广义Stein无偏风险估计与地球物理反问题正则化参数求取

Estimation of generalized Stein′s unbiased risk and selection of the regularization parameter in geophysical inversion problems

地球物理反演是获取地球信息的重要手段,其求解具有严重的不适定性.为获得稳定的反问题结果,通常需要在目标泛函中加入正则化约束项.正确地估计正则化参数一直是地球物理反问题中的难点.目前存在的选取方法需要根据大量的试验来确定正则化参数,工作量十分巨大,并且存在很大的经验性,很难得到最优的正则化参数.针对这个问题,本文提出了一种基于广义Stein无偏风险估计的正则化参数求取方法.该方法的具体思路是通过求解模型参数均方误差的广义Stein无偏风险估计函数,在反问题求解过程中自动求取正则化参数.本文模型测试结果表明,相比于目前常用的方法,通过该方法得到的正则化参数是最优的.

Inversion in geophysics is an important way to obtain earth′s information.However,it is usually an ill-posed problem.To obtain a stable inversion result,one needs to add a regularization constraint term into the objective function.The accurate estimation of this regularization parameter is a difficult task in geophysical inversion problems all the time.The existing methods determine this parameter based on trails which are very work-consuming.In addition,these methods are very empirical and hard to find the best one.To solve this problem,we propose a new method to select the regularization parameter based on estimation of the generalized Stein′s unbiased risk.Its specific idea is to solve the generalized Stein′s unbiased risk estimation function of the model′s mean-squared error and automatically to estimate the regularization parameter in the process of the geophysical inversion problem.Numerical tests on models indicate that the proposed method can estimate the optimal regularization parameter compared to the other existing methods.