Three-dimensional inverse scattering applied to cross-well induction sensors

Cross-well induction logging as known in the oil industry is a method for determining the electrical conductivity distribution between boreholes from the low-frequency electromagnetic field measurements in the boreholes. The authors discuss the reconstructions of the three-dimensional (3D) conductivity distribution using the contrast source inversion (CSI) method. In order to improve the reconstruction results, the concept of the extended Born approximation has been used to arrive at a preconditioning operator. Results of a number of numerical examples show that by using this preconditioning operator, a large conductivity contrast of the unknown objects (factor of 100) can be reconstructed up to an acceptable degree of accuracy. Moreover, in each iteration, the computational effort to generate the preconditioning operator is negligible.