Optimal design of focusing inductive arrays for inhomogeneous medium

The paper concerns the optimal design of an inductive source array for an inhomogeneous medium. The optimally designed array maximizes the response from an unknown inclusion in a known inhomogeneous reference medium. The problem is formulated as an optimization problem for array currents. This optimization problem is reduced to a generalized eigenvalue problem and solved numerically. The source array can be hardwired or can be simulated using simpler source data. To illustrate the technique, we consider a borehole source array designed for detecting a resistive bed using electromagnetic measurements in the borehole, when the invasion zone is highly conductive. The problem is known to be difficult for logging application. Comparison of the fields generated by the conventional and optimized sources show a tremendous increase in depth of field penetration.