Nonlinear Approximations for Electromagnetic Scattering from Electrical and Magnetic Inhomogeneities

We extend linear and nonlinear approximations for electromagnetic fields to a medium with inhomogeneous distribution of both electrical and magnetic material properties. These approximations are presented in the form of tensor integrals over a domain with anomalous pa­ rameters . The developed approximations combine the linear and nonlinear estimations depending on the ratio of complex conductivity and magnetic susceptibility perturbations. These approxima­ tions form a basis for fast EM modeling and imaging in multi-dimensional environments where joint electrical and magnetic inhomogeneity is an essential feature of the model. Numerical tests carried out for one-dimensional electromagnetic logging applications demonstrate the validity of the theory and the effectiveness of the proposed approximations.