J4 ›› 2011, Vol. 41 ›› Issue (1): 258-264.

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Computing Green’s Function of A Current Point Source in Layered Earths in A Closed Form by Multi-Exponential Series Approximation

WENG Ai-hua, LIU Yun-he, CHEN Yu-ling, GU Ding-yu, LIAO Xiang-dong, DONG Rui-chun   

  1. College of GeoExploration Science and Technology, Jilin University, Changchun 130026, China
  • Received:2010-03-24 Online:2011-01-26 Published:2011-01-26

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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)λmin=10-6, λmax=10，with number of samples N=128, and  λ sampled in logarithmic mode; (2) T2min=10-7,T2max=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

CLC Number: 

  • P631.325
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