Rl. Mackie et Tr. Madden, 3-DIMENSIONAL MAGNETOTELLURIC INVERSION USING CONJUGATE GRADIENTS, Geophysical journal international, 115(1), 1993, pp. 215-229
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.