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最近“感应测井的高次几何因子”一文利用微扰法第一次求得了全非均质情形感应测井响应的形式解,解答用级数表示。但对于非缓变电导率的介质,该文并没有从理论上证明级数的收敛。本文指出,对单一水平地层情形,截取[3]文形式解的一级项[下文公式(1)],得到的恰是文献[6]曾经给出的几何因子近似。但用它计算视电导率测井曲线,会造成测井曲线上人为的间断。因此,不能直接应用文[3]中的形式解的一级项来求非缓变电导率介质情况下的感应测井的响应。本文所作的分析,正是为按文献[4]的方法来利用文献[3]中形式解的一级项作准备。
The most recent “high-order geometric factor induction logging” article uses the perturbation method for the first time to obtain a formal solution to the response of an all-inhomogeneous case of induction logging. The solution is expressed in series. However, for non-uniform conductivity media, this paper does not theoretically prove the convergence of series. This paper points out that for a single horizontal formation, the first-order term [formula (1)] intercepted in [3] is exactly the geometric factor approximation given in [6]. However, using it to calculate the apparent conductivity logging curve can cause an artificial discontinuity in the logging curve. Therefore, it is not straightforward to apply the first-order term of the formal solution in [3] to find the response of an induction well without changing the conductivity medium. The analysis made in this paper is to prepare the first-order item of formal solution in [3] according to the method of [4].