地球构造反演问题的新途径

本文讨论地球内部构造反演问题的某些新途径.其内容如下:地球构造反问题与固有值反问题;反散射问题中介质间断性的成象与因果广义Radon变换,包含地球构造反问题的新提法,反散射问题的线性化,古典Radon变换与广义Radon变换,线性化反问题的渐近解,渐近解和偏移格式.

SOME NEW APPROACHS FOR INVERSION PROBLEMS OF EARTH STRUCTURE

In this paper, we discuss a number of new approachs for the inversion problems ofthe earth structure. The contents are as follows: the inverse problems of the earthstructure and the inverse problem of the eigenvalue (including the inverse problem ofthe eigenvalue, the inverse （problem of the earth structure by layers, the inverse problemof spherical earth structure）; imaging of the medium, discontinuities in the inverse scat-tering problems and causal generalized Radon transform （including a new formula-tion for the inverse problem of the earth structure, the linearization of the inverse scat-tering problem, classical Radon transform and generalized Radon transform, asymp-totic solution of linearized inverse problem with the fixed source, asymptotic solutionof linearized inverse problem when the observation positions depend on the source po-sitions, asymptotic solutions and migration schemes）.