1887
Volume 67, Issue 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

We consider a Bayesian model for inversion of observed amplitude variation with offset data into lithology/fluid classes, and study in particular how the choice of prior distribution for the lithology/fluid classes influences the inversion results. Two distinct prior distributions are considered, a simple manually specified Markov random field prior with a first‐order neighbourhood and a Markov mesh model with a much larger neighbourhood estimated from a training image. They are chosen to model both horizontal connectivity and vertical thickness distribution of the lithology/fluid classes, and are compared on an offshore clastic oil reservoir in the North Sea. We combine both priors with the same linearized Gaussian likelihood function based on a convolved linearized Zoeppritz relation and estimate properties of the resulting two posterior distributions by simulating from these distributions with the Metropolis–Hastings algorithm. The influence of the prior on the marginal posterior probabilities for the lithology/fluid classes is clearly observable, but modest. The importance of the prior on the connectivity properties in the posterior realizations, however, is much stronger. The larger neighbourhood of the Markov mesh prior enables it to identify and model connectivity and curvature much better than what can be done by the first‐order neighbourhood Markov random field prior. As a result, we conclude that the posterior realizations based on the Markov mesh prior appear with much higher lateral connectivity, which is geologically plausible.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12753
2019-02-22
2024-04-19
Loading full text...

Full text loading...

References

  1. AbendK., HarleyT. and KanalL.1965. Classification of binary random patterns. IEEE Transactions on Information Theory11, 538–544.
    [Google Scholar]
  2. AkiK. and RichardsP.G.1980. Quantitative Seismology: Theory and Methods. W.H.Freeman , New York.
    [Google Scholar]
  3. ArnesenP. and TjelmelandH.2017. Prior specification of neighbourhood and interaction structure in binary Markov random fields. Statistics and Computing27, 737–756.
    [Google Scholar]
  4. AsterR., BorchersB. and ThurberC.H.2011. Parameter Estimation and Inverse Problems, Elsevier, Amsterdam.
    [Google Scholar]
  5. BulandA. and OmreH.2003. Bayesian linearized AVO invserion. Geophysics68, 185–198.
    [Google Scholar]
  6. ConnollyP. and HughesM.2016. Stochastic inversion by matching to large numbers of pseudo‐wells. Geophysics81(2), M7–M22.
    [Google Scholar]
  7. CressieN. and DavidsonJ.1998. Image analysis with partially ordered Markov models. Computational Statistics and Data Analysis29, 1–26.
    [Google Scholar]
  8. EidsvikJ., MukerjiT. and SwitzerP.2004. Estimation of geological attributes from a well log: an application of hidden Markov chains. Mathematical Geology36, 379–397.
    [Google Scholar]
  9. EmeryX. and LantuéjoulC.2014. Can a training image be a substitute for a random field model? Mathematical Geosciences46, 133–147.
    [Google Scholar]
  10. FjeldstadT. and OmreH.2019. Bayesian inversion of convolved hidden Markov models with applications in reservoir prediction. IEEE Transations on Geoscience and Remote Sensing, to appear.
  11. GamermanD. and LopesH.F.2006. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, 2nd edn. Chapman & Hall/CRC, London.
    [Google Scholar]
  12. GilksW.R., RichardsonS. and SpiegelhalterD.J.1996. Markov Chain Monte Carlo in Practice. Chapman & Hall, London.
    [Google Scholar]
  13. GrabischM., MarichalJ.L. and RoubensM.2000. Equivalent representations of set functions. Mathematics of Operations Research25, 157–178.
    [Google Scholar]
  14. GranaD. and Della RossaE.2010. Probabilistic petrophysical‐properties estimation integrating statistical rock physics with seismic inversion. Geophysics75(3), O21–O37.
    [Google Scholar]
  15. GranaD., FjeldstadT. and OmreH.2017. Bayesian Gaussian mixture linear inversion for geophysical inverse problems. Mathematical Geosciences49, 493–515.
    [Google Scholar]
  16. GuardianoF. and SrivastavaR.1993. Multivariate geostatistics: beyond bivariate moments. In: Geostatistics Tróia'92 (ed. A.Soares ), pp. 133–144. Kluwer, Dordrecht.
    [Google Scholar]
  17. GunningJ. and GlinskyM.E.2007. Detection of reservoir quality using Bayesian seismic inversion. Geophysics72(3), R37–R39.
    [Google Scholar]
  18. HammerP.L. and HolzmanR.1992. Approximations of pseudo‐Boolean functions; applications to game theory. Methods and Models of Operation Research36, 3–21.
    [Google Scholar]
  19. HurnM., HusbyO. and RueH.2003. A tutorial on image analysis. In: Spatial Statistics and Computational Methods, Lecture Notes in Statistics, Vol. 173 (ed. J.Møller ), pp. 87–139. Springer.
    [Google Scholar]
  20. JournelJ. and ZhangT.2006. The necessity of a multiple‐point prior model. Mathematical Geology38, 591–610.
    [Google Scholar]
  21. KindermannR. and SnellJ.L.1980. Markov Random Fields and Their Applications. American Mathematical Society, Providence, RI.
    [Google Scholar]
  22. LangX. and GranaD.2017. Geostatistical inversion of prestack seismic data for the joint estimation of facies and impedances using stochastic sampling from Gaussian mixture posterior distribution. Geophysics82(4), M55–M65.
    [Google Scholar]
  23. LarsenA.L., UlvmoenM., OmreH. and BulandA.2006. Bayesian lithology/fluid prediction and simulation on the basis of a Markov‐chain prior model. Geophysics71(5), R69–R78.
    [Google Scholar]
  24. LuoX. and TjelmelandH.2019. Prior specification for binary Markov mesh models. Statistics and Computing, to appear.
  25. MariethozG. and CaersJ.2014. Multiple‐Point Geostatistics: Stochastic Modeling with Training Images. John Wiley & Sons.
    [Google Scholar]
  26. RimstadK., AvsethP. and OmreH.2012. Hierarchical Bayesian lithology/fluid prediction: a North Sea case study. Geophysics77(2), B69–B856.
    [Google Scholar]
  27. RimstadK. and OmreH.2010. Impact of rock‐physics depth trends and Markov random fields on hierarchical Bayesian lithology/fluid prediction. Geophysics75(4), R93–R108.
    [Google Scholar]
  28. RobertC.P. and CasellaG.1999. Monte Carlo Statistical Methods. Springer.
  29. SenM.K. and StoffaP.L.2013. Global Optimization Methods in Geophysical Inversion. Cambridge University Press.
    [Google Scholar]
  30. StienM. and KolbjørnsenO.2011. Facies modeling using a Markov mesh model specification. Mathematical Geosciences43, 611–624.
    [Google Scholar]
  31. StrebelleS.2002. Conditional simulation of complex geological structures using multiple‐point statistics. Mathematical Geology34, 1–21.
    [Google Scholar]
  32. TarantolaA.2005. Inverse Problem Theory. SIAM, Philidelphia.
    [Google Scholar]
  33. ToftakerH. and TjelmelandH.2013. Construction of binary multi‐grid Markov random field prior models from training images. Mathematical Geosciences45, 383–409.
    [Google Scholar]
  34. UlvmoenM. and OmreH.2010. Improved resolution in Bayesian lithology/fluid inversion from prestack seismic data and well observations: part 1‐methodology. Geophysics75(2), R21–R35.
    [Google Scholar]
  35. ZhangT., PedersenS.I., KnudbyC. and McCormickD.2012. Memory‐efficient categorical multi‐point statistics algorithms based on compact search trees. Mathematical Geosciences44, 863–879.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12753
Loading
/content/journals/10.1111/1365-2478.12753
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Computing aspects; Inverse problem; Inversion; Mathematical formulation; Seismics

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