确定地球重力场模型的最小二乘配置法与调和分析法的精度评析
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摘要
本文给出了利用卫星重力梯度张量TT_(zz)分量恢复地球重力场模型的最小二乘配置法与调和分析法的基本原理公式,通过数值实验对两种方法确定地球重力场模型的精度进行了比较,最后总结评述了两种方法在反演地球重力场模型时的优缺点.
Fundamental formulae of least squares collocation(LSC) method and spherical harmonic analysis method to recover the Earth ' s gravity field model(EGM) from T_(zz)component of satellite gravity gradients(SGG) are deduced,the precisions of these two methods in the determination of the EGM are compared by numerical experiments,and the advantage and disadvantage of these two methods in the recovery of the EGM are summarized and reviewed at last.
Fundamental formulae of least squares collocation(LSC) method and spherical harmonic analysis method to recover the Earth ' s gravity field model(EGM) from T_(zz)component of satellite gravity gradients(SGG) are deduced,the precisions of these two methods in the determination of the EGM are compared by numerical experiments,and the advantage and disadvantage of these two methods in the recovery of the EGM are summarized and reviewed at last.
引文
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Kotsakis C.2007.Least-squares collocation with covariancematching constrains[J].Journal of Geodesy,81(10):661-677.
Li Y C.2004.Theories and method of the recovery of the Earth's gravity field using satellite gravity gradients[D].Zhengzhou:The PLA Information Engineering University.
Liu X G,Wu X P,Wang B J,et al.2010a.Study on gridding methods of satellite gravity gradient data[J].Journal of Geodesy and Geodynamics(in Chinese),30(6):60-65.
Liu X G,Wu X P,Zhao D M,et al.2010b.Non-singular expression of the disturbing gravity gradients[J].Geodaetica et Cartographica Sinica(in Chinese),39(5):450-457.
Liu X G.2011.Theory and methods of the Earth's gravity field model recovery from GOCE dataGn Chinese)[D].Zhengzhou:The PLA Information Engineering University.
Liu X G,Li S S,Wu X.2011.Downward continuation of satellite gravity gradient data[J].Journal of Geodesy and Geodynamics(in Chinese),31(1):132-137.
LiuX G,Zhang L P,Wang J,et al.2012a.Establishment of harmonic analysis models of single component and composite components of disturbed gravity gradient tensor[J],Journal of Geodesy and Geodynamics(in Chinese),32(5):103-108,112.
Liu X G,Wu X P,Wang K.2012b.Construction of the least squares collocation models for single component and composite components of disturbed gravity gradients[J].Chinese J.Geophys.,55(5):1572-1580.
Luo Z C.1996.Theories and method of the determination of the earth's gravity field using satellite gravity gradientsGn Chinese)[D].Wuhan:Wuhan Technical University of Surveying and Mapping.
Luo Z C,Chao D B,Ning J S.1997.Spherical harmonic analysis on gravity gradient tensors[J].Journal of Wuhan Technical University of Surveying and Mapping(in Chinese),22(4):346-349.
Migliaccio F,Reguzzoni M,Sanso F.2004a.Space-wise approach to satellite gravity field determination in the presence of coloured noise[J].Journal of Geodesy(in Chinese),78:304-313.
Migliaccio F,Reguzzoni M,Sanso F,et al.2004b.GOCE:dealing with large attitude variations in the conceptual structure of the space-wise approach[C].//Proc.Second International GOCE User Workshop"GOCE,The Geoid and Oceanography",ESAESRIN,Frascati,Italy.
Tscherning C C.2001.Computation of spherical harmonic coefficients and their error estimates using least-squares collocation[J].Journal of Geodesy(inChinese),75(1):12-18.
Wu X.2009.Research of methods of spherical harmonic analysis of the Earth's gravity field(in Chinese)[D].Zhengzhou:Information Engineering University.
Wu X,Zhang C D,Zhao D M.2009a.Generalized torus harmonic analysis of satellite gravity gradients component[J].Geodaetica et Cartographica Sinica(in Chinese),38(2):101-107.
Wu X,Zhang CD,Zhao DM.2009b.Point-mass harmonic analysis method based on spherical boundary value problem[J].Chinese J.Geophys.(in Chinese),52(12):2993-3000.
Wu X,Zhang C D,Liu X G.2010.Least squares collocation harmonic analysis of the radial satellite gravity gradients[J],Geodaetica et Cartographica Sinica(in Chinese),39(5):471-477,483.
Wu X P.1991.Some analyses of the determination of the Earth's gravity field from the satellite gravity gradient and terrestrial data[J],Journal of the PLA Institute of Surveying and Mapping(in Chinese),(1):19-32.
Xu X Y.2008.Study of determining the Earth's gravity field from satellite gravity gradient and satellite-to-satellite tracking data(in Chinese)[D].Wuhan:Wuhan University.
Zhang C D.2000.Satellite gravimetry:foundation,modeling methods,and data processing algorithms(in Chinese)[D].Zhengzhou:Information Engineering University.
Zhang C D,Xu H Z,Wu X.2004.On the torus approach for gobal spherical harmonic computation[C].Hubei:Hubei Science and Technology Publishing House,302-314.
Zhang H,Chen Q.2005.Least squares collocation in calculating potential coefficient with satellite gravity gradiometry data[J].Geomatics and Spatial Information Technology(in Chinese),28(6):34-35.
Zhong B.2010.Study on the determination of the Earth's gravity field from satellite gravimetry mission GOCE[D].Wuhan:Wuhan University.
李迎春.2004.利用卫星重力梯度测量数据恢复地球重力场的理论与方法(inChinese)[D].郑州:解放军信息工程大学.
刘晓刚,吴晓平,王宝军,等.2010a.卫星重力梯度数据的网格化方法研究[J].大地测量与地球动力学,30(6):60-65.
刘晓刚,吴晓平,赵东明,等.2010b.扰动重力梯度的非奇异表示[J].测绘学报,39(5):450-457.
刘晓刚.2011.GOCE卫星测量恢复地球重力场模型的理论与方法[D].郑州:解放军信息工程大学.
刘晓刚,李珊珊,吴星.2011.卫星重力梯度数据的向下延拓[J].大地测量与地球动力学,31(1):132-137.
刘晓刚,张丽萍,王俊,等.2012a.扰动重力梯度张量单分量和组合分量调和分析法模型的建立[J].大地测量与地球动力学,32(5):103-108,112.
刘晓刚,吴晓平,王凯.2012b.扰动重力梯度张量单分量和组合分量最小二乘配置法模型的建立[J].地球物理学报,55(5):1572-1580.
罗志才.1996.利用卫星重力梯度数据确定地球重力场的理论与方法[D].武汉:武汉测绘科技大学.
罗志才,晁定波,宁津生.1997.重力梯度张量的球谐分析[J].武汉测绘科技大学学报,22(4):346-349.
吴星.2009.卫星重力梯度数据处理理论与方法[D].郑州:信息工程大学.
吴星,张传定,赵东明.2009a.卫星重力梯度分量的广义轮胎调和分析[J].测绘学报,38(2):101-107.
吴星,张传定,赵东明.2009b.基于球面边值问题的点质量调和分析方法[J].地球物理学报,52(12):2993-3000.
吴星,张传定,刘晓刚.2010.卫星重力径向梯度数据的最小二乘配置调和分析[J].测绘学报,39(5):471-477,483.
吴晓平.1991.利用卫星重力梯度与地面数据确定地球重力场的分析[J].解放军测绘学院学报,(1):19-32.
徐新禹.2008.利用卫星重力梯度及卫星跟踪卫星数据确定地球重力场的研究[D].武汉:武汉大学测绘学院.
张传定.2000.卫星重力测量-基础、模型化方法与数据处理算法[D].郑州:信息工程大学.
张传定,许厚泽,吴星.2004.地球重力场调和分析中的“轮胎”问题[C].湖北:湖北科学技术出版社,302-314.
张皞,陈琼.2005.卫星重力梯度数据解算位系数的最小二乘配置法[J].测绘与空间地理信息,28(6):34-35.
钟波.2010.基于GOCE卫星重力测量技术确定地球重力场的研究[D].武汉:武汉大学.
Kotsakis C.2007.Least-squares collocation with covariancematching constrains[J].Journal of Geodesy,81(10):661-677.
Li Y C.2004.Theories and method of the recovery of the Earth's gravity field using satellite gravity gradients[D].Zhengzhou:The PLA Information Engineering University.
Liu X G,Wu X P,Wang B J,et al.2010a.Study on gridding methods of satellite gravity gradient data[J].Journal of Geodesy and Geodynamics(in Chinese),30(6):60-65.
Liu X G,Wu X P,Zhao D M,et al.2010b.Non-singular expression of the disturbing gravity gradients[J].Geodaetica et Cartographica Sinica(in Chinese),39(5):450-457.
Liu X G.2011.Theory and methods of the Earth's gravity field model recovery from GOCE dataGn Chinese)[D].Zhengzhou:The PLA Information Engineering University.
Liu X G,Li S S,Wu X.2011.Downward continuation of satellite gravity gradient data[J].Journal of Geodesy and Geodynamics(in Chinese),31(1):132-137.
LiuX G,Zhang L P,Wang J,et al.2012a.Establishment of harmonic analysis models of single component and composite components of disturbed gravity gradient tensor[J],Journal of Geodesy and Geodynamics(in Chinese),32(5):103-108,112.
Liu X G,Wu X P,Wang K.2012b.Construction of the least squares collocation models for single component and composite components of disturbed gravity gradients[J].Chinese J.Geophys.,55(5):1572-1580.
Luo Z C.1996.Theories and method of the determination of the earth's gravity field using satellite gravity gradientsGn Chinese)[D].Wuhan:Wuhan Technical University of Surveying and Mapping.
Luo Z C,Chao D B,Ning J S.1997.Spherical harmonic analysis on gravity gradient tensors[J].Journal of Wuhan Technical University of Surveying and Mapping(in Chinese),22(4):346-349.
Migliaccio F,Reguzzoni M,Sanso F.2004a.Space-wise approach to satellite gravity field determination in the presence of coloured noise[J].Journal of Geodesy(in Chinese),78:304-313.
Migliaccio F,Reguzzoni M,Sanso F,et al.2004b.GOCE:dealing with large attitude variations in the conceptual structure of the space-wise approach[C].//Proc.Second International GOCE User Workshop"GOCE,The Geoid and Oceanography",ESAESRIN,Frascati,Italy.
Tscherning C C.2001.Computation of spherical harmonic coefficients and their error estimates using least-squares collocation[J].Journal of Geodesy(inChinese),75(1):12-18.
Wu X.2009.Research of methods of spherical harmonic analysis of the Earth's gravity field(in Chinese)[D].Zhengzhou:Information Engineering University.
Wu X,Zhang C D,Zhao D M.2009a.Generalized torus harmonic analysis of satellite gravity gradients component[J].Geodaetica et Cartographica Sinica(in Chinese),38(2):101-107.
Wu X,Zhang CD,Zhao DM.2009b.Point-mass harmonic analysis method based on spherical boundary value problem[J].Chinese J.Geophys.(in Chinese),52(12):2993-3000.
Wu X,Zhang C D,Liu X G.2010.Least squares collocation harmonic analysis of the radial satellite gravity gradients[J],Geodaetica et Cartographica Sinica(in Chinese),39(5):471-477,483.
Wu X P.1991.Some analyses of the determination of the Earth's gravity field from the satellite gravity gradient and terrestrial data[J],Journal of the PLA Institute of Surveying and Mapping(in Chinese),(1):19-32.
Xu X Y.2008.Study of determining the Earth's gravity field from satellite gravity gradient and satellite-to-satellite tracking data(in Chinese)[D].Wuhan:Wuhan University.
Zhang C D.2000.Satellite gravimetry:foundation,modeling methods,and data processing algorithms(in Chinese)[D].Zhengzhou:Information Engineering University.
Zhang C D,Xu H Z,Wu X.2004.On the torus approach for gobal spherical harmonic computation[C].Hubei:Hubei Science and Technology Publishing House,302-314.
Zhang H,Chen Q.2005.Least squares collocation in calculating potential coefficient with satellite gravity gradiometry data[J].Geomatics and Spatial Information Technology(in Chinese),28(6):34-35.
Zhong B.2010.Study on the determination of the Earth's gravity field from satellite gravimetry mission GOCE[D].Wuhan:Wuhan University.
李迎春.2004.利用卫星重力梯度测量数据恢复地球重力场的理论与方法(inChinese)[D].郑州:解放军信息工程大学.
刘晓刚,吴晓平,王宝军,等.2010a.卫星重力梯度数据的网格化方法研究[J].大地测量与地球动力学,30(6):60-65.
刘晓刚,吴晓平,赵东明,等.2010b.扰动重力梯度的非奇异表示[J].测绘学报,39(5):450-457.
刘晓刚.2011.GOCE卫星测量恢复地球重力场模型的理论与方法[D].郑州:解放军信息工程大学.
刘晓刚,李珊珊,吴星.2011.卫星重力梯度数据的向下延拓[J].大地测量与地球动力学,31(1):132-137.
刘晓刚,张丽萍,王俊,等.2012a.扰动重力梯度张量单分量和组合分量调和分析法模型的建立[J].大地测量与地球动力学,32(5):103-108,112.
刘晓刚,吴晓平,王凯.2012b.扰动重力梯度张量单分量和组合分量最小二乘配置法模型的建立[J].地球物理学报,55(5):1572-1580.
罗志才.1996.利用卫星重力梯度数据确定地球重力场的理论与方法[D].武汉:武汉测绘科技大学.
罗志才,晁定波,宁津生.1997.重力梯度张量的球谐分析[J].武汉测绘科技大学学报,22(4):346-349.
吴星.2009.卫星重力梯度数据处理理论与方法[D].郑州:信息工程大学.
吴星,张传定,赵东明.2009a.卫星重力梯度分量的广义轮胎调和分析[J].测绘学报,38(2):101-107.
吴星,张传定,赵东明.2009b.基于球面边值问题的点质量调和分析方法[J].地球物理学报,52(12):2993-3000.
吴星,张传定,刘晓刚.2010.卫星重力径向梯度数据的最小二乘配置调和分析[J].测绘学报,39(5):471-477,483.
吴晓平.1991.利用卫星重力梯度与地面数据确定地球重力场的分析[J].解放军测绘学院学报,(1):19-32.
徐新禹.2008.利用卫星重力梯度及卫星跟踪卫星数据确定地球重力场的研究[D].武汉:武汉大学测绘学院.
张传定.2000.卫星重力测量-基础、模型化方法与数据处理算法[D].郑州:信息工程大学.
张传定,许厚泽,吴星.2004.地球重力场调和分析中的“轮胎”问题[C].湖北:湖北科学技术出版社,302-314.
张皞,陈琼.2005.卫星重力梯度数据解算位系数的最小二乘配置法[J].测绘与空间地理信息,28(6):34-35.
钟波.2010.基于GOCE卫星重力测量技术确定地球重力场的研究[D].武汉:武汉大学.