Minimum support nonlinear parametrization in the solution of a 3D magnetotelluric inverse problem

Abstract

In this paper we describe a new approach to sharp boundary geophysical inversion. We demonstrate that regularized inversion with a minimum support stabilizer can be implemented by using a specially designed nonlinear parametrization of the model parameters. This parametrization plays the same role as transformation into the space of the weighted model parameters, introduced in the original papers on focusing inversion. It allows us to transform the nonquadratic minimum support stabilizer into the traditional quadratic minimum norm stabilizer, which simplifies the solution of the inverse problem. This transformation automatically ensures that the solution belongs to the class of models with a minimum support. The method is illustrated with synthetic examples of 3D magnetotelluric inversion for an earth conductivity structure. To simplify the calculations, in the initial stage of the iterative inversion we use the quasi-analytical approximation developed by Zhdanov and Hursán (2000 Inverse Problems 16 1297–322). However, to increase the accuracy of inversion, we apply rigorous forward modelling based on the integral equation method at the final stage of the inversion. To obtain a stable solution of a 3D inverse problem, we use the Tikhonov regularization method with a new nonlinear parametrization. This technique leads to the generation of a sharp image of anomalous conductivity distribution. The inversion is based on the regularized conjugate gradient method.