二维轴对称介质中电磁波测井的响应函数

The response functions of electromagnetic wave logs in the 2-D axis-symmetric formation

单发双收电磁波测井测的是两接收线圈的感应电动势之间的相位差和幅度比及测井响应与地层介电常数和电导率两者有关的一般情况,对此本文推导出其在二维轴对称介质中响应函数公式,给出它的快速算法.通过建立二维非均质反演Jacobi矩阵与响应函数的关系,开辟了Jacobi矩阵快速算法构造的有效途径.从理论上得到了在均匀介质中相位差和幅度比对地层的介电常数和电导率的空间分布探测特性具有交叉互补性的结果,即相位差对电导率(介电常数)的空间分布敏感区域和幅度比对介电常数(电导率)的空间分布敏感区域是相同的.

The fundamental feature of electromagnetic wave logs is the logging response （phase difference and amplitude ratio ） dependent on the dielectric constant and conductivity in general. In this paper we derived the response functions（RF） of the electromagnetic wave logs in a 2-D axis-symmetrical formation and proposed a fast algorithm based on the integral equation of electromagnetic field and the weak scattering approximation. Based on a relationship between the RF and Jacobi matrix, a novel method which is independent of the forward modeling for a fast algorithm of Jacobi matrix employing the RF was advanced. The theoretical results about the investigating characteristics of phase difference and amplitude ratio were also gained. It was shown that the phase difference is sensitive to the conductivity （dielectric constant） within substantially the same volume as the amplitude ratio is sensitive to the dielectric constant （conductivity） in homogeneous medium .