Electromagnetic Field in Multilayered Rough Medium by Generalized Reflection/Transmission Method

In this work, we propose a semi-analytical method for electromagnetic (EM) fields in the multilayered media with two-dimensional (2D) rough interfaces (TDRI). Unlike previous physical models that address 2D EM fields scattered by rough interfaces from a plane wave source, the EM field to be solved here is radiated by triaxial magnetic dipoles embedded in any layer. To efficiently solve such an asymmetric three-dimensional (3D) EM field, we divided it into upgoing and downgoing waves in the spectral domain, then those upgoing/downgoing waves in adjacent layers are analytically connected by the generalized transmission and reflection coefficients crossing the rough boundary zones. Affected by rough boundaries, the transmission and reflection coefficients are determined using the surface integral equation. In the course of solving integral equations, we tackle the challenges associated with the extended boundary conditions and mathematical techniques related to the matrix equations. The numerical results compared with the finite element method (FEM) validated our formulations. The provided method can be widely used for forward modeling and inversion in geophysical prospecting.