Smooth 2-D Inversion for Magnetotelluric Data Based on Statistical Criterion ABIC.

Abstract

We often apply a smoothness constraint to a two-dimensional (2-D) linearized least-squares inversion of magnetotelluric (MT) data to achieve a stable result. A substantial problem with this scheme lies in the choice of the optimum smoothness, and in this paper, a statistical approach which is very versatile for this purpose is presented. It uses a statistical criterion called ABIC (Akaike's Bayesian Information Criterion), which was derived by introducing the entropy-maximization theorem into the Bayes statistics. On applying the Bayesian procedure to 2-D MT inversion, we seek simultaneous minimization of data misfit and model roughness. ABIC works as a number that represents goodness, or an entropy, of a model in a sense of this simultaneous minimization. Tests with both synthetic and real field data have revealed the effectiveness of this method for non-linear inversion problems. Regardless of the magnitude of the observation error, the method objectively adjusts the tradeoff between the misfit and the roughness, and stable convergence is attained.