扰动重力梯度的球冠谐分析建模
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摘要
从球冠谐理论出发,详细推导了球冠坐标系下扰动重力梯度的无奇异性计算公式。基于Tikhonov正则化方法,利用GOCE卫星实际观测数据解算局部重力场球冠谐模型。数值计算表明,基于扰动重力梯度的球冠谐分析建模方法能够有效地恢复局部重力场中的短波信号,与GO_CONS_GCF_2_DIR_R5模型的差异在±0.3×10~(-5) m/s~2水平。
It is deduced that the non-singular computational formulae of the disturbing gravity gradients based on spherical cap harmonic analysis theory.On the basis of the Tikhonov regularization method,the spherical cap harmonic model of local gravity field is calculated using GOCE satellite real surveyingdata.Itisshownthatthe short wavelength information of local gravity field can be recovered from the disturbing gravity gradient data using spherical cap harmonic analysis method,and the difference with the GO_CONS_GCF_2_DIR_R5 model is at ±0.3×10~(-5)m/s~2.
It is deduced that the non-singular computational formulae of the disturbing gravity gradients based on spherical cap harmonic analysis theory.On the basis of the Tikhonov regularization method,the spherical cap harmonic model of local gravity field is calculated using GOCE satellite real surveyingdata.Itisshownthatthe short wavelength information of local gravity field can be recovered from the disturbing gravity gradient data using spherical cap harmonic analysis method,and the difference with the GO_CONS_GCF_2_DIR_R5 model is at ±0.3×10~(-5)m/s~2.
引文
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[5]张传定,吴晓平,陆仲连.全张量重力梯度数据的谱表示方法[J].测绘学报,2000,29(4):297-304.ZHANG Chuanding,WU Xiaoping,LU Zhonglian.Spectral Representation of the Full Gravity Tensor[J].Acta Geodaetica et Cartographica Sinica,2000,29(4):297-304.
[6]王燚,姜效典,李德勇.多源重力数据球冠谐模型抗差融合法[J].测绘学报,2015,44(9):952-957.DOI:10.11947/j.AGCS.2015.20140345.WANG Yi,JIANG Xiaodian,LI Deyong.The Robust Fusion of Multi-source Gravity Data Based on the Spherical Cap Harmonic Model[J].Acta Geodaetica et Cartographica Sinica,2015,44(9):952-957.DOI:10.11947/j.AGCS.2015.20140345.
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[10]王燚,姜效典.地球重力场球冠谐模型的分层构造和分析[J].大地测量与地球动力学,2014,34(5):30-34,39.WANG Yi,JIANG Xiaodian.Structure and Analysis of Multilayered Spherical Cap Harmonic Model[J].Journal of Geodesy and Geodynamics,2014,34(5):30-34,39.
[11]吴招才,刘天佑,高金耀.局部重力场球冠谐分析中的导数计算及应用[J].海洋与湖沼,2006,37(6):488-492.WU Zhaocai,LIU Tianyou,GAO Jinyao.Derivative Calculation and Application in Spherical Cap Harmonic Analysis of Local Gravity Field[J].Oceanologia et Limnologia Sinica,2006,37(6):488-492.
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[13]曹月玲,王解先.利用球冠谐分析拟合GPS水准高程[J].武汉大学学报(信息科学版),2008,33(7):740-743.CAO Yueling,WANG Jiexian.Application of Spherical Cap Harmonic Analysis to Fit GPS Level Height[J].Geomatics and Information Science of Wuhan University,2008,33(7):740-743.
[14]彭富清,于锦海.球冠谐分析中非整阶Legendre函数的性质及其计算[J].测绘学报,2000,29(3):204-208.PENG Fuqing,YU Jinhai.The Characters and Computation of Legendre Function with Non-integral Degree in SCHA[J].Acta Geodaetica et Cartographica Sinica,2000,29(3):204-208.
[15]HWANG C,CHEN S K.Fully Normalized Spherical Cap Harmonics:Application to the Analysis of Sea-level Data from TOPEX/Poseidon and ERS-1[J].Geophysical Journal International,1997,129(2):450-460.
[16]刘晓刚.GOCE卫星测量恢复地球重力场模型的理论与方法[D].郑州:信息工程大学,2011.LIU Xiaogang.Theory and Methods of the Earth’s Gravity Field Model Recovery from GOCE Data[D].Zhengzhou:Information Engineering University,2011.
[17]HOBSON E W.The Theory of Spherical and Ellipsoidal Harmonics[M].Cambridge:Cambridge University Press,1931.
[18]王竹溪,郭敦仁.特殊函数概论[M].北京:北京大学出版社,1989.WANG Zhuxi,GUO Dunren.Introduction to Special Function[M].Beijing:Peking University Press,1989.
[19]刘晓刚,吴晓平,赵东明,等.扰动重力梯度的非奇异表示[J].测绘学报,2010,39(5):450-457.LIU Xiaogang,WU Xiaoping,ZHAO Dongming,et al.Nonsingular Expression of the Disturbing Gravity Gradients[J].Acta Geodaetica et Cartographica Sinica,2010,39(5):450-457.
[20]赵建虎,王胜平,刘辉,等.海洋局域地磁场球冠谐分析建模方法研究[J].测绘科学,2010,35(1):50-52,9.ZHAO Jianhu,WANG Shengping,LIU Hui,et al.Study on Establishing Local Geomagnetic Model Using Spherical Cap Harmonic Analysis[J].Science of Surveying and Mapping,2010,35(1):50-52,9.
[21]罗志才,钟波,宁津生,等.卫星重力梯度测量确定地球重力场的理论与方法[M].武汉:武汉大学出版社,2015.LUO Zhicai,ZHONG Bo,NING Jinsheng,et al.Theory and Method for Determining the Earth’s Gravity Field from Satellite Gravity Gradiometry[M].Wuhan:Wuhan University Press,2015.
[22]韦博成,鲁国斌,史建清.统计诊断引论[M].南京:东南大学出版社,1991.WEI Bocheng,LU Guobin,SHI Jianqing.Introduction to Statistical Diagnostics[M].Nanjing:Publishing House of Dongnan University,1991.
[23]黄谟涛,欧阳永忠,刘敏,等.融合海域多源重力数据的正则化点质量方法[J].武汉大学学报(信息科学版),2015,40(2):170-175.HUANG Motao,OUYANG Yongzhong,LIU Min,et al.Regularization of Point-mass Model for Multi-source Gravity Data Fusion Processing[J].Geomatics and Information Science of Wuhan University,2015,40(2):170-175.
[24]HANSEN P C.Analysis of Discrete Ill-posed Problems by Means of the L-curve[J].SIAM Review,1992,34(4):561-580.
[2]孟嘉春,蔡喜楣.卫星重力梯度测量及其应用前景探讨[J].地球物理学报,1991,34(3):369-376.MENG Jiachun,CAI Ximei.Approach on Satellite Gravity Gradiometry and Its Vistas of Applications[J].Acta Geophysica Sinica,1991,34(3):369-376.
[3]吴星,张传定,赵东明.卫星重力梯度分量的广义轮胎调和分析[J].测绘学报,2009,38(2):101-107.WU Xing,ZHANG Chuanding,ZHAO Dongming.Generalized Torus Harmonic Analysis of Satellite Gravity Gradients Component[J].Acta Geodaetica et Cartographica Sinica,2009,38(2):101-107.
[4]REED G B.Application of Kinem atical Geodesy for Determining the Short Wave Length Components of the Gravity Field by Satellite Gradiometry[R].Columbus:Ohio State University,1973.
[5]张传定,吴晓平,陆仲连.全张量重力梯度数据的谱表示方法[J].测绘学报,2000,29(4):297-304.ZHANG Chuanding,WU Xiaoping,LU Zhonglian.Spectral Representation of the Full Gravity Tensor[J].Acta Geodaetica et Cartographica Sinica,2000,29(4):297-304.
[6]王燚,姜效典,李德勇.多源重力数据球冠谐模型抗差融合法[J].测绘学报,2015,44(9):952-957.DOI:10.11947/j.AGCS.2015.20140345.WANG Yi,JIANG Xiaodian,LI Deyong.The Robust Fusion of Multi-source Gravity Data Based on the Spherical Cap Harmonic Model[J].Acta Geodaetica et Cartographica Sinica,2015,44(9):952-957.DOI:10.11947/j.AGCS.2015.20140345.
[7]HAINES G V.Spherical Cap Harmonic Analysis[J].Journal of Geophysical Research:Solid Earth,1985,90(B3):2583-2591.
[8]申宁华,王光杰,王喜臣.球冠谐和分析算法及其在中国大陆航磁异常分析中的应用[J].物探化探计算技术,1998,20(1):9-18.SHEN Ninghua,WANG Guangjie,WANG Xichen.Spherical Cap Harmonic Analysis and Its Application to the Analysis of the Aeromagnetic Anomalies in China[J].Computing Techniques for Geophysical and Geochemical Exploration,1998,20(1):9-18.
[9]LI Jiancheng,CHAO Dingbo,NING Jinsheng.Spherical Cap Harmonic Expansion for Local Gravity Field Representation[J].Manuscripta Geodaetica,1995,20(2):265-277.
[10]王燚,姜效典.地球重力场球冠谐模型的分层构造和分析[J].大地测量与地球动力学,2014,34(5):30-34,39.WANG Yi,JIANG Xiaodian.Structure and Analysis of Multilayered Spherical Cap Harmonic Model[J].Journal of Geodesy and Geodynamics,2014,34(5):30-34,39.
[11]吴招才,刘天佑,高金耀.局部重力场球冠谐分析中的导数计算及应用[J].海洋与湖沼,2006,37(6):488-492.WU Zhaocai,LIU Tianyou,GAO Jinyao.Derivative Calculation and Application in Spherical Cap Harmonic Analysis of Local Gravity Field[J].Oceanologia et Limnologia Sinica,2006,37(6):488-492.
[12]BRUINSMA S L,FRSTE C,ABRIKOSOV O,et al.The New ESA Satellite-only Gravity Field Model via the Direct Approach[J].Geophysical Research Letters,2013,40(14):3607-3612.
[13]曹月玲,王解先.利用球冠谐分析拟合GPS水准高程[J].武汉大学学报(信息科学版),2008,33(7):740-743.CAO Yueling,WANG Jiexian.Application of Spherical Cap Harmonic Analysis to Fit GPS Level Height[J].Geomatics and Information Science of Wuhan University,2008,33(7):740-743.
[14]彭富清,于锦海.球冠谐分析中非整阶Legendre函数的性质及其计算[J].测绘学报,2000,29(3):204-208.PENG Fuqing,YU Jinhai.The Characters and Computation of Legendre Function with Non-integral Degree in SCHA[J].Acta Geodaetica et Cartographica Sinica,2000,29(3):204-208.
[15]HWANG C,CHEN S K.Fully Normalized Spherical Cap Harmonics:Application to the Analysis of Sea-level Data from TOPEX/Poseidon and ERS-1[J].Geophysical Journal International,1997,129(2):450-460.
[16]刘晓刚.GOCE卫星测量恢复地球重力场模型的理论与方法[D].郑州:信息工程大学,2011.LIU Xiaogang.Theory and Methods of the Earth’s Gravity Field Model Recovery from GOCE Data[D].Zhengzhou:Information Engineering University,2011.
[17]HOBSON E W.The Theory of Spherical and Ellipsoidal Harmonics[M].Cambridge:Cambridge University Press,1931.
[18]王竹溪,郭敦仁.特殊函数概论[M].北京:北京大学出版社,1989.WANG Zhuxi,GUO Dunren.Introduction to Special Function[M].Beijing:Peking University Press,1989.
[19]刘晓刚,吴晓平,赵东明,等.扰动重力梯度的非奇异表示[J].测绘学报,2010,39(5):450-457.LIU Xiaogang,WU Xiaoping,ZHAO Dongming,et al.Nonsingular Expression of the Disturbing Gravity Gradients[J].Acta Geodaetica et Cartographica Sinica,2010,39(5):450-457.
[20]赵建虎,王胜平,刘辉,等.海洋局域地磁场球冠谐分析建模方法研究[J].测绘科学,2010,35(1):50-52,9.ZHAO Jianhu,WANG Shengping,LIU Hui,et al.Study on Establishing Local Geomagnetic Model Using Spherical Cap Harmonic Analysis[J].Science of Surveying and Mapping,2010,35(1):50-52,9.
[21]罗志才,钟波,宁津生,等.卫星重力梯度测量确定地球重力场的理论与方法[M].武汉:武汉大学出版社,2015.LUO Zhicai,ZHONG Bo,NING Jinsheng,et al.Theory and Method for Determining the Earth’s Gravity Field from Satellite Gravity Gradiometry[M].Wuhan:Wuhan University Press,2015.
[22]韦博成,鲁国斌,史建清.统计诊断引论[M].南京:东南大学出版社,1991.WEI Bocheng,LU Guobin,SHI Jianqing.Introduction to Statistical Diagnostics[M].Nanjing:Publishing House of Dongnan University,1991.
[23]黄谟涛,欧阳永忠,刘敏,等.融合海域多源重力数据的正则化点质量方法[J].武汉大学学报(信息科学版),2015,40(2):170-175.HUANG Motao,OUYANG Yongzhong,LIU Min,et al.Regularization of Point-mass Model for Multi-source Gravity Data Fusion Processing[J].Geomatics and Information Science of Wuhan University,2015,40(2):170-175.
[24]HANSEN P C.Analysis of Discrete Ill-posed Problems by Means of the L-curve[J].SIAM Review,1992,34(4):561-580.
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