Electromagnetic inversion using quasi‐linear approximation

Abstract

Three‐dimensional electromagnetic inversion continues to be a challenging problem in electrical exploration. We have recently developed a new approach to the solution of this problem based on quasi‐linear approximation of a forward modeling operator. It generates a linear equation with respect to the modified conductivity tensor, which is proportional to the reflectivity tensor and the complex anomalous conductivity. We solved this linear equation by using the regularized conjugate gradient method. After determining a modified conductivity tensor, we used the electrical reflectivity tensor to evaluate the anomalous conductivity. Thus, the developed inversion scheme reduces the original nonlinear inverse problem to a set of linear inverse problems. The developed algorithm has been realized in computer code and tested on synthetic 3-D EM data. The case histories include interpretation of a 3-D magnetotelluric survey conducted in Hokkaido, Japan, and the 3-D inversion of the tensor controlled‐source audio magnetotelluric data over the Sulphur Springs thermal area, Valles Caldera, New Mexico, U.S.A.