电磁波测井资料反演中Jacobi矩阵的快速算法及其特性分析

针对采用单发双收探头同时测量相位差和幅度比,测井响应与地层介电常数和电阻率两者都有关的电磁波测井资料反演问题，构造了其反演目标函数Jacobi矩阵〖WTHX〗J的快速算法.J直接给出了测井响应随地层参数变化的关系，利用J和它转置矩阵J〖WTBZ〗T的有意义乘积〖WTHX〗J·J〖WTBZ〗T和〖WTHX〗J〖WTBZ〗T.〖WTHX〗J〖WTBZ〗可以方便地对在非均质地层中测井响应特征和仪器的探测特性进行考察分析，为测井资料处理方法研究与仪器改进提供依据.

On the fast algorithm and characteristic analysis of Jacobi matrix in the inversion of electromagnetic wave logs

Since the most time consuming part of the inversion is the calculation of the Jacobi matrix, it is very important to perform these computations efficiently. In this paper, for the inversion problems of the electromagnetic wave logs which are the logging response (phase difference and amplitude ratio) dependent on both dielectric constant and conductivity in general, a fast algorithm of Jacobi matrix was advanced. The Jacobi matrix shows the change rate of a logging response to a formation parameter. With the Jacobi matrix 〖WTHX〗J〖WTBZ〗 and its transpose 〖WTHX〗J〖WTBZ〗T, we could define two significative matrix 〖WTHX〗J〖WTBZ〗·〖WTHX〗J〖WTBZ〗T and 〖WTHX〗J〖WTBZ〗T·〖WTHX〗J〖WTBZ〗. Based on 〖WTHX〗J〖WTBZ〗·〖WTHX〗J〖WTBZ〗T and 〖WTHX〗J〖WTBZ〗T·〖WTHX〗J〖WTBZ〗, the response characteristics and detecting characteristics of the electromagnetic wave logs in the 2 D inhomogenous formation can be understood. Especially the new knowledge could provide theoretically guidance to the inversion problems of the electromagnetic wave logs.