Bayesian inversion of geoelectrical resistivity data

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 65, Issue 3, 2003, Pages 619-642

  Andersen, Kim E ^a   Brooks, Stephen P ^b   Hansen, Martin B ^a  

^a AALBORG UNIVERSITY   (Denmark)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Bayesian inference; Coupling; Inverse problems; Markov chain Monte Carlo methods; Multigrid methods; Stochastic geometry

Indexed keywords

EID: 0042672866     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00406     Document Type: Article

References (37)

1. Andersen, K. E., Brooks, S. P. and Hansen, M. B. (2001) A Bayesian approach to crack detection in electrically conducting media. Inv. Probl., 17, 121-136.
2. Arak, T., Clifford, P. and Surgailis, D. (1993) Point-based polygonal models for random graphs. Adv. Appl Probab., 25, 348-372.
3. Arak, T. and Surgailis, D. (1989) Markov fields with polygonal realisations. Probab. Theory Reltd Flds, 80, 543-579.
4. Boerner, D. E. and West, G. F. (1989) Fréchet derivatives and single scattering theory. Geophys. J. Int., 98, 385-390.
5. Brooks, S. P. (1998) Markov chain Monte Carlo method and its application. Statistician, 47, 69-100.
6. Brown, W. G. (1964) Enumeration of triangulations of the disk. Proc. Lond. Math. Soc., 14, 746-768.
7. Christensen, N. B. and Sørensen, K. I. (1998) Surface and borehole electric and electromagnetic methods for hydrogeological investigations. Eur. J. Environ. Engng Geophys., 3, 75-90.
8. Daily, W., Ramirez, A., LaBrecque, D. and Barber, W. (1995) Electrical resistance tomography at the Oregon Graduate Institute, J. Geophys., 33, 227-237.
9. Edwards, L. S. (1977) A modified pseudosection for resistivity and IP. Geophysics, 42, 275-283.
10. Fox, C. and Nicholls, G. K. (1997) Sampling conductivity images via MCMC. In The Art and Science of Bayesian Image Analysis: Proc. Leeds A. Statist. Res. Wrkshp (eds K. V Mardia, C. A. Gill and R. Aykroyd), pp. 91-100. Leeds: Leeds University Press.
11. Geyer, C. J. (1991) Markov chain Monte Carlo maximum likelihood. In Computing Science and Statistics: Proc. 23rd Symp. Interface, pp. 156-163. Fairfax: Interface Foundation.
12. Geyer, C. J. and Thompson, E. A. (1995) Annealing Markov chain Monte Carlo with applications to ancestral inference. J. Am. Statist. Ass., 90, 909-920.
13. Goodman, J. and Sokal, A. D. (1989) Multigrid Monte Carlo method: conceptual foundations. Phys. Rev. D, 40, 2035-2072.
14. Green, P. (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711-732.
15. Hastings, W. K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
16. Heilmann-Clausen, C., Nielsen, O. B. and Gersner, F. (1985) Lithostratigraphy and depositional environments in the Upper Paleocene and Eocene of Denmark. Bull. Geol. Soc. Denmark, 33, 287-323.
17. Higdon, D., Lee, H. and Bi, Z. (2001) A Bayesian approach to characterizing uncertainty in inverse problems using coarse and fine scale information. Technical Report. Institute of Statistics and Decision Sciences, Duke University, Durham.
18. Jacobsen, B. H. (1993) Practical methods of a priori covariance specification for geophysical inversion. In Proc. Interdisciplinary Inversion Wrkshp 2 (ed. K. Mosegaard), pp. 1-10. Copenhagen, University of Copenhagen.
19. Jacobsen, B. H., Møller, I., Jensen, J. and Effersø, F. (1999) Multichannel deconvolution, MCD, in geophysics and helioseismology. Phys. Chem. Earth, 24, 215-220.
20. Kaipio, J. P., Kolehmainen, V., Somersalo, E. and Vauhkonen, M. (2000) Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography. Inv. Probl., 16, 1487-1522.
21. Kirsch, A. (1996) An Introduction to the Mathematical Theory of Inverse Problems. New York: Springer.
22. Li, Y. and Oldenburg, D. W. (1992) Approximate inverse mappings in DC resistivity problems. Geophys. J. Int., 109, 343-362.
23. Liu, J. S. and Sabatti, C. (1998) Simulated sintering: Markov chain Monte Carlo with spaces of varying dimensions (with discussions). In Bayesian Statistics 6 (eds J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith), pp. 389-413. Oxford: Oxford University Press.
24. Loke, M. H. and Barker, R. D. (1995) Rapid least-squares inversion of apparent resistivity pseudosections by a quasi-Newton method. Geophysics, 60, 1682-1690.
25. Marini, E. and Parisi, G. (1992) Simulated tempering: a new Monte Carlo scheme. Europhys. Lett., 19, 451-458.
26. Matérn, B. (1986) Spatial Variation, 2nd edn. Berlin: Springer.
27. McGillivray, P. R. (1992) Forward modeling and inversion of DC resistivity and MMR data. PhD Thesis. University of British Columbia, Vancouver.
28. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953) Equations of state calculations by fast computing machines. J. Chem. Phys., 21, 1087-1092.
29. Møller, I., Jacobsen, B. H. and Christensen, N. B. (2001) Rapid inversion of 2-D geoelectrical data by multichannel deconvolution. Geophysics, 66, 800-808.
30. Mosegaard, K. (1998) Resolution analysis of general inverse problems through inverse Monte Carlo sampling. Inv. Probl., 14, 405-426.
31. Mosegaard, K. and Tarantola, A. (1995) Monte Carlo sampling of solutions to inverse problems. J. Geophys. Res. B, 100, 12431-12447.
32. Nicholls, G. K. (1998) Bayesian image analysis with Markov chain Monte Carlo and coloured continuum triangulation models. J. R. Statist. Soc. B, 60, 643-659.
33. Nielsen, O. B. (1973) Eocæne aflejringer i Ølst-området og deres indpasning i pmrådets kvartærgeologi. Dansk Geologisk Forening, Årskrift 1972, pp. 100-110. Copenhagen: Dansk Geologisk Forening.
34. Panissod, C., Dabas, M., Hesse, A., Jolivet, A., Tabbagh, I and Tabbagh, A. (1998) Recent developments in shallow-depth electrical and electrostatic prospecting using mobile arrays. Geophysics, 63, 1542-1550.
35. Pearl, J. (1988) Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. San Mateo: Morgan Kaufmann.
36. Robert, C. P. and Casella, G. (1999) Monte Carlo Statistical Methods. New York: Springer.
37. Sørensen, K. I. (1996) Pulled array continuous electrical profiling. Frst Break, 14, 85-90.