Bayesian inversion with Markov chains-II. The one-dimensional DC multilayer case

Geophysical Journal International

Volumn 138, Issue 3, 1999, Pages 769-783

  Schott, Jean Jacques ^a   Roussignol, Michel ^b   Menvielle, Michel ^c,d   Nomenjahanary, Flavien R ^e  

^a Ecole et Observatoire des Sciences de la Terre   (France)

^b UNIVERSITÉ GUSTAVE EIFFEL   (France)

^c SERVICE D AÉRONOMIE DU CNRS   (France)

^d UNIVERSITÉ PARIS SACLAY   (France)

^e Geophys Institute and Observatory   (Madagascar)

Author keywords

Electrical resistivity; Inversion; Layered media; Monte Carlo Markov chain

Indexed keywords

BAYESIAN ANALYSIS; MAGNETOTELLURIC METHOD; MARKOV CHAIN;

EID: 0032746911     PISSN: 0956540X     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-246X.1999.00905.x     Document Type: Article

References (38)

1. Backus, G.E., 1988. Bayesian inference in geomagnetism, Geophys. J., 92, 125-142.
2. Barker, R.D., 1989. Depth of investigation of collinear symmetrical four-electrode arrays, Geophysics, 54, 1031-1037.
3. Bayes, T., 1763. An essay toward solving a problem in the doctrine of chance, Phil. Trans. R. Soc. Lond., 53, 370-418.
4. Caperaa, Ph. & Van Cutsem, B., 1988. Méthodes et Modèles en Statistique Non Paramétrique, Exposé Fondamental. Presses de l'Univeristé Laval, Bordas, Paris.
5. Constable, S.C., Parker, R.L. & Constable, C.G., 1987. Occam's inversion: a practical algorithm for generating smooth models from electromagnetic sounding data, Geophysics, 52, 289-300.
6. Craven, P. & Whaba, G., 1979. Smoothing noisy data with spline functions, Numer. Math., 31, 377-403.
7. Das, U.C. & de Hoop, A.T., 1995. Efficient computation of apparent resistivity curves for depth profiling of a layered earth, Geophysics, 60, 1691-1697.
8. Feller, W., 1970. An Introduction to Probability Theory and Its Applications, Vol. 1, Wiley, New York.
9. Gosh, D.P., 1971a. The application of linear filter theory to the direct interpretation of geoelectrical resistivity sounding measurements, Geophys. Prospect., 19, 192-217.
10. Gosh, D. P., 1971b. Inverse filter coefficients for the computation of apparent resistivity standard curves for a horizontally stratified earth, Geophys. Prospect., 19, 769-775.
11. Grandis, H., 1994. Imagerie électromagnétique bayésienne par la simulation d'une chaîne de Markov, Phd thesis, Univ. Paris VII.
12. Grandis, H., Menvielle, M. & Roussignol, M., 1999. Bayesian inversion with Markov chains - I. The magnetotelluric one-dimensional case, Geophys. J. Int., 138, 757-768 (this issue).
13. Gupta, P.K., Nivas, S. & Gaur, V.K., 1997. Straightforward inversion of vertical sounding data, Geophysics, 62, 775-785.
14. Jackson, D.D. & Matsura, M., 1985. A Bayesian approach to nonlinear inversion, J. Geophys. Res., 90, 581-591.
15. Jouanne, V., 1991. Application des techniques statistiques bayesiennes à l'inversion de données électromagnétiques, Phd thesis, Univ. Paris VII.
16. Kim, H.S. & Lee, K., 1996. Response of a multilayered earth with layers having exponentially varying resistivities, Geophysics, 61, 180-191.
17. Koefoed, O., 1979. Geosounding principles, 1, Methods in Geochemistry and Geophysics, 14A, Elsevier, Amsterdam.
18. Kunetz, G., 1966. Principles of direct current resistivity prospecting, Geoexploration Monographs, eds Braekken, H. & Van Nostrand, R., Gebrüder Bornträger, Berlin.
19. Loke, M.H. & Barker, R.D., 1995. Improvements to the Zohdy method for inversion of resistivity sounding and pseudosection data, Comput. Geosci., 21, 321-332.
20. Meju, M.A., 1992. An effective ridge regression procedure for resistivity data inversion, Comput. Geosci., 18, 99-118.
21. Meju, M.A., 1994. Geophysical data analysis: understanding inverse problems. Theory and practice, Course Notes Series, Vol. 6, ed. Domenico, S.N., SEG, Tulsa.
22. Metropolis, N., Rosenbluth A.W., Rosenbluth, M.N., Teller, A.H. & Tellet, E., 1953. Equation of state calculations by fast computing machines, J. Chem. Phys., 1, 1087-1092.
23. Mosegaard, K., & Tarantola, T., 1995. Monte Carlo sampling of solutions to inverse problems, J. geophys. Res., 100, 12 431-12 447.
24. Robert, C., 1996. Méthodes de Monte Carlo par Chaînes de Markov. Economica Paris.
25. Roy, A. & Apparao, A., 1971. Depth of investigation in direct current methods, Geophysics, 36, 943-959.
26. Sen, M.K. & Stoffa, P.L., 1996. Bayesian inference, Gibbs' sampler and uncertainty estimation in geophysical inversion, Geophys. Prospect., 44, 313-350.
27. Sen, M.K., Bhattacharya, B.B. & Stoffa, P.L., 1993. Nonlinear inversion of resistivity sounding data, Geophysics, 58, 496-507.
28. Sheriff, S.D., 1992. Forward modelling of electrical sounding experiments using convolution and a spreadsheet, Comput. Geosci., 18, 75-78.
29. Silverman, B.W., 1985. Some aspects of the spline smoothing approach to non-parametric regression curve fitting, J. R. Stat. Soc., 47, 1-52.
30. Simms, J.E. & Morgan, F.D., 1992. Comparison of four least-squares inversion schemes for studying equivalence in one-dimensional resistivity interpretation, Geophysics, 57, 1282-1293.
31. Smith, J.T. & Booker, J.R., 1988. Magnetotelluric inversion for minimum structures, Geophysics, 53, 1565-1576.
32. Straub, A., 1995a. General formulation of the electrical stratified problem with a boundary integral equation, Geophysics, 60, 1656-1670.
33. Straub, A., 1995b. Properties of the kernel function in electric stratified problems, Geophysics, 60, 1671-1681.
34. Tarits, P., Jouanne, V., Menvielle, M. & Roussignol, M., 1994. Bayesian statistics of non-linear inverse problems: example of the magnetotelluric 1-D inverse problem, Geophys. J. Int., 119, 353-368.
35. Tierney, L., 1994. Markov chains for exploring posterior distributions, Ann. Stat., 22, 1701-1762.
36. Vandervelpen, B.P.A. & Sparry, R.J., 1993. A computer program to process resistivity sounding data on PC compatibles, Comput. Geosci., 19, 691-704.
37. Xu, B.W. & Barker, R.D., 1994. Filter coefficients for offset Wenner and Wenner resistivity sounding interpretation, Comput. Geosci., 20, 671-680.
38. Zohdy, A.A.R., 1989. A new method for the automatic interpretation of Schlumberger and Wenner sounding curves, Geophysics, 54, 245-253.