3-DIMENSIONAL MAGNETOTELLURIC INVERSION USING CONJUGATE GRADIENTS

We have developed an inversion procedure that uses conjugate gradient relaxation methods. Although one can generalize the method to all inve rse problems, we demonstrate its use to invert magnetotelluric data fo r 3-D earth models. This procedure allows us to bypass the actual comp utation of the sensitivity matrix A or the inversion of the A(T)A term . In fact, with the relaxation approach, one only needs to compute the effect of the sensitivity matrix or its transpose multiplying an arbi trary vector. We show that each of these requires one forward problem with a distributed set of sources either in the volume (for A multiply ing a vector) or on the surface (for A(T) multiplying a vector). This significantly reduces the computational requirements needed to do a 3- D inversion. For this paper, we have simplified the boundary condition s by assuming the model is repeated in the horizontal directions, but this is not a necessary constraint of the method. The algorithm reduce s data errors to the 2 per cent level for noise-free synthetic 3-D mag netotelluric data.