关于解地球物理中病态方程的若干问题

讨论了三种重要的数值方法：１．吉洪诺夫正则化方法和适应正则化方法；２．预条件子方法；３．数值相关性技术．首先对这几种方法的新进展进行了评述，其次提出了几种合理选择正则子的方法并且建立了一个适应正则化算法．根据地球物理中病态方程的特性，推广了预条件子的概念并且提出了选择预条件子的若干方法．同时讨论了这些方法在地球物理中的应用．

SOMEASPECTSFORSOLVINGILL-POSED EQUATION IN GEOPHYSICS

In this paper,we study some problems and numerical methods for solving ill-posed equations which happen in geophysies.We mainly discuss three important numerical methodS:(1)Tikhonov regularization and adaptive regulariztion methods,(2) pre conditioner method;(3)numerical relative technique.Frist we give a survey of new development of these methods.Secondly,unlike much of the current emphasis on choice of regularization parameter in research on regularization method,we present several methods for properly choosing regularizer and establish a new framework of adaptive regularization algorithm.Thirdly,according to the characteristics of ill-posed equtions in geophysics, we extend the concept of preconditioner and give several methods of choosing preconditioner.Moreover we also discuss the application of these methods in geophysics.