PRACTICAL STRATEGIES FOR THE SOLUTION OF LARGE-SCALE ELECTROMAGNETIC INVERSE PROBLEMS

Nonlinear inverse problems in electromagnetics are typically solved by dividing the Earth into cells of constant conductivity, linearizing t he equations about a current model, computing the sensitivities, and t hen solving an optimization problem to obtain an updated estimate of t he conductivity. In principle, this procedure can be implemented for a ny size problem, but in practice the computations involved may be too large for the available computing hardware. In electromagnetics this i s currently the situation irrespective of whether the interpreter has access to a workstation or a supercomputer. In addition to the demands imposed by the need to compute the predicted responses from a specifi ed model (i.e., invoking a forward mapping) there are two computationa l roadblocks encountered when solving an inverse problem: (1) calculat ion of the sensitivity matrix and (2) solution of the resultant large system of equations. If either of these operations cannot be carried o ut in reasonable time then an alternate strategy is required. Such str ategies include generalized subspace methods, conjugate gradient metho ds, or approximate inverse mapping (AIM) procedures. The theoretical f oundations and computational details of these strategies are explored in this paper with the ultimate goal that the inversionist, after asse ssing his/her computing power and knowing the time required to perform forward modeling, can generate a methodology by which to solve the pr oblem. The methodologies are compared quantitatively by considering an archetypal inversion problem in electromagnetics, the inversion of dc potential data to recover the electrical conductivity.