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Volume 53, Issue 5
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

We describe a method to invert a walkaway vertical seismic profile (VSP) and predict elastic properties (P‐wave velocity, S‐wave velocity and density) in a layered model looking ahead of the deepest receiver. Starting from Bayes's rule, we define a posterior distribution of layered models that combines prior information (on the overall variability of and correlations among the elastic properties observed in well logs) with information provided by the VSP data. This posterior distribution of layered models is sampled by a Monte‐Carlo method. The sampled layered models agree with prior information and fit the VSP data, and their overall variability defines the uncertainty in the predicted elastic properties. We apply this technique first to a zero‐offset VSP data set, and show that uncertainty in the long‐wavelength P‐wave velocity structure results in a sizable uncertainty in the predicted elastic properties. We then use walkaway VSP data, which contain information on the long‐wavelength P‐wave velocity (in the reflection moveout) and on S‐wave velocity and density contrasts (in the change of reflectivity with offset). The uncertainty of the look‐ahead prediction is considerably decreased compared with the zero‐offset VSP, and the predicted elastic properties are in good agreement with well‐log measurements.

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2005-08-15
2024-04-16

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References

  1. AkiK. and RichardsP.G.1980. Quantitative Seismology: Theory and Methods , Vol. 1. W.H. Freeman & Co.
    [Google Scholar]
  2. BorlandW.H., HayashidaN., KusakaH., LeaneyW.S. and NakanishiS.1998. Drill bit seismic, vertical seismic profiling, and seismic depth imaging to aid drilling decisions in the Tho Tinh structure, Nam Con Son basin, Vietnam. Butsuri-Tansa (Geophysical Exploration)51, 27–44.
    [Google Scholar]
  3. BulandA. and OmreH.2003a. Bayesian linearized AVO inversion. Geophysics68, 185–198.
    [Google Scholar]
  4. BulandA. and OmreH.2003b. Joint AVO inversion, wavelet estimation and noise‐level estimation using a spatially coupled hierarchical Bayesian model. Geophysical Prospecting51, 531–550.
    [Google Scholar]
  5. ByunB.S., CorriganD. and GaiserJ.E.1989. Anisotropic velocity analysis for lithology discrimination. Geophysics54, 1564–1574.
    [Google Scholar]
  6. CastagnaJ.P., BatzleM.L. and EastwoodR.L.1985. Relationships between compressional‐wave and shear‐wave velocities in clastic silicate rocks. Geophysics50, 571–581.
    [Google Scholar]
  7. ChibS. and GreenbergE.1995. Understanding the Metropolis‐Hastings algorithm. The American Statistician49, 327–335.
    [Google Scholar]
  8. DuijndamA.J.W.1988. Bayesian estimation in seismic inversion, part I: Principles. Geophysical Prospecting36, 878–898.
    [Google Scholar]
  9. GardnerG.H.F., GardnerL.W. and GregoryA.R.1974. Formation velocity and density: The diagnostic basis for stratigraphic traps. Geophysics39, 770–780.
    [Google Scholar]
  10. GilksW.R.
    , RichardsonS. and SpiegelhalterD.J. (eds) 1996. Markov Chain Monte Carlo in Practice . Chapman and Hall, London .
    [Google Scholar]
  11. GoetzJ.F., DupalL. and BowlerJ.1979. An investigation into discrepancies between sonic log and seismic check shot velocities. Journal of the Australian Petroleum Exploration Association19, 131–141.
    [Google Scholar]
  12. GouveiaW.P. and ScalesJ.A.1998. Bayesian seismic waveform inversion: parameter estimation and uncertainty analysis. Journal of Geophysical Research103, 2759–2779.
    [Google Scholar]
  13. GreenP.J.1995. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika82, 711–732.
    [Google Scholar]
  14. GriveletP.A.1985. Inversion of vertical seismic profiles by iterative modeling. Geophysics50, 924–930.
    [Google Scholar]
  15. GullS.F.1988. Bayesian inductive inference and maximum entropy. In: Maximum Entropy and Bayesian Methods in Science and Engineering (eds G.J.Erickson and C.R.Smith ), Vol. 1, pp. 53–74. Kluwer Academic Press, Dordrecht .
    [Google Scholar]
  16. JacksonD.D.1979. The use of a priori data to resolve non‐uniqueness in linear inversion. Geophysical Journal of the Royal Astronomical Society57, 137–157.
    [Google Scholar]
  17. JacksonD.D. and Matsu'uraM.1985. A Bayesian approach to nonlinear inversion. Journal of Geophysical Research90, 581–591.
    [Google Scholar]
  18. JaynesE.T.2003. Probability Theory: The Logic of Science . Cambridge University Press.
    [Google Scholar]
  19. JefferysW.H. and BergerJ.O.1992. Ockham's razor and Bayesian analysis. American Scientist80, 64–72.
    [Google Scholar]
  20. KassR.E. and WassermannL.1996. The selection of prior distributions by formal rules. Journal of the American Statistical Association91, 1343–1370.
    [Google Scholar]
  21. KennettP., IresonR.L. and ConnP.J.1980. Vertical seismic profiles: Their applications in exploration geophysics. Geophysical Prospecting28, 676–699.
    [Google Scholar]
  22. LeaneyW.S.1990. Parametric wavefield decomposition and applications. 60th SEG meeting, San Francisco , USA, Expanded Abstracts, 1097–1100.
  23. LeaneyW.S.1999. Walkaway Q inversion. 69th SEG meeting, Houston , USA , Expanded Abstracts, 1311–1314.
  24. LeaneyW.S.2000. Look‐ahead walkaways using effective VTI models. 70th SEG meeting, Calgary , Canada , Expanded Abstracts, 1743–1747.
  25. MaceD. and LaillyP.1986. Solution of the VSP one‐dimensional inverse problem. Geophysical Prospecting34, 1002–1021.
    [Google Scholar]
  26. MalinvernoA.2000. A Bayesian criterion for simplicity in inverse problem parametrization. Geophysical Journal International140, 267–285.
    [Google Scholar]
  27. MalinvernoA.2002. Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem. Geophysical Journal International151, 675–688.
    [Google Scholar]
  28. MalinvernoA. and BriggsV.A.2004. Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and Empirical Bayes. Geophysics69, 1005–1016.
    [Google Scholar]
  29. MalinvernoA. and LeaneyW.S.2000. A Monte Carlo method to quantify uncertainty in the inversion of zero‐offset VSP data. 70th SEG meeting, Calgary , Canada , Expanded Abstracts, 2393–2396.
  30. MallickS.1995. Model‐based inversion of amplitude‐variations‐with‐offset data using a genetic algorithm. Geophysics60, 939–954.
    [Google Scholar]
  31. MosegaardK., SinghS., SnyderD. and WagnerH.1997. Monte Carlo analysis of seismic reflections from Moho and the W reflector. Journal of Geophysical Research102, 2969–2981.
    [Google Scholar]
  32. MosegaardK. and TarantolaA.1995. Monte Carlo sampling of solutions to inverse problems. Journal of Geophysical Research100, 12431–12447.
    [Google Scholar]
  33. OldenburgD., ScheuerT. and LevyS.1983. Recovery of acoustic impedance from reflection seismograms. Geophysics48, 1318–1337.
    [Google Scholar]
  34. PayneM.A.1994. Looking ahead with vertical seismic profiles. Geophysics59, 1182–1191.
    [Google Scholar]
  35. PetersonR.A., FillipponeW.R. and CokerF.B.1955. The synthesis of seismograms from well log data. Geophysics20, 516–538.
    [Google Scholar]
  36. RosenkrantzR.D.1977. Inference, Method and Decision: Toward a Bayesian Philosophy of Science . D. Reidel Publishing Co., Dordrecht , Holland .
    [Google Scholar]
  37. RubinsteinR.Y.1981. Simulation and the Monte Carlo Method . John Wiley & Sons, Inc.
    [Google Scholar]
  38. SambridgeM. and MosegaardK.2002. Monte Carlo methods in geophysical inverse problems. Reviews of Geophysics40(3), 1009, DOI: doi:10.1029/2000RG000089
     [Google Scholar]
  39. SayersC.M.1995. Anisotropic velocity analysis. Geophysical Prospecting43, 541–568.
    [Google Scholar]
  40. SenM.K. and StoffaP.L.1995. Global Optimization Methods in Geophysical Inversion . Advances in Exploration Geophysics, Vol. 4. Elsevier Science Publishing Co.
    [Google Scholar]
  41. SenaA.G.1991. Seismic traveltime equations for azimuthally anisotropic and isotropic media: Estimation of interval elastic properties. Geophysics56, 2090–2101.
    [Google Scholar]
  42. SiviaD.S.1996. Data Analysis: A Bayesian Tutorial . Clarendon Press, Oxford .
    [Google Scholar]
  43. StewartR.R., HuddlestonP.D. and KanT.K.1984. Seismic versus sonic velocities: A vertical seismic profiling study. Geophysics49, 1153–1168.
    [Google Scholar]
  44. TarantolaA.1987. Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation . Elsevier Science Publishing Co.
    [Google Scholar]
  45. TarantolaA. and ValetteB.1982a. Inverse problems = quest for information. Journal of Geophysics50, 159–170.
    [Google Scholar]
  46. TarantolaA. and ValetteB.1982b. Generalized nonlinear inverse problems solved using the least squares criterion. Reviews of Geophysics and Space Physics20, 219–232.
    [Google Scholar]
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Monte‐Carlo Bayesian look‐ahead inversion of walkaway vertical seismic profiles
Geophysical Prospecting 53, 689 (2005); https://doi.org/10.1111/j.1365-2478.2005.00496.x
/content/journals/10.1111/j.1365-2478.2005.00496.x
/content/journals/10.1111/j.1365-2478.2005.00496.x
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