电极型电阻率测井反演算法研究

AN ALGORITHM FOR THE INVERSE PROBLEM OF ELECTRODE-TYPE RESISTIVITY MEASUREMENTS

低频电极型测井仪的响应总是受井眼、围岩和侵入的影响，而传统的测井综合解释无法完全有效地校正这些影响．本文将收敛速度快而效果好的变形波恩迭代（DBIM）方法用于处理轴对称二维非均匀介质分布的电导率反演问题．在每次迭代过程中采用了快速的半解析的模式匹配的正演方法，半解析地表达出反演中所需计算的格林函数的偏导数；并在此基础上半解析地求出了反演的非线性积分方程中的积分运算，大大提高了反演速度和精度．

Logging response of electrode-type resistivity tools is always affected by the shoulder, borehole and invasion. But conventional synthetic interpretation can't correct these effects fully. In this paper, the distorted Born iterative method(DBIM) is applied to deal with the nonlinear inversion problem of the conductivity distribution in a twodimensional axisymmetric medium. In each iteration of the DBIM, an efficient numerical mode-matching (NMM) method is used to solve the forward problem. This method provides a semianalytic expression for the Green's function and its derivatives required in the inversion, and then deduces a semianalytic expression of the integration in the nonlinear integral equation. Therefore, the efficiency and accuracy are improved dramatically.