Abstract:

A novel method is developed to compute the Green’s function of a current point source buried in electrical conductive layered earths. In this method, the kernel function of Green’s function is firstly approximated by multiexponential series with the fact that the function is real and mono-decay or mono-increase, and then with the help of Somerfeld-Lipschtz integration, the Green’s function can be expressed in a closed form of the summation of a finite series. Numerical results show that with the following optimized parameters, one can get a highly accurate computation of Green’s function: (1)λ_min=10^-6, λ_max=10，with number of samples N=128, and  λ sampled in logarithmic mode; (2) T_2min=10^-7,T_2max=10³, T₂ is sampled in logarithmic mode with 64 samples; (3) the most optimized regularization parameter α² could be 10^-5, and the simplest model is the preferred solution constraint.

Key words: electromagnetic method, Green’s function, layered earth, current point source, multiexponential approximation, Prony series