卫星重力梯度边值问题的点质量调和分析  

Point-mass Harmonic Analysis of Satellite Gradiometry Boundary Value Problem

作　　者：吴星[1,2] 张传定[3] 王凯[4] 

机构地区：[1]总装备部工程设计研究总院,北京100028 [2]海军海洋测绘研究所,天津300061 [3]中国科学院研究生院地球科学学院,北京100049 [4]信息工程大学测绘学院,河南郑州450052

出　　处：《测绘学报》2011年第2期213-219,共7页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(40774031);解放军信息工程大学博士生创新基金(200707)

摘　　要：研究并建立由全球重力梯度复组合分量及全张量解算全球点质量模型的基本方程,进一步推导得到基于卫星重力梯度的单定边值问题和超定边值问题的点质量调和分析解。通过采用分块循环矩阵分解大型线性方程组的方法,实现点质量调和分析解的稳定解算。最后运用EGM2008模型进行模拟数值计算,验证卫星重力梯度边值问题的点质量调和分析法的有效性和可行性。结果表明,在适当选取埋藏深度的情况下,点质量调和分析法能够以较高的精度恢复重力场,并且精度略优于广义轮胎调和分析方法。The basic equations for the solution of global point-mass model based on the complex combination and complete tensor components of global gravity gradient were studied and established in this paper,from which point-mass harmonic analysis solutions of single determined and over determined boundary value problems based on satellite gravity gradient were attained.The stability of point-mass harmonic analysis solutions was obtained via the decomposition of large linear equations using blocked cyclic matrices.Finally,simulation experiments with EGM2008 were made to validate the validity and feasibility of point-mass harmonic analysis of satellite gravity gradient boundary value problems.Results indicate that with proper depths of the point masses,point-mass harmonic analysis could recover an earth gravity field model at a higher precision which is a little better than that from the generalized torus harmonic analysis.

关 键 词：点质量模型 卫星重力梯度 边值问题 调和分析 GOCE 

分 类 号：P223[天文地球—大地测量学与测量工程]