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利用共轭梯度法的电阻率三维反演研究
引用本文:吴小平,徐果明.利用共轭梯度法的电阻率三维反演研究[J].地球物理学报,2000,43(3):420-427.
作者姓名:吴小平  徐果明
作者单位:中国科学技术大学地球空间科学系,合肥230026
基金项目:教育部科研基金!97035815,中国科技大学青年科学基金!KA0712
摘    要:利用共轭梯度(CG)迭代技术,实现了直流电阻率测量数据的三维最小构造反演。 首先,运用共轭梯度迭代算法解反问题的线性方程组,只需求Jacobian矩阵G与任一向量x的 乘积Gx及G与任何一向量y的乘积Gy,再引入G的Rodi算法,则Gx及Gy均可在每次反 演迭代中的一次正演计算后一并求得.因此,每次反演迭代仅需一次正演计算,大大加快了 计算速度;而且避免了直接求 G以及 GG的逆矩阵,也避免了存储 G和 GG所需庞大的存储 量。另外,由于反演参数太多,求模型光滑约束的最小构造反演能够有效地消除多余构造信 息,得到可靠的反演结果。将这3种方法和技术融合于三维反演中,取得了好的反演效果.为 改进传统最小构造反演收敛慢的问题,还提出了一种新的反演迭代技术,仅需10次左右甚至 更少迭代即可收敛。

关 键 词:电阻率E-SCAN  地电测量  共轭梯度法  最小构造反演  
文章编号:0001-5733(2000)03-0420-08
收稿时间:1999-10-05

STUDY ON 3-D RESISTIVITY INVERSION USING CONJUGATE GRADIENT METHOD
WU XIAO-PING,XU GUO-MING.STUDY ON 3-D RESISTIVITY INVERSION USING CONJUGATE GRADIENT METHOD[J].Chinese Journal of Geophysics,2000,43(3):420-427.
Authors:WU XIAO-PING  XU GUO-MING
Institution:Department of Earth and Space Science, University of Science and Technology of China, Hefei 230026, China
Abstract:We present a 3-D minimum structure inversion algorithm for d. c. resistivity data, using conjugate gradient (CG) relaxation techniques. Firstly, the minimum structure inverse equations are solved. In doing so, the CG relaxation technique only requires the results of derivative matrix G and its transpose G~T multipled by a vectors, i.e. Gx and G~Ty, respectively. Then the Rodi method is introduced to compute, and the Jcobian matrix G, Gx and G~Ty can be got after one forward calculation in each inverse iteration. Therefore, only one forward calculation is required in each inversion iteration, the inversion is computed much quickly. Additionally, we are able to bypass the actual computation of the derivative matrix G and the inversion of G~TG, also to avoid the huge storage for G and G~TG. On the other hand, since there are so many inversion parameters, we impose a smoothness constraint on the model in minimum structure inversion to solve the smoothest solution which effectively erases unnecessary structures, obtains trustworthy results close to true model. We firstly merge these methods and techniques into 3-D resistivity inversion and obtain very promising results, which have been tested on 3--D synthetic data. A new iterative technique is also, developed to deal with the problem of very slow convergence rate in traditional minimum. structure inversion, it shows that only about ten iterations or less are required to reach the convergence.
Keywords:Resistivity  E-SCAN geoelectriacl measurement Conjugate gradient (CG) method  Minimun structure inversion  
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