Electromagnetic imaging of scattering objects in cross-borehole measurements

A reconstruction algorithm of imaging scattering objects in cross-borehole measurements is presented. The authors define a cost functional as the norm of the discrepancy between the measured scattered field and the calculated one for an estimated object function. Then the inverse scattering problem can be treated as an optimization problem where the object function is determined by minimizing the functional. Applying the steepest descent method to the problem, one can derive an iterative formula for reconstructing the object function. Computer simulations are performed for some two-dimensional dielectric circular cylinders. It is seen from the simulated results that the reconstructed images of complex indices of refraction based on the proposed algorithm show good agreement with the true profiles even for cases where the Born or the Rytov approximation breaks down