求解一类地球物理反问题的一种信赖域方法

针对常见地球物理反问题的不适定性,本文研究地球物理领域中经过对数学模型的处理最终为病态线性方程组的问题。应用目前流行的信赖域算法,并用带有信赖域技巧的截断共扼梯度法来解信赖域子问题。该方法是一种迭代正则化方法,它具有自动调节正则化参数的功能,克服了常用的Tikhonov正则化方法中正则化参数求取的困难。本文给出了一定条件下方法的收敛性证明,理论和实际资料的试算表明了算法的正确有效性,从而可以解决这类地球物理反问题。

A Trust Region Algorithm to Solve a Kind of Geophysical Inverse Problem

In view of the ill-posedness of many geophysical inverse problems,in this paper we solve ill-posed linear set of equations that are derived from processing geophysical inverse problem.We apply the popular trust region algorithm and truncated conjugate gradient algorithm with trust region skills to solve trust region subproblems.It is a kind of itertive regularization method,and has the function adjusting regularization parameters automatically,so it overcomes the difficulties when solving the regularization parameters.Under very mild conditions,this paper gives the proof of convergence.From the results processing theoretic and practical data,it can be proved that the algorithm is both correct and valid.Hence,the algorithm in this paper is a promising way to deal with this kind of geophysical inverse problem.