A New Approximation for 3D Electromagnetic Scattering in the Presence of Anisotropic Conductive Media

Abstract

Accurate and efficient modeling of three-dimensional (3D) electromagnetic (EM) scattering remains an open challenge in the presence of anisotropic conductive media. Numerical algorithms used to simulate the response of dipping and anisotropic rock formations can easily exceed standard computer resources as EM fields become fully coupled in general. In the past, several scattering approximations have been developed to efficiently simulate complex EM problems arising in the probing of subsurface rock formations. These approximations include the Born, Rytov, Extended Born (ExBorn) and quasi-linear (QL) methods, among others. However, so far none of these approximations have been adapted to simulate scattering in the presence of anisotropic conductive media. In this paper, we describe and benchmark a novel EM scattering approximation that remains accurate and efficient in the presence of 3D anisotropic conductive media. The approximation is based on the integral formulation of EM scattering and takes advantage of the spatial smoothness and general vectorial properties of EM fields internal to scatterers. A general vectorial formulation is used to properly account for complex EM coupling due to anisotropy. Several numerical examples borrowed from borehole induction logging are used to describe and assess the accuracy and efficiency of the new EM scattering approximation. The approximation allows one to accurately simulate the EM response of more than 1 million cells within a few minutes of CPU time on a serial computer with standard memory and speed resources.