One of the most challenging problems in electromagnetic (EM) geophysical methods is developing fast and stable methods of imaging inhomogeneous underground structures using EM data. In our previous publications we developed a novel approach to this problem, using EM migration.In this paper we demonstrate that there is a very close connection between the method of EM migration and the solution of the conventional EM inverse problem. Actually, we show that migration is an approximate inversion. It realizes the first iteration in the inversion algorithm, based on the minimization of the residual field energy flow through the profile of observations. This new theoretical result opens a way for formulating a new imaging condition. We compare this new imaging condition with the traditional one, obtained for simplified geoelectrical models of the subsurface structures.This result also leads to the construction of a solution of the inverse EM problem, based on iterative EM migration in the frequency domain, and gradient (or conjugate gradient) search for the optimal geoelectrical model. However, the authors have found that in the framework of this method, even the first iteration, based on the migration of the residual field, generates a reasonable geoelectrical image of the subsurface structure.
IntroductionOne of the most challenging problems in electromagnetic (EM) geophysical methods is developing fast and stable methods of imaging inhomogeneous underground structures using EM data. Solution of this problem is important for many practical applications ranging from mineral exploration to waste and building site characterization. In the papers (Zhdanov et al., 1995) and (Zhdanov et al., 1996) and the references therein we have developed a novel approach to EM imaging based on the notion of EM migration. The method includes downward continuation of the observed field or one of its components in reverse time and application of the corresponding imaging conditions. However, until recently the relationship between EM migration imaging and traditional EM inversion have remained unexplored. The conventional EM inversion means a method which predicts the geoelectrical model generating the theoretical data closed to observations. The EM migration introduced in our previous publications constructed an image of subsurface geoelectrical structures, and there was no guarantee this image, if included in a geoelectrical model, would give rise to theoretical EM fields that matched those observed. Meanwhile, Tarantola (1987) demonstrated that seismic wave migration, which was the prototype for EM migration, can be treated exactly as the first iteration in some general wave inversion scheme. In this paper we formulate an important new result: EM migration, as the solution of the boundary value problem for the adjoint Maxwell's equation in frequency domain, can be clearly associated with the inverse problem solution. In other words, we prove that a geoelectrical model constructed on the basis of migration images would actually generat...