Data space conjugate gradient inversion for 2-D magnetotelluric data

A data space approach to magnetotelluric (MT) inversion reduces the size of the system of equations that must be solved from M × M, as required for a model space approach, to only N × N, where M is the number of model parameter and N is the number of data. This reduction makes 3-D MT inversion on a personal computer possible for modest values of M and N. However, the need to store the N × M sensitivity matrix J remains a serious limitation. Here, we consider application of conjugate gradient (CG) methods to solve the system of data space Gauss-Newton equations. With this approach J is not explicitly formed and stored, but instead the product of J with an arbitrary vector is computed by solving one forward problem. As a test of this data space conjugate gradient (DCG) algorithm, we consider the 2-D MT inverse problem. Computational efficiency is assessed and compared to the data space Occam's (DASOCC) inversion by counting the number of forward modelling calls. Experiments with synthetic data show that although DCG requires significantly less memory, it generally requires more forward problem solutions than a scheme such as DASOCC, which is based on a full computation of J.