Electromagnetic modeling of three-dimensional bodies in layered earths using integral equations

Abstract

An algorithm based on the method of integral equations has been developed to simulate the electromagnetic response of 3-D bodies in layered earths. The inhomogeneities are replaced mathematically by an equivalent current distribution which is approximated by pulse basis functions. A matrix equation is constructed using the electric dyadic Green's function appropriate to a layered earth and is solved for the vector current in each cell. Subsequently, scattered fields are found by integrating electric and magnetic dyadic Green's functions over the scattering currents. Efficient evaluation of the dyadic Green's functions is a major consideration in reducing computation time. It is found that tabulation/interpolation of the six electric and five magnetic Hankel transforms defining the secondary Green's functions is preferable to any direct Hankel transform calculation using linear filters. A comparison of responses over elongate 3-D bodies with responses over 2-D bodies of identical cross section using plane wave incident fields is the only check available on our solution. Agreement is excellent; however, the length that a 3-D body must have before departures between 2-D transverse electric and corresponding 3-D signatures are insignificant depends strongly on the layering. The 2-D transverse magnetic and corresponding 3-D calculations agree closely regardless of the layered host.