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本文采用递推矩阵方法计算径向成层介质的Green函数,针对不同的仪器参数和发射频率、给定一些不同的典型的侵入带电阻率和原状地层电阻率,使侵入带半径在一定范围内连续变化,考察相位移电阻率和幅度衰减电阻率随侵入带半径的不同而变化的情况,分析相位移电阻率和幅度衰减电阻率径向探测特性的不同并确定仪器的径向探测深度。根据圆柱形层界面处电场和磁场的连续性条件得到确定待定系数的矩阵方程组并通过递推方法快速求解。只需改变方程组中源项元素的位置,就可以方便地得到当源点和场点在任意层时的Green函数,形式简洁、易于编程。采用将变型Bessel函数的指数项单独列出的方式有效地解决了Green函数计算中的上溢问题。用上述Green函数对随钻电磁波电阻率测量仪器进行数值模拟,分析了钻铤的影响规律、井眼校正方法、仪器的径向探测特性和垂向分辨率。所得到的结论可为随钻电磁波电阻率测量仪器的研制和使用提供理论指导。
In this paper, we use the recursive matrix method to calculate the Green function of the radial stratified medium. For different instrument parameters and emission frequency, given some different typical resistivity of intrusion zone and the original formation resistivity, the radius of intrusion zone is within a certain range The changes of phase displacement resistivity and amplitude attenuation resistivity with the radius of invaded zone were investigated. The difference between phase displacement resistivity and amplitude attenuation resistivity radial detection characteristics was analyzed and the radial depth of detection was determined. According to the continuity condition of electric field and magnetic field at the interface of cylindrical layer, the matrix equations for determining the undetermined coefficients are obtained and solved quickly by recursion method. Simply change the position of the source item in the system, we can easily get the Green function when the source point and the field point are at any layer, which is simple in form and easy to program. The method of listing the exponential term of variant Bessel function is used to effectively solve the problem of overflow in the calculation of Green function. The above Green function is used to simulate the electromagnetic wave resistivity measurement while drilling. The influence law of drill collar, wellbore correction method, radial detection characteristics and vertical resolution of the instrument are analyzed. The conclusions obtained can provide theoretical guidance for the development and application of the electromagnetic wave resistivity measurement instrument while drilling.