Electromagnetic Waves in Multilayered Generalized Anisotropic Media

Abstract

This paper presents the formulations for calculating the electromagnetic (EM) fields in multilayered generalized anisotropic media. Maxwell’s equations are written into a first-order differential (in $z$ ) equation concerning the transverse electric and magnetic field components in the spectral domain. The equation can be solved to obtain the EM fields in a homogeneous anisotropic medium. For fields in layered anisotropic media, the local transmission and reflection matrices, the global reflection matrices, and the recursion relations of the wave amplitudes at interfaces are derived and used to express the EM fields in arbitrary layers. The electric and magnetic dipole sources can locate in arbitrary layers, and the medium can have both full-tensor magnetic and dielectric anisotropy. The singular behavior of the solution in the close vicinity of the dipole source is subtracted to make the integrands decay rapidly as functions of $k_{x}$ and $k_{y}$ . The contributions of the subtracted part are calculated analytically. A three-layer anisotropic medium is modeled to show the convergence of the integrals with the singularity subtraction. To validate the algorithm for multilayered generalized anisotropic media, a five-layer medium is modeled and compared with finite element method results. The algorithm is also applied in geophysical EM well logging by modeling the triaxial induction logging tool. The responses in vertical and deviated wells are computed and compared with finite element results. The good agreement between the two results further validates the algorithm and demonstrates its capability to model induction logging tools in multilayered generalized anisotropic media.