过套管电阻率测井的地层电阻率快速反演算法  

A fast inversion algorithm of formation resistivity for resistivity logging through casing

作　　者：刘福平[1,2] 王安玲[1] 刘华群[1] 杨长春[2] 

机构地区：[1]北京印刷学院,北京102600 [2]中国科学院地质与地球物理研究所,北京100029

出　　处：《地球物理学报》2016年第6期2326-2332,共7页Chinese Journal of Geophysics

基　　金：北京市自然科学基金重点项目B类(KZ201510015015);北京市自然科学基金(4142016);北京市教委项目(KM201510015009;KM201410015006;PXM2016_014223_000025)资助

摘　　要：过套管电阻率测井是通过测量套管壁电势实现测量地层的视电阻率,基于传输线方程理论,针对层状地层,给出了套管壁电势、电流对地层横向电阻导数的微分方程(称Jacobi矩阵微分方程)及边界条件;利用Jacobi矩阵微分方程边值问题导出了过套管电阻率测井反演地层参数的Jacobi矩阵系数的解析表示,利用Marquardt方法实现了过套管测井的地层电阻率反演;通过计算对Jacobi矩阵的特性进行了探讨,并获得了较快的计算速度(因为Jacobi矩阵是用解析解表示的),反演结果与地层模型取得了较好的逼近.本文实现了过套管电阻率测井地层参数的Jacobi系数矩阵的快速计算及地层电阻率反演,为进一步开展电阻率测井数据处理提供了理论依据和快速反演算法.The resistivity logging through casing is that the potential distribution on the metal casing is measured to realize the measurement of formation resistivity.For this method,this study derived the differential equations of Jacobi matrix from the transmission line equation and its boundary conditions for a multi-layered formation,which are the derivative equations of the potential and current with respect to the transverse resistance of formation.With the differential equations we have given the analytic formula of the Jacobi matrix and realized the inversion of formation resistivity（Marquardt inversion method）.With computing examples,the characteristics of Jacobi matrix were discussed,and the fast computing speed was obtained,in which the results of inverse are in excellent agreement with the model of formation.The realization of formation resistivity inversion and its fast computation of Jacobi matrix provide a theoretical basis and a fast inversion algorithm for the further development of the resistivity logging and data processing.

关 键 词：过套管电阻率测井 JACOBI矩阵 传输线方法 测井响应 反演计算 

分 类 号：P631[天文地球—地质矿产勘探]