构造成像中一类双曲型方程不适定问题的数值解法（Ⅰ）基本问题与逼近问题  

NUMERICAL SOLUTION METHOD FOR A CLASS OF ILLPOSED PROBLEM OF HYPERBOLIC EQUATION ABOUT STRUCTURE IMAGE(Ⅰ):BASIC PROBLEM AND APPROXIMATE PROBLEM

作　　者：范尚武[1] 

机构地区：[1]中国科学院计算数学与科学工程计算研究所

出　　处：《地球物理学报》1995年第A01期22-30,共9页Chinese Journal of Geophysics

基　　金：国家自然科学基金委员会;中国科学院;中国石油天然气总公司和大庆石油管理局联合资助

摘　　要：研究了地球物理构造成像中一类双曲方程不适定问题的数值求解方法，讨论了这类基本问题的不适定性，提出了数值求解方面的逼近问题，给出了讨论问题的基本空间，论证了基本空间为Ｈｉｌｂｅｒｔ空间及基本空间上关于连续映射与收敛性方面的若干结果，从而为讨论逼近问题的适定性与收敛性奠定了基础．In this paper, the numerical solution method for a class of improperly-posed problem of hyperbolic partial differential equation is researched. This class of problem describes structure image in geophysics.The improperly-posedness of such basic problem is discussed.The approximate problem with respect to numerical solution of basic problem is proposed. In addition, the basic space used to discussing the problem is formulated.It is proved that the basic space is Hilbert space.Simulteniously,some results concerning the convergence and the continuous image are also analysed.The above lays the foundation for demonstration of properly-posedness and convergence of the approximate problem.

关 键 词：构造成像 不适定问题 双曲型方程 地震勘探 

分 类 号：P631.44[天文地球—地质矿产勘探]