求解地震反演中的l_1模极小化模型

英文篇名：METHODS FOR THE MODEL OF l_1-NORM MINIMIZATION IN SEISMIC INVERSE
中文刊名：南京大学学报(数学半年刊)
英文刊名：Journal of Nanjing University(Mathematical Biquarterly)
作者：林小围 ; 孔敏
英文作者：Lin Xiaowei (Nanjing University Jinling College ; 210089 ; Nanjing PRC/ (Department of Mathematics ; Nanjing University ; 210093 ; Nanjing PRC) Kong Min (Department of Mathematics ; Nanjing University ; 210093 ; Nanjing PRC)
中文关键词：地震反演 ; l_1模 ; 单调变分不等式 ; 带邻近点项的Lagrange乘子法 ; 自调比
英文关键词：seismic inverse model ; monotone variational inequalities ; Lagrangian method with proximal term ; self-adaptive
出版日期：2011-11-30
机构：南京大学数学系;南京大学金陵学院;
年：2011
期：02
出版单位：南京大学学报(数学半年刊)

摘要

本文首先介绍地震反演的l_1模极小化模型,其次介绍带邻近点项的Lagrange乘子法,并证明其收敛性.然后将带邻近点项的Lagrange乘子法应用于地震反演的l_1模问题的求解.最后通过分析算法的收敛性条件对算法进行改进,从而得到自调比的带邻近点项的Lagrange乘子法.数值试验表明,改进的算法效率得到大大的提高,迭代次数减少约60%以上,计算时间也相应的减少,而且其效率受所添加的邻近点项的影响很小.
The Lagrangian method with proximal term(Algorithm 1) is introduced for solving the seismic inverse model.We analyze the convergence condition of the algorithm and obtain improved algorithm(AlgorithmⅡ,Ⅲ).Numerical result shows that AlgorithmⅢis greatly efficient.Comparing with AlgorithmⅠ,no more than 40%iterations it needs to solve the model,and its efficiency is not strongly affected by proximal term.

引文

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