Analysis of electrical conductivity imaging

Abstract

We investigate the feasibility of imaging the electrical conductivity in a cross‐section of an object (such as a core sample) by numerical inversion of low‐frequency, electromagnetic (EM) boundary data. Current flow is assumed to be confined to the cross‐section, which is modeled as a network of resistors. The network serves as a discrete approximation of the distributed‐parameter system that is described mathematically by Maxwell’s equations for steady current flow in a nonhomogeneous medium. A complete set of linearly independent voltage vectors is applied to the peripheral nodes, and the resulting node currents serve as the measured data for estimating the internal conductivity pattern (image). We generate estimates of this conductivity image by using an iterative process on network equations that are linearized in the unknown conductance variables. The mathematical feasibility of this approach is demonstrated by computer simulation studies using data generated from the network model. Reconstructed images are presented for sample conductance patterns under both ideal and noisy data conditions. An error analysis is performed to relate data noise to image‐estimation error.