Singularity-free Green’s function for EM sources embedded in a stratified medium

Abstract

We present a method to unify the calculation of Green’s functions for an electromagnetic (EM) transmitting source embedded in a homogeneous stratified medium. A virtual interface parallel to layer interfaces is introduced through the source location. The potentials for Green’s function are derived by decomposing the partial wave solutions to Helmholtz’s equations into upward and downward within boundaries. The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level. The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface. Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters, whereas the kernel connected with the stratified media stays unchanged. Hence, the present method can be easily applied to EM transmitting sources with little modification. The application of the proposed method to the marine controlled-source electromagnetic method (MCSEM) demonstrates its simplicity and flexibility.