任意球冠下Stokes-Neumman混合边值问题的球谐函数有限逼近方法  

Spherical Harmonic Finite Approximation Method for the Stokes-Neumman Mixed Boundary Value Problem with a Sphere Cap

作　　者：曾艳艳[1,2] 于锦海[1,2] 万晓云[1,2] 

机构地区：[1]中国科学院计算地球动力学重点实验室,北京100049 [2]中国科学院大学地球科学学院,北京100049

出　　处：《武汉大学学报（信息科学版）》2014年第1期65-69,共5页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金资助项目(41274034;41074015;41104047)~~

摘　　要：首先研究了任意球冠下Stokes-Neumman混合边值问题的求解方法,然后利用EGM08重力场模型对建立的求解方法进行模拟计算。结果表明,给出的解算方法能达到亚mm量级的精度。作为Stokes-Neumman混合边值问题的应用拓展,用于精化局部大地水准面,结果表明,若不顾及边界效应,计算精度至少达到5cm。因此,本文建立的Stokes-Neumman混合边值问题的解法不仅理论上可行,而且能保持足够的计算精度,适用于多种类型重力观测数据的综合处理。A method solving the Stokes-Neumman Mixed Boundary Value Problem （S-N MBVP） with a sphere cap is studied in this paper. First, we discuss the method for S N MBVP with the polar cap. Then S-N MBVP with general sphere cap is solved with the help of coordinate transformation. The transformation between spherical coefficients in different coordinate systems is also studied. By making use of the imitation computation for the EGM08 model, it is concluded that the solution method given in the paper can be accurate to submillimeter level. S-N MBVP can be used to refine the local geoid, our results show the recovered height of a geoid in the interior of the spherical cap can reach to the accuracy of 5 centimeters. Our results show that the proposed method not only is effective in theory, but also has sufficient precision to deal with many kinds of gravity data.

关 键 词：重力场 任意球冠 混合边值问题 球谐函数 

分 类 号：P223.0[天文地球—大地测量学与测量工程]