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基于TSVD求解大地电磁不适定反演问题

发表时间:2009-11-15  浏览量:1280  下载量:483
全部作者: 柳建新,孙娅,郭荣文,童孝忠,王浩,郭振威
作者单位: 中南大学信息物理工程学院,有色资源与地质灾害探查湖南省重点实验室
摘 要: 针对不适定问题引入了截断奇异值分解(truncated singular value decomposition, TSVD)正则化方法。该方法主要建立在第一类算子方程的算子矩阵进行奇异值分解的基础上,然后根据奇异值的特征选取最佳正则化参数确定滤子函数,从而达到对该类函数的噪声去除效果。在确定正则化参数时,分别采用了广义交叉验证(generalized cross-validation,GCV)和L-Curve两种方法。最后,以大地电磁一维反演为例,论证了TSVD方法的准确性和实用性。并对比不同噪声、相同迭代次数下的反演结果,得到噪声越大、TSVD方法越有效的结论。
关 键 词: 地球探测与信息技术;不适定问题;截断奇异值分解正则化方法;正则化滤子函数;一维大地电磁反演
Title: TSVD methods for MT discrete linear ill-posed problems
Author: LIU Jianxin, SUN Ya, GUO Rongwen, TONG Xiaozhong, WANG Hao, GUO Zhenwei
Organization: Key Laboratory of Non-ferrous Resources and Geological Hazard Detection, School of Info-physics and Geomatics Engineering, Central South University
Abstract: The truncated singular value decomposition (TSVD) regularized method was introduced for ill-posed problems in this paper. This method was mainly built on the operator matrix’s singular value decomposition in the first class of operator equations, and then the best regularization parameters were selected in accordance with the characteristics of singular value so as to identify filter function, thereby removing noise of the function. Generalized cross-validation (GCV) and L-Curve were adopted in determining the regularization parameter. Finally, one-dimensional magnetotelluric inversion was selected as an example to demonstrate the TSVD about accuracy and practicality. By comparing the inversion results under different noises and the same iterations, a conclusion was obtained that the greater the noise in the observation vector was, the more effective the TSVD method became.
Key words: geo-information science and technology; ill-posed problem; truncated singular value decomposition regularization method; parameter filter function; one-dimensional magnetotelluric inversion
发表期数: 2009年11月第21期
引用格式: 柳建新,孙娅,郭荣文,等. 基于TSVD求解大地电磁不适定反演问题[J]. 中国科技论文在线精品论文,2009,2(21):2284-2290.
 
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