1887
Volume 51, Issue 6
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

The main objective of the AVO inversion is to obtain posterior distributions for P‐wave velocity, S‐wave velocity and density from specified prior distributions, seismic data and well‐log data. The inversion problem also involves estimation of a seismic wavelet and the seismic‐noise level. The noise model is represented by a zero mean Gaussian distribution specified by a covariance matrix. A method for joint AVO inversion, wavelet estimation and estimation of the noise level is developed in a Bayesian framework. The stochastic model includes uncertainty of both the elastic parameters, the wavelet, and the seismic and well‐log data. The posterior distribution is explored by Markov‐chain Monte‐Carlo simulation using the Gibbs' sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The use of a coloured seismic‐noise model resulted in about 10% lower uncertainties for the P‐wave velocity, S‐wave velocity and density compared with a white‐noise model. The uncertainty of the estimated wavelet is low. In the Heidrun example, the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results.

Loading

Article metrics loading...

/content/journals/10.1046/j.1365-2478.2003.00390.x
2003-10-23
2024-03-28
Loading full text...

Full text loading...

References

  1. AkiK. and RichardsP.G.1980. Quantitative Seismology . W.H. Freeman & Co.
    [Google Scholar]
  2. AndersonT.W.1984. An Introduction to Multivariate Statistical Analysis . John Wiley & Sons Inc.
    [Google Scholar]
  3. BulandA., KolbjørnsenO. and OmreH.2003. Rapid spatially coupled AVO inversion in the Fourier domain. Geophysics68, 824–836.
    [Google Scholar]
  4. BulandA. and LandrøM.2001. The impact of common offset migration on porosity estimation by AVO inversion. Geophysics66, 755–762.
    [Google Scholar]
  5. BulandA., LandrøM., AndersenM. and DahlT.1996. AVO inversion of Troll Field data. Geophysics61, 1589–1602.
    [Google Scholar]
  6. BulandA. and OmreH.2003a. Bayesian linearized AVO inversion. Geophysics68, 185–198.
    [Google Scholar]
  7. BulandA. and OmreH.2003b. Bayesian wavelet estimation from seismic and well data. Geophysics68, in press.
    [Google Scholar]
  8. CarlinB.P.1996. Hierarchical longitudinal modelling. In: Markov Chain Monte Carlo in Practice (eds W.R.Gilks , S.Richardson and D.J.Spiegelhalter ), pp. 303–319. Chapman & Hall.
    [Google Scholar]
  9. ChenM., ShaoQ. and IbrahimJ.2000. Monte Carlo Methods in Bayesian Computation . Springer‐Verlag, Inc.
    [Google Scholar]
  10. ChristakosG.1992. Random Field Models in Earth Sciences . Academic Press Inc.
    [Google Scholar]
  11. DuijndamA.J.W.1988a. Bayesian estimation in seismic inversion. Part I: Principles. Geophysical Prospecting36, 878–898.
    [Google Scholar]
  12. DuijndamA.J.W.1988b. Bayesian estimation in seismic inversion. Part II: Uncertainty analysis. Geophysical Prospecting36, 899–918.
    [Google Scholar]
  13. GemanS. and GemanD.1984. Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence6, 721–741.
    [Google Scholar]
  14. GilksW.R., RichardsonS. and SpiegelhalterD.J.1996. Markov Chain Monte Carlo in Practice . Chapman & Hall.
    [Google Scholar]
  15. GouveiaW.P. and ScalesJ.A.1998. Bayesian seismic waveform inversion: parameter estimation and uncertainty analysis. Journal of Geophysical Research103, 2759–2779.
    [Google Scholar]
  16. HampsonD. and RussellB.1990. AVO inversion: theory and practice. 60th SEG meeting, San Francisco , USA , Expanded Abstracts, 1456–1458.
    [Google Scholar]
  17. LauritzenS.L.1996. Graphical Models . Oxford University Press.
    [Google Scholar]
  18. MalinvernoA.2000. A Bayesian criterion for simplicity in inverse problem parametrization. Geophysical Journal International140, 267–285.
    [Google Scholar]
  19. OmreH., SølnaK. and TjelmelandH.1993. Simulation of random functions on large lattices. In: Geostatistics Tróia '92 (ed. A.Soares ), pp. 179–199. Kluwer Academic Press.
    [Google Scholar]
  20. RobertC.P.1994. The Bayesian Choice . Springer‐Verlag, Inc.
    [Google Scholar]
  21. ScalesJ.A. and TenorioL.2001. Prior information and uncertainty in inverse problems. Geophysics66, 389–397.
    [Google Scholar]
  22. SmithG.C. and GidlowP.M.1987. Weighted stacking for rock property estimation and detection of gas. Geophysical Prospecting35, 993–1014.
    [Google Scholar]
  23. SpiegelhalterD.J., BestN.G., GilksW.R. and InskipH.1996. Hepatitis B: A case study in MCMC methods. In: Markov Chain Monte Carlo in Practice (eds W.R.Gilks , S.Richardson and D.J.Spiegelhalter ), pp. 21–43. Chapman & Hall.
    [Google Scholar]
  24. TarantolaA. and ValetteB.1982. Inverse problems = quest for information. Journal of Geophysics50, 159–170.
    [Google Scholar]
  25. UlrychT.J., SacchiM.D. and WoodburyA.2001. A Bayes tour of inversion: a tutorial. Geophysics66, 55–69.
    [Google Scholar]
  26. WangY.1999. Simultaneous inversion for model geometry and elastic parameters. Geophysics64, 182–190.
    [Google Scholar]
  27. WangY., WhiteR.E. and PrattG.2000. Seismic amplitude inversion for interface geometry: practical approach for application. Geophysical Journal International142, 162–172.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1046/j.1365-2478.2003.00390.x
Loading
/content/journals/10.1046/j.1365-2478.2003.00390.x
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