Electromagnetic Fields in Full-Parameter Uniaxial Anisotropic Planar-Stratified Media

In this article, we present a derivation for analytical expressions of the electromagnetic (EM) fields radiated by triaxial magnetic/electric point sources in planar-stratified media. The permittivity, permeability, and conductivity of each layer may exhibit uniaxial anisotropy. First, a hybrid potential method is adopted to solve the Maxwell's equations in homogeneous anisotropic medium. Based on those hybrid potentials, the explicit expressions of field components are presented in spatial domain. Those algebraic solutions will be beneficial to character analysis and numerical computation. Second, the spectral-domain EM field in planar-stratified media is divided into the upgoing and downgoing waves. We solve them using the generalized reflection/transmission method, where the generalized transmission plays an important role in the recurrence relation. The discrete complex image method (DCIM) is implemented to the numerical integral of the field from spectral domain to spatial domain. The proposed method allows forward modeling and data processing in EM logging. Finally, a rapid apparent conductivity extraction method is presented for triaxial induction logging.