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《Chinese Journal of Geophysics》 2007-02
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On the fast algorithm and characteristic analysis of Jacobi matrix in the inversion of electromagnetic wave logs

XING Guang-Long~ 1,2 , YANG Shan-De~2, LI Shu-Guang~11 College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China2 College of Physics, Jilin University, Changchun 130023, China  
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 J and its transpose J~T, we could define two significative matrix J·J~T and J~T·J. Based on J·J~T and J~T·J, 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.
【Fund】: 国家自然科学基金项目(49774241);; 燕山大学博士基金项目(B121)资助
【CateGory Index】: P631.84
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