中文摘要：

应用数值模式匹配算法研究层状非均质各向异性地层中多分量感应测井响应的数值模拟方法。针对柱状界面上积累面电荷对共轴线圈系电磁响应的影响，通过傅氏级数展开与分离变量技术以及电阻率径向导数的奇异性，推导出关于电磁场水平分量的2个奇异算子方程。该奇异算子有效描述了井壁以及侵入带与原状地层分界面上积累面电荷的效应。在此基础上，利用模式匹配技术给出层状非均质各向异性地层中磁场并矢Green函数的半解析解以及多分量感应测井响应的计算方法，最后通过数值模拟结果对该算法进行检验并考察不同井眼泥浆电阻率以及不同侵入深度情况下多分量感应测井仪器的响应特征。

英文摘要：

In this paper, numerical matching mode responses of multicomponent induction logging method （NMM） will be applied to simulate the tool （MCIL） in a stratified inhomogeneous anisotropic medium. Aiming at problems on the influence of accumulation surface charges on cylindrical interfaces on the EM fields of coplanar coil system, two singular differential equations are derived about horizontal components of EM fields by using Fourier series expanding, separation variable and the singularity of derivative of formation conductivity function with respective to radial distance. The singular differential equations rightly describe the effect of the accumulation surface charges on the EM fields. Then, based on the technique of NMM, it will he given the semianalytic expression of the magnetic dyadic Green＇ s function, and the method to compute the MCIL responses. Finally, numerical results validate the algorithm and further investigate MCIL response characters in the cases of different mud resistivities and variable invasion depths.