焦石坝地区页岩Cole-Cole模型参数的快速计算方法  

A fast computing method for rock electric parameters of Cole-Cole model in Jiaoshiba Zone

作　　者：刘智颖 张柏桥[1] 许巍[2] 罗兵[1] 李铭华[1] 黎伟[1] LIU Zhiying;ZHANG Baiqiao;XU Wei;LUO Bing;LI Minghua;LI Wei(Research Institute of Exploration and Development,Sinopec Jianghan Oilfield,Wuhan,Hubei 430223,China;College of Geophysics and Petroleum Resources,Yangtze University,Wuhan,Hubei 430100,China)

机构地区：[1]中国石化江汉油田分公司勘探开发研究院,湖北武汉430223 [2]长江大学地球物理与石油资源学院,湖北武汉430100

出　　处：《油气藏评价与开发》2020年第5期42-48,共7页Petroleum Reservoir Evaluation and Development

基　　金：湖北省教育厅青年人才项目“大斜度井中随钻电磁波测井响应数值模拟”(Q20171304)。

摘　　要：利用不同频率的电源下测量的岩心复电阻率,计算Cole-Cole模型中的4个模型参数(ρ0、m、τ和c),是岩心复电阻率频谱实验中重要的非线性寻优问题。然而,在焦石坝地区,参数τ很小,参数c变化范围大,使得最小二乘法寻优程序难以收敛。针对该问题,对寻优程序的初始值预估算法和最优迭代步长进行了研究。改进后的最小二乘法寻优程序,收敛速度明显加快,并且很好地避免了原有程序中参数τ值超出定义域而产生的计算错误的问题。研究表明,根据Cole-Cole模型函数的极值性质和渐近性质,可以直接求解参数τ,并且可以得出其余3个模型参数很好的迭代初始值。此外,将最小二乘法误差函数的梯度计算公式展开为泰勒级数,可以获得最优迭代步长,大幅提高算法收敛速度。Calculation of 4 parameters,ρ0,m,τand c,of Cole-Cole model by complex rock core resistivity data measured with multi-frequency is an important nonlinear optimization problem in rock core complex resistivity experiments.However,in Jiaoshiba Zone,a very smallτand c with big value range cause the difficulty of the convergence of optimization program.Therefore,the initial value determination and optimized iteration step have been studied.The improved program performances well on the speed of convergence,and avoids the calculation failure caused by out-range of the parameterτ.The study indicates that according to the maximum property and asymmetry property,the parameterτcan be obtained directly,and good iteration initial values of the rest 3 parameters can be obtained either.Meanwhile,by transforming the error function to be Tyler series,the optimized iteration step can be obtained and the convergence speed can be upgraded significantly.

关 键 词：标准Cole-Cole模型 最小二乘法 梯度下降算法 迭代初始值预估 最优步长 龙马溪组页岩 

分 类 号：P315.69[天文地球—地震学]