用垂直数值模式匹配方法计算多频电磁测井响应

利用垂直数值模式匹配方法计算了轴对称介质模型的电磁测井响应，该算法既可用于低频感应测井仪的响应模拟，也可用于高频电磁波传播测井仪的响应模拟。所用的垂直数值模式匹配（Vertical numeric mode matching,VNMM）方法将电性参数既有径向变化又有垂向变化的轴对称二维介质模型分成多个径向柱和环形区域，各个径向柱环形域的电性参数只有垂向层状变化。介质中的电场表示成垂向上的垂直特征模式与径向解析函数的乘积。垂直特征模式用一维有限元计算。利用介质中柱环形域的界面上电场与磁场切向分量的连续性条件导出了各个柱形界面的透射系数和反射系数。应用该方法对不同泥浆性能的测井环境进行了模拟。计算了电阻率差较小的水淹层、低电阻率储层的高频电磁测井响应，得到了有意义的结果。

Calculating Multi-frequency Electromagnetic Logging Responses with Vertical Eigenstate Method

The response of the electromagnetic logging tool was simulated using the vertical numeric mode matching method (VNMM). The VNMM is suitable both for the low frequency induction logging tool and the high frequency electromagnetic propagation logging tool. In the vertical numeric mode matching method, the axi-symmetric two-dimensional problem was separated into two related one-dimensional problem. In the radial direction, the medium was divided into several annulus domains, whereas in the vertical direction, it was regarded as combinations of horizontal layers. The total field is represented by the production of the vertical eigen-modes and the radial analytic function. The vertical eigen-mode was solved by one-dimensional finite element method (FEM). By using the continuity of the tangential components of the electric and magnetic fields in the vertical boundaries in radial direction, the transparent and reflection coefficients were derived. Several kinds of profiles in different borehole environments were simulated. Simulated responses of the electromagnetic logging tool in the water flooded oil bearing formation, the low resistivity oil-bearing formation and the thinly bedded oil-bearing formation are easy to obtain from VNMM.