Calculation of spatial-domain Green’s functions for multi-layered media by discrete complex image method

Key words:  discrete complex image method  layered media  Green’s function  generalized pencil of function method  Som-merfeld integral

Abstract:

The Green’s functions for multi-layered media are needed when crosshole electromagnetic imaging is applied to stratified media. According to the boundary conditions, the spectral domain Green’s functions for multi-layered media were formed. Then the spatial domain Green’s functions can be obtained by the inverse Fourier transformation, which are represented by the SommeaielH integrals. In order to avoid the singularity in the integration, the integrand was expressed to be sum of complex exponential terms by using discrete complex image method (DCIM). With generalized pencil of function (GPOF) method introduced, the number, location and intensity of images were obtained without extracting the quasi-static and surface wave terms in the integrand, which makes DCIM more efficient for multi-layered media. As a numerical example, the vector and scalar potential for a vertical magnetic dipole immersed in seven layers media were calculated, and the results got by DCIM and precise integration show that the DCIM is very accurate.