用改进的光滑约束最小二乘正交分解法实现电阻率三维反演  

3-D resistivity inversion by the least-squares QR factorization method under improved smoothness constraint condition

作　　者：宛新林[1] 席道瑛[1] 高尔根[1] 沈兆武[2] 

机构地区：[1]中国科学技术大学地球与空间科学学院,合肥230026 [2]中国科学技术大学工程科学学院,合肥230026

出　　处：《地球物理学报》2005年第2期439-444,共6页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目 (4 0 1740 5 0 )资助

摘　　要：对三维电阻率反演问题进行了深入研究,提供了一种利用地表观测数据实现三维反演的实用算法.该方法应用有限差分求正演解,并通过对粗糙度矩阵元素进行适当改进,使之适用于各种情况下粗糙度矩阵的求取,进而建立在模型的总粗糙度极小条件下的反演方程.对反演方程采用收敛速度快且稳定的最小二乘正交分解(LSQR)法进行迭代求解,在迭代求解过程中只需利用偏导数矩阵和其转置矩阵乘以一个向量的结果,回避了直接求偏导数矩阵的繁琐计算,节省了内存,加快了反演的计算速度.不同的计算实例表明上述方法是求解大规模三维电阻率反演问题的有效方法.In this paper, we have deeply studied 3-D resistivity inversion, providing a practical algorithm of \{3-D\} inversion. Using the finite difference method to solve the 3-D forward problem, we have properly improved the elements of roughness matrix in order to form the roughness matrix in different cases, setting up the inversion equation under the condition that the total roughness of the model is minimum. It is fast and stable that using the least-squares QR factorization(LSQR) algorithm to solve inversion equations. The LSQR algorithm only requires the result of the derivative matrix and its transpose multiplying vectors, therefore we avoid direct and complicated computations of the derivative matrix. The above approach reduces the need for computer memory, and speeds up the inversion calculation. Two different calculation examples show that the above approach is efficacious for solving large scale 3-D resistivity inversion.

关 键 词：三维反演 偏导数矩阵 光滑约束 LSQR算法 

分 类 号：P631[天文地球—地质矿产勘探]