关于非均匀介质中电导率按深度变化时的势及其视电阻率函数

本文共分六部分内容。在前言中,简述了电测深方面有关研究的情况,尤其叙述了E.S.Sampaio（1976）的结果。 因本文采用的方法不同,从而求解了适合要求的微分方程定解问题,获得了电导率以 （其中α、σ0、σ1均为正实数,β为实数）按深度变化时势的分布。 其次,当β=0时,对电导率σ=（σ0+σ1z）α按深度变化时势的分布,应用Bessel函数的积分表达时,明显地改进和推广了E.S.Sampaio（1976）结果中的重要部分。 最后,结合实际作出了第一类、第二类标准化视电阻率函数。这种视电阻率函数,推广了Wenner和Schlumberger分别作出的视电阻率函数的有关部分,对电阻率法和激发极化法,都有其理论价值和实际意义。

ON THE POTENTIAL AND THE APPARENT RESISTIVITY FUNCTION IN AN INHOMOGENEOUS MEDIUM WHOSE CONDUCTIVITY VARYING WITH DEPTH

We started out by finding the exact solution of the differential equation of the problem. The potential distribution is obtained for the medium with conductivity varying with depth as: σ = （σ0 + σ1z）αeβz （where α,σ0,σ1 are positive real unmbers,β is a real number）. Then,the potential distribution is obtained when the conductivity varies with depth according to σ = （σ0 + σ1z）α,（α > 0） as β = 0,which we apply the integration of Bessel function to express it obviously the important part in the result[3] of E. S. Sampaio are improved and expanded. Finally,we formed type one and type two normalized apparent resistivity functions,which include the apparent resistivity function of Wenner and Schlumberger as a special case.