisotropic media, several parameters govern the propagation of the compressional waves. To correctly invert surface recorded seismic data in anisotropic media, a multi‐parameter inversion is required. However, a tradeoff between parameters exists because several models can explain the same dataset. To understand these tradeoffs, diffraction/reflection and transmission‐type sensitivity‐kernels analyses are carried out. Such analyses can help us to choose the appropriate parameterization for inversion. In tomography, the sensitivity kernels represent the effect of a parameter along the wave path between a source and a receiver. At a given illumination angle, similarities between sensitivity kernels highlight the tradeoff between the parameters. To discuss the parameterization choice in the context of finite‐frequency tomography, we compute the sensitivity kernels of the instantaneous traveltimes derived from the seismic data traces. We consider the transmission case with no encounter of an interface between a source and a receiver; with surface seismic data, this corresponds to a diving wave path. We also consider the diffraction/reflection case when the wave path is formed by two parts: one from the source to a sub‐surface point and the other from the sub‐surface point to the receiver. We illustrate the different parameter sensitivities for an acoustic transversely isotropic medium with a vertical axis of symmetry. The sensitivity kernels depend on the parameterization choice. By comparing different parameterizations, we explain why the parameterization with the normal moveout velocity, the anellipitic parameter η, and the δ parameter is attractive when we invert diving and reflected events recorded in an active surface seismic experiment.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12361
2016-02-04
2024-03-28
Loading full text...

Full text loading...

References

  1. AlkhalifahT.2000. An acoustic wave equation for anisotropic media. Geophysics65(4), 1239–1250.
    [Google Scholar]
  2. AlkhalifahT.2003. Tau migration and velocity analysis: Theory and synthetic examples. Geophysics68(4), 1331–1339.
    [Google Scholar]
  3. AlkhalifahT. and BednarJ.B.2000. Building a 3D anisotropic model: Its implication to travel‐time calculation and velocity analysis. 70th SEG Annual international Meeting, Calgary, Canada, Expanded Abstracts, 965–968.
  4. AlkhalifahT. and PlessixR.E.2014. A recipe for practical full waveform inversion in anisotropic media: An analytical parameter resolution study. Geophysics79(3), R91–R101.
    [Google Scholar]
  5. BakkerP. and GerritsenS.2013. Developing angle‐domain wave path tomography for velocity analysis in complex settings. 75th EAGE Conference & Exhibition, London, U.K.
  6. CaraM. and LevequeJ.1987. Waveform inversion using secondary observables. Geophysical Research Letters14(14), 1046–1049.
    [Google Scholar]
  7. ČervenýV.2001. Seismic Ray Theory. Cambridge University Press.
    [Google Scholar]
  8. ChoiY. and AlkhalifahT.2011. Frequency‐domain waveform inversion using the unwrapped phase. 81st SEG Annual international Meeting, Las Vegas, USA, SEG Expanded Abstracts, 2576–2580.
  9. ChoiY. and AlkhalifahT.2013. Frequency‐domain waveform inversion using the phase derivative. Geophysical Journal International195(3), 1904–1916.
    [Google Scholar]
  10. DahlenF.A., HungS.H. and NoletG.2000. Fréchet kernels for finite‐frequency traveltimes‐I. Theory. Geophysical Journal International141(1), 157–174.
    [Google Scholar]
  11. DjebbiR. and AlkhalifahT.2013. Finite frequency traveltime sensitivity kernels for acoustic anisotropic media: Angle dependent bananas. 83rd SEG meeting, Houston, USA, Expanded Abstracts, 4858–4863.
  12. DjebbiR. and AlkhalifahT.2014. Traveltime sensitivity kernels for wave equation tomography using the unwrapped phase. Geophysical Journal International197(2), 975–986.
    [Google Scholar]
  13. DuveneckE., MilcikP., BakkerP.M. and PerkinsC.2008. Acoustic VTI wave equations and their application for anisotropic reverse time migration. 78th SEG Meeting, Las Vegas, USA, Expanded Abstracts, 2186–2190.
  14. FomelS.2011. Theory of 3‐D angle gathers in wave‐equation seismic imaging. Journal of Petroleum Exploration and Production Technology1(1), 11–16.
    [Google Scholar]
  15. GauthierO., VirieuxJ. and TarantolaA.1986. Two‐dimensional non‐linear inversion of seismic waveforms: Numerical results. Geophysics51(7), 1387–1403.
    [Google Scholar]
  16. GholamiY., BrossierR., OpertoS., RibodettiA. and VirieuxJ.2013a. Which parameterization is suitable for acoustic vertical transverse isotropic full waveform inversion? Part 1: Sensitivity and trade‐off analysis. Geophysics78(2), R81–R105.
    [Google Scholar]
  17. GholamiY., BrossierR., OpertoS., RibodettiA. and VirieuxJ.2013b. Which parameterization is suitable for acoustic vertical transverse isotropic full waveform inversion? Part 2: Synthetic and real data case studies from Valhall. Geophysics78(2), R107–R124.
    [Google Scholar]
  18. LaillyP.1983. The seismic problem as a sequence of before‐stack migrations. In: Conference on Inverse Scattering: Theory and Applications (ed. J. BeeBednar ), pp. 206–220. Society for Industrial and Applied Mathematics.
    [Google Scholar]
  19. LiuY., DongL., WangY., ZhuJ. and MaZ.2009. Sensitivity kernels for seismic fresnel volume tomography. Geophysics74(5), U35–U46.
    [Google Scholar]
  20. MarqueringH., DahlenF.A. and NoletG.1999. Three‐dimensional sensitivity kernels for finite frequency traveltimes: the banana‐doughnut paradox. Geophysical Journal International137(3), 805–815.
    [Google Scholar]
  21. MarqueringH., NoletG. and DahlenF.A.1998. Three‐dimensional waveform sensitivity kernels. Geophysical Journal International132(3), 521–534.
    [Google Scholar]
  22. MoraP.1987. Nonlinear two‐dimensional elastic inversion of multioffset seismic data. Geophysics52(9), 1211–1228.
    [Google Scholar]
  23. PlessixR.E.2013. A pseudo‐time formulation for acoustic full waveform inversion. Geophysical Journal International192(2), 613–630.
    [Google Scholar]
  24. PlessixR.E. and CaoQ.2011. A parametrization study for surface seismic full waveform inversion in an acoustic vertical transversely isotropic medium. Geophysical Journal International185(1), 539–556.
    [Google Scholar]
  25. PrattR.G., SongZ.M., WilliamsonP. and WarnerM.1996. Two‐dimensional velocity models from wide‐angle seismic data by wavefield inversion. Geophysical Journal International124(2), 323–340.
    [Google Scholar]
  26. PruchaM.L., BiondiB.L. and SymesW.W.1999. Angle‐domain common image gathers by wave equation migration. 69th SEG meeting, Houston, USA, SEG Expanded Abstracts, 824–827.
  27. RickettJ.E. and SavaP.C.2002. Offset and angle‐domain common image‐point gathers for shot profile migration. Geophysics67(3), 883–889.
    [Google Scholar]
  28. SieminskiA., TrampertJ. and TrompJ.2009. Principal component analysis of anisotropic finite frequency sensitivity kernels. Geophysical Journal International179(2), 1186–1198.
    [Google Scholar]
  29. SniederR.1989. Retrieving both the impedance contrast and background velocity: A global strategy for the seismic reflection problem. Geophysics54(8), 991–1000.
    [Google Scholar]
  30. SniederR. and LomaxA.1996. Wavefield smoothing and the effect of rough velocity perturbations on arrival times and amplitudes. Geophysical Journal International125(3), 796–809.
    [Google Scholar]
  31. StopinA., PlessixR.E. and Al AbriS.2014. Multiparameter waveform inversion of a large wide azimuth low‐frequency land data set in Oman. Geophysics79(3), WA69–WA77.
    [Google Scholar]
  32. TarantolaA.1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics49(8), 1259–1266.
    [Google Scholar]
  33. ThomsenL.1986. Weak elastic anisotropy. Geophysics51(10), 1954–1966.
    [Google Scholar]
  34. TrompJ., TapeC. and LiuQ.2005. Seismic tomography, adjoint methods, time reversal and banana‐doughnut kernels. Geophysical Journal International160(1), 195–216.
    [Google Scholar]
  35. TsvankinI.2001. Seismic Signatures and Analysis of Reflection Data in Anisotropic Media. Pergamon.
    [Google Scholar]
  36. VirieuxJ. and OpertoS.2009. An overview of full‐waveform inversion in exploration geophysics. Geophysics74(6), WCC1–WCC26.
    [Google Scholar]
  37. WoodwardM.J.1992. Wave‐equation tomography. Geophysics, 57(1), 15–26.
    [Google Scholar]
  38. XieX.B. and YangH.2008. The finite‐frequency sensitivity kernel for migration residual moveout and its applications in migration velocity analysis. Geophysics6(73), S241–S249.
    [Google Scholar]
  39. ZhouB. and GreenhalghS.A.2011. Computing the sensitivity kernels for 2.5‐D seismic waveform inversion in heterogeneous, anisotropic media. Pure and Applied Geophysics, 168(10), 1729–1748.
    [Google Scholar]
  40. ZhouB. and GreenhalghS.2009. On the computation of the Frechet derivatives for seismic waveform inversion in 3‐D general anisotropic, heterogeneous media. Geophysics74(5), WB153–WB163.
    [Google Scholar]
  41. ZhouY.2009. Multimode surface wave sensitivity kernels in radially anisotropic earth media. Geophysical Journal International176(3), 865–888.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12361
Loading
/content/journals/10.1111/1365-2478.12361
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