Quasi-analytical approximations and series in electromagnetic modeling

The quasi-linear approximation for electromagnetic forward modeling is based on the assumption that the anomalous electrical field within an inhomogeneous do­ main is linearly proportional to the background (nor ­ mal) field through an electrical reflectivity tensor t In the original formulation of the quasi-linear approxima­ tion, 1 was determined by solving a minimization prob ­ lem based on an integral equation for the scattering cur­ rents. This approach is much less time-consuming than the full integral equation method ; however, it still re­ quires solution of the corresponding system of linear equations. In this paper, we present a new approach to the approximate solution of the integral equation us­ ing 1 through construction of quasi-analytical expres ­ sions for the anomalo us electromagnetic field for 3-D and 2-D models. Quasi-analytical solutions red uce dra­ matically the computational effort related to forward electromagnetic modeling of inhomo geneous geoelec­ trical structures. In the last sections of this paper, we extend the quasi-analytical method using iterations and develop higher order approximations resulting in quasi­ analytical series whichprovide improved accuracy.Com­ putation of these series is based on repetitive applica­ tion of the given integral contraction operator, which insures rapid convergence to the correct result. Numer ­ ical studies demonstrate that quasi-analytical series can be treated as a new powerful method of fast but rigorous forward modeling solution.