【摘要】 关于电阻率测井边值问题的解法,从电流守恒这一条件出发得出了两个积分方程,其中一个和Al’pin在1964年得出的相同。本文重点放在另一个积分方程上。与Al’pin的方程不同,它的未知函数是电位本身,而不是边界面上的电流源分布。给出了两个例子,第一个例子是一泥浆电导率为σ_m的井穿过一电导率为σ₁的无限厚地层,其结果与理论值一致;第二个例于是一泥浆电导率为σ_m的井穿过电导率分别为σ₁和σ₂的两无限厚地层,其结果与Schlumberger的电模型结果一致。更多还原

【Abstract】 The fundamental boundary-value problem involving a current electrode in an inhomogeneous medium is solved. Two integral equations are obtained by imposing the condition of conservation of electric currents. Emphasis is placed on the solution of one of the integral equations involving potentials in a step-wise inhomogeneous medium. Two examples are shown. The first one is concerned with a well with mud conductivty σm in a thick bed of conductivity σqq1.In the second one the tool response is calculated when it is in a well with mud conductivity σm crossing a boundary separating two beds with conductivities σ1 and σ2 respectively. Results agree with other theoretical data for the first case. For the second case, they agree well with experimental data obtained from Schlumberger’s resistor network model.更多还原