Fast three-dimensional electromagnetic nonlinear inversion in layered media with a novel scattering approximation

Abstract

This paper presents a fast three-dimensional (3D) electromagnetic nonlinear inversion method in a multilayered medium via a novel scattering approximation. Using the superposition principle, we introduce a new source-dependent but diagonal scattering tensor. The approximate analytical expressions for the three scattering diagonal components are derived. Numer- ical tests show that the new approximation has better accuracy and wider range of applicability than the existing approximations such as the extended Born approximation and the quasi-analytical approximation. The computational speed of the new scattering approximation is essentially the same as the Born approximation.With such a new approximation, we further develop an efficient linearized 3D electromagnetic inversion method in a layered medium. In this method, the inverse problem is cast into a weighted least-squares problem solved via a conjugate gradient scheme. In terms of eigenvalue analysis, we propose a choice of the data and model weighting matrices that can be constructed for a general, complex Fréchet sensitivity matrix. The suggested weights help the selection of the regularization factor within the specified range of [0, 1] for the inverse problem, and improves the condition of the original imaging system. Synthetic tomography experiments demonstrate the efficiency of the new scattering approximation and the fast 3D EM imaging technique.