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

In this paper we describe a new approach to shar p boundary geophy sical inversion. We demon strate that regularized inversion with a minimum support stabilizer can be implemented by using a specially designed nonl inear parametrization of the mode l parameters . Thi s parametrization plays the same role as transformation into the space of the weighted model parameters, introd uced in the origi nal papers on focusing inversion . It allows us to transform the nonquadrati c minim um support stabilizer into the traditional quadrati c minimum norm stabilizer, which simplifies the solution of the inverse problem. Thi s transformation automatically ensures that the solution belongs to the class of model s with a minimum support. The method is illustrated with synthetic examples of 3D magnetotell uric 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 Hursan (2000 Inverse Problems 16 1297322). However, to increase the accura cy of inversion, we apply rigorou s forward modelling based on the integral equa tion 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 . Thi s techn ique leads to the generation of a sharp image of anomalous conductiv ity distribution. The inversion is based on the regularized conjugate gradient method .