A hybrid three‐dimensional electromagnetic modeling scheme

We present an efficient numerical method for computing electromagnetic (EM) scattering of arbitrary three‐dimensional (3-D) local inhomogeneities buried in a uniform or two‐layered earth. In this scheme the inhomogeneity is enclosed by a volume whose conductivity is discretized by a finite‐element mesh and whose boundary is only a slight distance away from the inhomogeneity. The scheme uses two sets of independent equations. The first is a set of finite‐element equations derived from a variational integral, and the second is a mathematical expression for the fields at the boundany in terms of electric fields inside the boundary. The Green’s function is used to derive the second set of equations. An iterative algorithm has been developed to solve these two sets of equations. The solutions are the electric fields at nodes inside the finite‐element mesh. The scattered fields anywhere may then be obtained by performing volume integrations over the inhomogeneous region. The scheme is used for modeling 3-D inhomogeneities with plane‐wave and magnetic dipole sources. The results agree with earlier model analyses using the finite‐element technique.