Cross-borehole inverse scattering using a boundary finite-element method

The problem of the reconstruction of the shape of a perfectly conducting cylinder in a cross-borehole configuration is addressed. The initial data is the harmonic electromagnetic field diffracted by the object to a receiving borehole. The method is based on an iterative conjugate gradient algorithm which requires the solving of two reciprocal direct diffraction problems at each step. These problems are investigated with a rigorous boundary integral method and finite elements. A simple and original regularization scheme is presented, which ensures the robustness of the algorithm. Numerical examples with lossy embedding media and additional random noise for both and polarizations are given.