两种模型的球面数值积分的比较研究  

Comparison Study of the Numerical Calculations of the Spherical Integral Based on Two Models

作　　者：田伟[1] 申文斌[1,2] 李进[1] 

机构地区：[1]武汉大学测绘学院,武汉市珞喻路129号430079 [2]武汉大学地球空间环境与大地测量教育部重点实验室,武汉市珞喻路129号430079

出　　处：《武汉大学学报（信息科学版）》2009年第9期1116-1121,共6页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金资助项目(40637034;40574004);国家863计划资助项目(2006AA12Z211)

摘　　要：基于球面上N个点的Thomson均匀分布,提出了一种新的球面数值积分方法,并推导出相应的数值积分公式。在取消点列分布的均匀分布后,给出了不规则点列分布下的积分的一般表达式,并统一了不同分划下球面数值积分的形式。通过数值计算比较,分析了经纬格网划分和Thomson均匀分布下数值积分的结果:在数据点个数相等的条件下,对于Possion积分球面位分布为常数的情况,利用Thomson均匀分布得到的计算结果的精度要比利用格网划分法得到的结果的精度高一个数量级;对于分布比较接近地球真实引力位分布的较复杂情况,Thomson均匀分布计算结果的优越性有所降低,但仍优于经纬格网划分法。We present a new approach to proceed numerical integral on a sphere and derives the corresponding numerical integral formulas. If the condition of uniform distribution on the sphere is ignored, a general expression of the spherical numerical integral formula based on the irregular distribution of N points on a sphere is introduced, and some spherical numerical integral formulas, which are based upon different division approaches on a sphere, are unified. By numerical calculations, we compare and analyze the results under the grid division and uniform distribution with equal number of data points in models., in the case of constant spherical potential, and the more complicated potential distribution （EGM96） which approximates the real case better, the accuracy of calculations using the Thomson uniform distribution model is higher and better than that using the grid division model.

关 键 词：边值问题 Thomson均匀分布 球面数值积分 

分 类 号：P223.0[天文地球—大地测量学与测量工程]