Three-dimensional magnetotelluric inversion using conjugate gradients

Abstract

W e have developed an inversion procedure that uses conjugate gradient relaxation methods. Although o n e can generalize t h e method to all inverse problems, we demonstrate its use to invert magnetotelluric data for 3-D earth models. This procedure allows us to bypass the actual computation of the sensitivity matrix A or the inversion of the ATA term. In fact, with the relaxation approach, o n e only needs to compute the effect of t h e sensitivity matrix or its transpose multiplying an arbitrary vector. W e show that each of these requires one forward problem with a distributed set of sources either in the volume (for A multiplying a vector) o r on the surface (for AT multiplying a vector). This significantly reduces the computational requirements needed t o d o a 3-D inversion. For this paper, we have simplified the boundary conditions by assuming the model is repeated in the horizontal directions, but this is not a necessary constraint of the method. T h e algorithm reduces data errors t o the 2 per cent level for noise-free synthetic 3-D magnetotelluric data.