High-performance three-dimensional electromagnetic modelling using modified Neumann series. Anisotropic earth

We have developed a modified Neumann series (MNS) technique to solve Maxwell's equations for three-dimensional anisotropic earth. We assume that both conductivity and dielectric permittivity are 3 x 3 matrices, elements of which are complex-valued functions of space coordinates and frequency, whereas the magnetic permeability is symmetric 3 x 3 matrix with elements being real-valued functions of depth. Both conduction and displacement currents are taken into account. In order to derive the MNS solution, we impose the positiveness condition of Joule losses inside anisotropic earth. The MNS solution so obtained is valid for any frequency range and for arbitrary three-dimensional anisotropic earth.