Variational solution about over-determined geodetic boundary value problem and its related theories  

作　　者：YU JinHai1,2 & PENG FuQing3 1 Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China 2 College of Earth Scienc, Graduate University of Chinese Academy of Sciences, Beijing 100049, China 3 Zhenghou Institute of Surveying and Mapping, Zhengzhou 450052, China 

出　　处：《Science China Earth Sciences》2007年第4期555-562,共8页中国科学（地球科学英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 40374001)

摘　　要：A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro- posed in the paper, with the help of minimizing some kinds of quadratic functional in calculus of variation. At first, the so-called variational solution for over-determined geodetic boundary value problem is defined in terms of principles in calculus of variation. Then theoretical properties related with the solution are derived, especially for its existence, uniqueness and optimal approximation. And then the computational method of the solution is discussed, and its expression is exhibited under the case that all boundaries are spheres. Finally an arithmetic example about EGM96 gravity field model is given, and the computational results show that the proposed method can efficiently raise accuracy to deal with gravity data. In all, the variational solution of over-determined geodetic boundary value problem can not only fit to deal with many kinds of gravity data in a united form, but also has strict mathematical basements.A new solving method for Laplace equation with over-determined geodetic boundary conditions is proposed in the paper, with the help of minimizing some kinds of quadratic functional in calculus of variation. At first, the so-called variational solution for over-determined geodetic boundary value problem is defined in terms of principles in calculus of variation. Then theoretical properties related with the solution are derived, especially for its existence, uniqueness and optimal approximation. And then the computational method of the solution is discussed, and its expression is exhibited under the case that all boundaries are spheres. Finally an arithmetic example about EGM96 gravity field model is given, and the computational results show that the proposed method can efficiently raise accuracy to deal with gravity data. In all, the variational solution of over-determined geodetic boundary value problem can not only fit to deal with many kinds of gravity data in a united form, but also has strict mathematical basements.

关 键 词：earth’s GRAVITY field over-determined boundary value problem QUADRATIC functional. VARIATIONAL solution optimal approximation 

分 类 号：P223[天文地球—大地测量学与测量工程]