关于感应测井的响应

ON THE RESPONSE OF INDUCTION LOG

中山大学

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。

Not long ago, the author of the paper entitled "The high-order geometric factors of induction logging[3] has,for the first time,determined a formal solution of induction log in total inhomogeneous media which is represented by an infinite series using the micro-disturbance technique. But the convergence of the series has not yet been proved theoretically for the media with non-slowly varying conductivities.Tt is remarked in the paper that in the case of single horizontal layer the result turned out exactly the same as the geometric factor approximation given in[6] while taking off the first-order term of formal solu-tion[3]. However, the unexpected discontinuities on apparent resistivity log might occur for having used such an approximation. Thus one cannot expect the desirable accuracy for utilizing immediately the first-order term of the series given In[3] to the response of induction logging in the non-slowly varying conductivity media. The analysis made in the paper is just to pave the way for utilizing the first-order term of the series solution described as in[3] referred to[4].