Quasi-analytical approximations and series in electromagnetic modeling

The quasi-linear approximation for electromagnetic forward modeling is base d on the assumption that the anomalous electrical field within an inhomogen eous domain is linearly proportional to the background (normal) field throu gh an electrical reflectivity tensor <(<lambda>)over cap>. In the original formulation of the quasi-linear appruximation, <(<lambda>)over cap> was det ermined by solving a minimization probIem based on an integral equation for the scattering currents. This approach is much less time-consuming than th e full integral equation method; however, it still requires solution of the corresponding system of linear equations. In this paper, we present a new approach to the approximate solution of the integral equation using <(<lamb da>)over cap> through construction of quasi-analytical expressions for the anomalous electromagnetic held for 3-D and 2-D models. Quasi-analytical sol utions reduce dramatically the computational effort related to forward elec tromagnetic modeling of inhomogeneous geoelectrical structures. In the last sections of this paper, we extend the quasi-analytical method using iterat ions and develop higher order approximatipns resulting in quasianalytical s eries which provide improved accuracy. Computation of these series is based on repetitive application of the given integral contraction operator, whic h insures rapid convergence to the correct result. Numerical studies demons trate that quasi-analytical series can be treated as a new powerful method of fast but rigorous forward modeling solution.