General Formula for the Kernel Function in the Formal Electric Potential Equation for <I>n</I>-Layer Resistivity Problem

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  • 電気探査学における<I>n</I>-層問題の電位式に含まれる核函数の一般公式
  • 電気探査学におけるn-層問題の電位式に含まれる核函数の一般公式
  • デンキ タンサガク ニ オケル n-ソウ モンダイ ノ デンイシキ ニ フクマレル カク カンスウ ノ イッパン コウシキ

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Abstract

A explicit expression for the kernel function involved in the formal electric potential equation for the general case of n layered media, each layer being homogeneous and isotropic, is given in the form_??_<BR>where<BR>where_??_called the elementary symmetric expression of k1, ..., kn-1 with their induced exponential functions of h1, ..., hn-1, _??_<BR>and the symbol kj, j=1, 2, ..., n-1, is resistivity factors, hj layer-depth, λ a parameter and n the number of layers.<BR>By making use of the general formula, the kernel function for the special case of five layered media is given in the paragraph 2·4. In section 3, the basic method of expressing the kernel function is suggested with an example such as n=6. Finally, some properties of the kernel function are explained in the subsequent section of the present paper.

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