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Volume 54 Supplement 5

Special Issue: Electromagnetic Induction in the Earth

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Thin-sheet electromagnetic inversion modeling using Monte Carlo Markov Chain (MCMC) algorithm

Abstract

The well-known thin-sheet modeling has become a very useful interpretation tool in electromagnetic (EM) methods. The thin-sheet model approximates fairly well 3-D heterogeneities having a limited vertical dimension. This type of approximation leads to amenable computation of EM response of a relatively complex conductivity distribution. This paper describes the integration of thin-sheet forward modeling into an inversion method based on a stochastic Monte Carlo Markov Chain (MCMC) algorithm. Effective exploration of the model space is performed using a biased sampler capable to avoid entrapment to local minima frequently encountered in a such highly nonlinear problem. Results from inversion of synthetic EM data show that the algorithm can reasonably resolve the true structure. Effectiveness and limitations of the proposed inversion method is discussed with reference to the synthetic data inversions.

References

  • Grandis, H., Imagerie electromagnetique Bayesienne par la simulation d’une chaîne de Markov, Ph.D. thesis, Université Paris 7, 278 pp., 1994.

  • Grandis, H., Application of magnetotelluric (MT) method in mapping basement structures: Example from Rhine-Saone Transform Zone, France, Indonesian Mining Journal, 3, 16–25, 1997.

    Google Scholar 

  • Grandis, H., M. Menvielle, and M. Roussignol, Bayesian inversion with Markov chains—I. The magnetotelluric one-dimensional case, Geophys. J. Inter., 138, 757–768, 1999.

    Article  Google Scholar 

  • Grandis, H., M. Menvielle, and M. Roussignol, Monte Carlo Markov Chains for non-linear inverse problems: an algorithm, Mathematical Geology, 2002 (submitted).

  • Heerman, D. W., Computer simulation methods in theoretical physics, Springer-Verlag, Berlin, 1990.

    Book  Google Scholar 

  • Jackson, D. D. and M. Matsu’ura, A bayesian approach to nonlinear inversion, J. Geophys. Res., 90(B1), 581–591, 1985.

    Article  Google Scholar 

  • Jain, M. K., S. R. K. Iyengar, and R. K. Jain, Numerical methods for scientific and engineering computation, Wiley Eastern, 1987.

  • Jouanne, V., Application des techniques statistiques bayesiennes à l’inversion de données électromagnétiques, Ph.D. thesis, Université Paris 7, 1991.

  • McKirdy, D. McA., J. T. Weaver, and T. W. Dawson, Induction in a thin sheet of variable conductance at the surface of a stratified earth—II: Three-dimensional theory, Geophys. J. Roy. astr. Soc., 80, 177–194, 1985.

    Article  Google Scholar 

  • Menvielle, M., J. C. Rossignol, and P. Tarits, The coast effect in terms of deviated electric currents: a numerical study, Phys. Earth Planet. Inter., 28, 118–128, 1982.

    Article  Google Scholar 

  • Robert, C., L’analyse Statistique Bayesienne, 393 pp., Economica, Paris, 1992.

    Google Scholar 

  • Robert, C., Méthodes de Monte Carlo par Chaînes de Markov, 393 pp., Economica, Paris, 1996.

    Google Scholar 

  • Rothman, D. H., Automatic estimation of large residual statics corrections, Geophysics, 51, 332–346, 1986.

    Article  Google Scholar 

  • Roussignol, M., V. Jouanne, M. Menvielle, and P. Tarits, Bayesian electromagnetic imaging, in Computer Intensive Methods, edited by W. Hardle and L. Siman, pp. 85–97, Physical Verlag, 1993.

  • Schott, J.-J., M. Roussignol, M. Menvielle, and F. R. Nomenjahanary, Bayesian inversion with Markov chains—II. The one-dimensional DC multilayer case, Geophys. J. Inter., 138, 769–783, 1999.

    Article  Google Scholar 

  • Sen, M. K. and P. L. Stoffa, Bayesian inference, Gibbs’ sampler and uncertainty estimation in geophysical inversion, Geophys. Prosp., 44, 313–350, 1996.

    Article  Google Scholar 

  • Tarits, P., V. Jouanne, M. Menvielle, and M. Roussignol, Bayesian statistics of non-linear inverse problems: examples of the magnetotelluric 1-D inverse problem, Geophys. J. Inter., 119, 353–368, 1994.

    Article  Google Scholar 

  • Vasseur, G. and P. Weidelt, Bimodal electromagnetic induction in nonuniform thin sheets with an application to the northern Pyrenean induction anomaly, Geophys. J. Roy. astr. Soc., 51, 669–690, 1977.

    Article  Google Scholar 

  • Wang, L. J. and F. E. M. Lilley, Inversion of magnetometer array data by thin-sheet modeling, Geophys. J. Inter., 137, 128–138, 1999.

    Article  Google Scholar 

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Correspondence to Hendra Grandis.

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Grandis, H., Menvielle, M. & Roussignol, M. Thin-sheet electromagnetic inversion modeling using Monte Carlo Markov Chain (MCMC) algorithm. Earth Planet Sp 54, 511–521 (2002). https://doi.org/10.1186/BF03353042

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  • DOI: https://doi.org/10.1186/BF03353042

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