An Efficient 3D Integral Equation Method for Computation of Electromagnetic Wavefields in a Layered Configuration Containing Inhomogeneous Objects

This paper is concerned with the source-type of integral equation to compute the electromagnetic scattering by an inhomogeneous 3D object in a planar layered medium in the frequency domain. By decomposing the scattered field into a particular and a general constituent, the structure of the integral operator of the integral equation is constructed. The particular constituent represents the scattered field inside the layer that embodies the contrasting object, due to the presence of virtual contrast sources inside the inhomogeneous object, while the general constituent represents the interaction with the other layers due to the presence of source distributions on each side of the layer that embodies the contrasting object. The particular constituent has a convolution structure in all spatial directions. The general constituent consists of two terms; one has again a convolution structure with respect to all spatial coordinates, while the other has a convolution structure with respect to the horizontal coordinates and a correlation structure in the vertical coordinates. These properties facilitate a fast and efficient computation of the integral operator with the help of Fast Fourier Transforms. In view of numerical efficiency, it is desirable to keep the spatial derivatives outside the Fourier integral, rather than to consider them as spectral multiplications with the wave vector inside the Fourier integral. The method is applied to simulate the geophysical low-frequency electromagnetic problem, i.e., the controlled-source electromagnetic (CSEM) method.