求解地震反演中的l1模极小化模型

摘要

本文首先介绍地震反演的l1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l1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 (Algorithm Ⅱ,Ⅲ). Numerical result shows that Algorithm III is greatly efficient. Comparing with Algorithm I, no more than 40% iterations it needs to solve the model, and its efficiency is not strongly affected by proximal term.