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Book Chapter

Three-Dimensional Inversion of MT Fields Using Bayesian Statistics

By
Vjacheslav Spichak
Vjacheslav Spichak
Geophysical Research Center, Varshavskoe sh.8, Moscow 113105, Russia.Laboratoire de Physique de la Terre et des Planètes (URA 1369), Université Paris Sud, Bat. 504, 91405 ORSAY CEDEX, France.
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Michel Menvielle
Michel Menvielle
Laboratoire de Physique de la Terre et des Planètes (URA 1369), Université Paris Sud, Bat. 504, 91405 ORSAY CEDEX, France.
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Michel Roussignol
Michel Roussignol
Equipe de Mathématiques Appliquées, Université de Marne la Vallée, 2 rue de la Butte Verte, Noisy le Grand Cedex 93166, France.
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Published:
January 01, 1999

Summary

Bayesian statistics provide a formalism for inversion of magnetotelluric (MT) data in 3-D structures composed of elementary homogeneous domains. Available information (including assumptions about the model) is put in a probability density function (PDF) for prior values of the conductivities in the region of the search; the parameters to be found are the posterior values of the conductivity.

A stochastic algorithm called a Gibbs sampler estimates the posterior PDF. The outer cycle of the iterative inversion consists of scanning the homogeneous domains in the region of the search; the inner cycle involves solution of the forward problem for a set of models. This process represents a Markov chain, whose transition law converges to the marginal PDF of the parameters.

The inner cycle uses the finite-difference program FDM3D-MT, which computes electromagnetic responses in the frequency domain for 1-D, 2-D, or 3-D models. Iterative solution of the finite-difference equations is very fast and reduces greately the total CPU time since the results of the previous cycle are used as starting points for the next forward model. In most of our tests, the outer iteration converges in 15–20 iterations, which allows an attack on 3-D problems even on microcomputers. Examples show how the quantity and quality of data and the prior information affect the results of inversion.

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Contents

Geophysical Developments Series

Three-Dimensional Electromagnetics

Society of Exploration Geophysicists
Volume
7
ISBN electronic:
9781560802154
Publication date:
January 01, 1999

GeoRef

References

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