1887
Volume 30, Issue 4
  • E-ISSN: 1365-2117

Abstract

Abstract

We consider the problem of conditioning a geological process‐based computer simulation, which produces basin models by simulating transport and deposition of sediments, to data. Emphasising uncertainty quantification, we frame this as a Bayesian inverse problem, and propose to characterise the posterior probability distribution of the geological quantities of interest by using a variant of the ensemble Kalman filter, an estimation method which linearly and sequentially conditions realisations of the system state to data. A test case involving synthetic data is used to assess the performance of the proposed estimation method, and to compare it with similar approaches. We further apply the method to a more realistic test case, involving real well data from the Colville foreland basin, North Slope, Alaska.

Loading

Article metrics loading...

/content/journals/10.1111/bre.12273
2017-12-27
2020-02-18
Loading full text...

Full text loading...

References

  1. Bertoncello, A., Sun, T., Li, H., Mariethoz, G. & Caers, J. (2013) Conditioning surface‐based geological models to well and thickness data. Math. Geosci., 45(7), 873–893.
    [Google Scholar]
  2. Charvin, K., Gallagher, K., Hampson, G.L. & Labourdette, R. (2009) A Bayesian approach to inverse modelling of stratigraphy, part 1: Method. Basin Res., 21(1), 5–25.
    [Google Scholar]
  3. Chen, Z. (2003) Bayesian filtering: From Kalman filters to particle filters, and beyond. Statistics, 182(1), 1–69.
    [Google Scholar]
  4. Christ, A., Schenk, O. & Salomonsen, P. (2016) Using stratigraphic forward modeling to model the brookian sequence of the alaska north slope. In: Geostatistical and Geospatial Approaches for the Characterization of Natural Resources in the Environment (Ed. by N.Raju ), pp. 623–626. Springer, Cham.
    [Google Scholar]
  5. Dobson, A.J. & Barnett, A. (2008) An Introduction to Generalized Linear Models. CRC Press.
    [Google Scholar]
  6. Edwards, J., Lallier, F. & Caumon, G. (2016) Using a forward model as training model for 3D stochastic multi‐well correlation. In Second Conference on Forward Modelling of Sedimentary Systems. EAGE.
  7. Emerick, A.A. & Reynolds, A.C. (2013) Ensemble smoother with multiple data assimilation. Comput. Geosci., 55, 3–15.
    [Google Scholar]
  8. Evensen, G. (2009) Data Assimilation: The Ensemble Kalman Filter. Springer, Berlin.
    [Google Scholar]
  9. Frolov, S., Baptista, A.M., Leen, T.K., Lu, Z. & van der Merwe, R. (2009) Fast data assimilation using a nonlinear Kalman filter and a model surrogate: An application to the Columbia River estuary. Dyn. Atmos. Oceans, 48(1), 16–45.
    [Google Scholar]
  10. Gneiting, T. & Raftery, A.E. (2007) Strictly proper scoring rules, prediction, and estimation. J. Am. Stat. Assoc., 102(477), 359–378.
    [Google Scholar]
  11. Hutton, E.W. & Syvitski, J.P. (2008) Sedflux 2.0: An advanced process response model that generates three‐dimensional stratigraphy. Comput. Geosci., 34(10), 1319–1337.
    [Google Scholar]
  12. Keys, W. S. (1996) A Practical Guide to Borehole Geophysics in Environmental Investigations. CRC Press, Boca Raton, FL.
    [Google Scholar]
  13. Killeen, P. (1982) Gamma‐ray logging and interpretation. In: Developments in Geophysical Exploration Methods–3 (Ed. by A.A.Fitch ), 95–150. Springer, Dordrecht.
    [Google Scholar]
  14. Laloy, E., Beerten, K., Vanacker, V., Christl, M., Rogiers, B. & Wouters, L. (2017) Bayesian inversion of a CRN depth profile to infer Quaternary erosion of the northwestern Campine Plateau (NE Belgium). Earth Surface Dynamics, 5(3), 331.
    [Google Scholar]
  15. Lopez, S., Cojan, I., Rivoirard, J. & Galli, A. (2009) Process‐based stochastic modelling: Meandering channelized reservoirs. In: Analogue and Numerical Modelling of Sedimentary Systems: From Understanding to Prediction (Ed. by P.de Boer , G.Postma , K.van der Zwan , P.Burgess & P.Kukla ), vol. 40, pp. 139–144. Wiley‐Blackwell, Oxford, UK.
    [Google Scholar]
  16. Nychka, D. & Anderson, J. L. (2010) Data assimilation. In: Handbook of Spatial Statistics (Eds. by A.Gelfand , P.Diggle , P.Guttorp & M.Fuentes ), pp. 89–106. Chapman & Hall/CRC, New York.
    [Google Scholar]
  17. Paola, C. (2000) Quantitative models of sedimentary basin filling. Sedimentology, 47(s1), 121–178.
    [Google Scholar]
  18. Pyrcz, M. J. & Deutsch, C. V. (2014) Geostatistical Reservoir Modeling. Oxford University Press, New York.
    [Google Scholar]
  19. Sacchi, Q., Weltje, G.J. & Verga, F. (2015) Towards process‐based geological reservoir modelling: Obtaining basin‐scale constraints from seismic and well data. Mar. Pet. Geol., 61, 56–68.
    [Google Scholar]
  20. Sætrom, J. & Omre, H. (2013) Uncertainty quantification in the ensemble Kalman filter. Scand. J. Stat., 40(4), 868–885.
    [Google Scholar]
  21. Sakov, P. & Bertino, L. (2011) Relation between two common localisation methods for the EnKF. Comput. Geosci., 15(2), 225–237.
    [Google Scholar]
  22. Schenk, O., Magoon, L. B., Bird, K. J. & Peters, K. E. (2012) Petroleum system modeling of northern Alaska. In: Basin Modeling: New Horizons in Research and Applications (Ed. by K.E.Peters , D.J.Durry & M.Kacewicz ), American Association of Petroleum Geologists Hedberg Series, no. 4, pp. 317–338. American Association of Petroleum Geologists (AAPG).
  23. Storms, J.E. (2003) Event‐based stratigraphic simulation of wave dominated shallow‐marine environments. Mar. Geol., 199(1), 83–100.
    [Google Scholar]
  24. Strebelle, S. (2002) Conditional simulation of complex geological structures using multiple‐point statistics. Math. Geol., 34(1), 1–21.
    [Google Scholar]
  25. Syvitski, J.P. & Hutton, E.W. (2001) 2D SEDFLUX 1.0 C: An advanced process‐response numerical model for the fill of marine sedimentary basins. Comput. Geosci., 27(6), 731–753.
    [Google Scholar]
  26. Tarantola, A. (2005) Inverse Problem Theory and Methods for Model Parameter Estimation. Society for Industrial and Applied Mathematics, Philadelphia, PA.
    [Google Scholar]
  27. Tetzlaff, D.M. (2005) Modelling coastal sedimentation through geologic time. J. Coastal Res., 21(3), 610–617.
    [Google Scholar]
  28. Tetzlaff, D. M. & Harbaugh, J. W. (1989) Simulating Clastic Sedimentation. Computer Methods in the Geosciences. vanNostrand Reinholt, New York, NY.
    [Google Scholar]
  29. Tetzlaff, D. & Priddy, G. (2001) Sedimentary process modeling: From academia to industry. In Geologic Modeling and Simulation (eds. by D.F.Merriam & J.C.Davis ), pp. 45–69. Springer, New York.
    [Google Scholar]
  30. U.S. Geological Survey
    U.S. Geological Survey (1981) Wildcat well Tunalik 1, LAS‐format well log data. https://certmapper.cr.usgs.gov/data/PubArchives/of00-200/wells/TUNALIK1/LAS/TU1LAS.HTM.
http://instance.metastore.ingenta.com/content/journals/10.1111/bre.12273
Loading
/content/journals/10.1111/bre.12273
Loading

Data & Media loading...

  • Article Type: Research Article
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