Fast and stable two-dimensional inversion of magnetotelluric data

Abstract

The two-dimensional (2-D) magnetotelluric (MT) inverse problem still poses difficult challenges in spite of efforts to develop fast and efficient methods for its solution. In this paper, we present a new approach for the solution of overparameterized cases based on regularization theory and full 2-D, quasi-analytic, calculation of the Frechet derivatives. For the forward solution we use a fast and efficient finite difference formulation to the solution of the MT equations in both transverse electric (TE) and transverse magnetic (TM) modes based on the balance method. The Frechet derivative matrix is obtained as a solution to simple forward and back substitution of the LU decomposed matrix of coefficients from the forward problem utilizing the principle of reciprocity. Magnetotelluric data is usually contaminated by noise, so that its inverse problem is ill-posed. In order to constrain the solution to a set of acceptable models, Tikhonov regularization is applied and yields a regularized parametric functional. The regularized conjugate gradient method is then utilized to minimize the parametric functional. Results of inversion for a set of synthetic data and for a set of CSAMT data from Kennecott Exploration show that the method yields models which are physically and geologically reasonable for both synthetic and real data sets.