Audio‐frequency electromagnetic tomography in 2-D

Abstract

The mathematical formulation of acoustic diffraction tomography is applied to the problem of low frequency, diffusive electromagnetic (EM) fields. EM tomographic inversion, in two‐dimensional (2-D) Cartesian geometry, is illustrated for a crosshole source‐receiver configuration. The object function of the conductivity distribution is related to the transformed and filtered data by an inverse Fourier transform in the vertical direction and an inverse Laplace transform in the lateral direction. The reconstructed conductivity image is found to be a band‐limited version of the actual conductivity distribution. To stabilize the inversion, a regularized least‐squares method is used for image reconstruction. As in the seismic case, the inversion quality can be understood by inspecting the wavenumber domain coverage of the object function. Numerical experiments show that the resolution is better in the vertical direction than in the horizontal and it is also a function of source operating frequency. The position and attitude of the target are recovered well.