电阻率三维反演中偏导数矩阵的求取与分析  

Derivation and analysis of partial derivative matrix in resistivity 3-D inversion

作　　者：吴小平[1] 徐果明[1] 

机构地区：[1]中国科学技术大学地球与空间科学系

出　　处：《石油地球物理勘探》1999年第4期363-372,共10页Oil Geophysical Prospecting

摘　　要：利用共轭梯度选代技术的电阻车三维反演法是近年来发展的快造、有效的方法，它只需求取Jacobian矩阵G与任一向量x的乘积Gx及GT与任一向量y的乘积结果GTy，避免直接求取G和GTG，从而大大地减少了工作量。在此基础上，本文引入求取G的Rodi算法，导出了E-SCAN三维数据反演中Gx及GTy的拓展形式，只需作一次正演便可同时求得Gx及GTy，实现了每次反演迭代仅需作一次正演计算，从而大大地提高了运算速度。此外，本文还对灵敏度矩阵进行了分析，讨论了E-SCAN测量区域以外的分群情况，这对实际数据的反演解释有重要的意义。The resistivity 3-D inversion method that involves conjugate gradient iterative operation is a new efficient method. It only estimates Gx (product of Jacobian matrix G and any vector x ) and GTy (product of GT and any vector y ), and avoids direct derivation of G and GTG, thus reducing operation greatly. Then, authors deduce Rodi algorithm for estimating G, and give the expansions of Gx and G'y in ESCAN 3-D data inversion. It is found from minute analysis that Gx and GTy can be deduced simultaneously in once forward operation to achieve single forward operation for each inverse iteration, thus speeding up operation greatly- In addition, sensitivity matrix is analysed; and resolution outside E-SCAN area is discussed, which is significant to inverse interpretation of real data.

关 键 词：电阻率 三维反演 共轭梯度 偏导数矩阵 电法勘探 

分 类 号：P631.322[天文地球—地质矿产勘探]