Open AccessThree‐dimensional magnetotelluric inversion using conjugate gradients
Author(s) -
Mackie Randall L.,
Madden Theodore R.
Publication year - 1993
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1993.tb05600.x
Subject(s) - magnetotellurics , inversion (geology) , conjugate gradient method , computation , inverse problem , algorithm , geology , geophysics , geodesy , mathematics , mathematical analysis , physics , seismology , tectonics , electrical resistivity and conductivity , quantum mechanics
Summary We have developed an inversion procedure that uses conjugate gradient relaxation methods. Although one can generalize the 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 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 arbitrary vector. We show that each of these requires one forward problem with a distributed set of sources either in the volume (for A multiplying 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 conditions by assuming the model is repeated in the horizontal directions, but this is not a necessary constraint of the method. The algorithm reduces data errors to the 2 per cent level for noise‐free synthetic 3‐D magnetotelluric data.