Quasi-linear approximation in 3-D electromagnetic modeling

The Born approximation in electromagnetic (EM) numerical modeling has limited application for solving 3-D electromagnetic induction problems, because in structures with high conductivity contrasts and at high frequencies, this approximation is inaccurate. In this paper, we develop a new and relatively simple approximation for the EM field called a quasi-linear approximation, which is based on the evaluation of the anomalous field E ª by a linear transformation of the normal (primary) field: E ª = λEn, where λ is called the electrical reflectivity tensor. The reflectivity tensor inside inhomogeneities can be approximated by a slowly varying function that can be determined numerically by a simple optimization technique. The new approximation gives an accurate estimate of the EM response for conductivity contrasts of more than one hundred to one, and for a wide range of frequencies. It also opens the possibility for fast 3-D electromagnetic inversion.