Three-Dimensional Inversion of MT Fields Using Bayesian Statistics
Vjacheslav Spichak, Michel Menvielle, Michel Roussignol, 1999. "Three-Dimensional Inversion of MT Fields Using Bayesian Statistics", Three-Dimensional Electromagnetics, Michael Oristaglio, Brian Spies
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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.