电阻率测井三维模式匹配法中的平面数值分析

Numerical analysis of 3-D numerical mode-matching method in resistivity logs

在地层非轴对称条件下建立了新型的坐标系,详细介绍了计算电阻率测井响应的三维模式匹配理论。在井轴与地层法线所形成的平面上用数值方法计算,与此面垂直的方向上用解析方法计算;详细推导了平面上的偏微分方程及其相应的等价变分问题;选定平面三角形基函数作为型函数,确定了单元方程和单元矩阵;给出了网格划分方法及其总体矩阵的安装方法;最后通过求解广义特征值问题完成了平面二维区域的数值分析。结果表明,在均匀介质中,新方法的数值结果与解析分析的结果是一致的,精度也得到了保证,验证了平面数值分析方法的正确性,为进一步完成全三维的模式匹配作好了准备。

In nonsymmetric model, a new coordinate was set up and the 3-D numerical mode-matching （NMM） theory was introduced. The numerical analysis was used to the plane of formation normal and borehole axis, and analysis method was adopted to the direction normal to the plane. And differential coefficient on the plane and the equivalent variation equation were deduced. The triangle base function was selected as shape function, and cell equation and cell matrix were constructed. The mesh method and the total matrix assembling from local matrices were given in detail. Finally, the numerical analysis was completed after the solution of generalized eigenvalue problem. In homogeneous media, the NMM results agree well with the analytical solution, and the validity was verified. All research results prepare for further 3-D NMM.