Variational Bayesian inversion of electromagnetic geophysical data

What is it about?

Inversion of electromagnetic data is dealt with for a geophysical application. The goal is to retrieve a map of conductivity of an unknown body embedded in a layered underground from measurements of the scattered electric field that results from its interaction with a known interrogating wave. This constitutes an inverse scattering problem whose associated forward problem is described by means of electric field domain integral equations. The inverse problem is solved in a Bayesian framework in which prior information is introduced via a Gauss-Markov-Potts model. This model describes the body as being composed of a finite number of different materials distributed into compact homogeneous regions. The posterior distribution of the unknowns is approached by means of the variational Bayesian approximation as a separable distribution that minimizes the Kullback-Leibler divergence with respect to the posterior law. Thus, we get a parametric model for the distributions of the induced currents, the conductivity contrast, and the various parameters of the prior model that are obtained following a semisupervised iterative approach. This method is applied to multifrequency synthetic data corresponding to a 3D crosswell configuration in which the sought body is made of two separated anomalies, a conductive heterogeneity and a resistive one, and its results are compared with that given by the classic contrast source inversion (CSI).

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