【摘要】 本文讨论了介质不均匀性对场的相互作用,用微扰法求出了一系列修正项。这些修正项把均匀介质的电场逐步修改成非均匀介质的电场。随着所含修正项数的增多,所得结果逼近真实值的精度也增加,达到任何预先给定的标准。用一个其严格解已知的例子验证了本方法的正确性。定义几何因子为视电阻率对电导率的泛函微商。利用一级几何因子,我们推导出了径向和轴向几何因子。前者Roy和Dhar已经导出,与我们的结果差一常系数。轴向几何因子可用于直流电测井的数字解释。更多还原

【Abstract】 A successive approximation method solving electrostatic field of inhomogeneous medium is proposed, which yields results with increasing accuracy when the number of correction terms increases. The method is verified with a simple example. Geo-metrical factors are defined as the functional derivatives of apparent resistivity with rcspect to conductivity. As in induction logging, we derived radial and axial geo-metrical factors. The integrated radial geometrical factor plotted against L/d is the approximation of the departure curve. Comparasons between them are provided to show to what an extent the approximation is good.更多还原