海洋重力场特征统计模型计算与分析
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摘要
海洋重力场特征参数在地球重力场逼近计算和海上测量优化设计中具有重要的应用价值。基于卫星测高重力在海域具有覆盖范围广且分布均匀的独特优势,提出了利用最新卫星测高重力数据集开展海洋重力场特征统计模型计算和分析的研究方案,给出了代表误差和协方差函数模型参数的计算公式,定义并研究了海洋广义布格重力异常的变化特征,提出了等精度和非等精度拟合经验协方差函数的计算模型。利用中国近海及西太平洋海区超过50万个5′×5′方块的1′×1′网格卫星测高重力异常数据,首次计算得到一组有代表性的中国周边海域重力场特征统计模型参数,较好地揭示了海洋重力场有别于陆地重力场的变化特征,利用海面船测重力数据对计算结果进行了可靠性检核,提出了相应的模型参数修正方案和使用建议。
Statistical model parameters of marine gravity field character are valuable to the approximation of the earth's gravitational field and the optimum programming of marine gravity surveying. In view of the distinction of satellite altimetry data with large coverage and even distribution, a study strategy is proposed to develop the analysis and calculation of the statistical models of marine gravity field character using the latest satellite altimetry data. The computation formulas of commission error and covariance function model parameters of gravity anomalies are given in detail. A generalized Bouguer anomaly is defined, and the change character of which is researched. Equal and unequal weight models are suggested to fit the experienced covariance function. A set of statistical model parameter of gravity field character for the sea area around China is calculated using 1′×1′grid of satellite altimetry data from more than 500 thousands of 5′×5′cell, and which show different change characteristics of marine gravity field from that of land area. The reliability of the calculated model parameters is validated using ship-borne gravity anomalies. Some corrections are presented to add to the above parameters, and a final set of statistical model parameter of marine gravity field character is obtained. A suggestion is given for use of the new model parameters.
Statistical model parameters of marine gravity field character are valuable to the approximation of the earth's gravitational field and the optimum programming of marine gravity surveying. In view of the distinction of satellite altimetry data with large coverage and even distribution, a study strategy is proposed to develop the analysis and calculation of the statistical models of marine gravity field character using the latest satellite altimetry data. The computation formulas of commission error and covariance function model parameters of gravity anomalies are given in detail. A generalized Bouguer anomaly is defined, and the change character of which is researched. Equal and unequal weight models are suggested to fit the experienced covariance function. A set of statistical model parameter of gravity field character for the sea area around China is calculated using 1′×1′grid of satellite altimetry data from more than 500 thousands of 5′×5′cell, and which show different change characteristics of marine gravity field from that of land area. The reliability of the calculated model parameters is validated using ship-borne gravity anomalies. Some corrections are presented to add to the above parameters, and a final set of statistical model parameter of marine gravity field character is obtained. A suggestion is given for use of the new model parameters.
引文
[1] Guan Zelin, Ning Jinsheng. Shape of the Earth and Its External Gravity Field[M].Beijing: Surveying and Mapping Press,1981(管泽霖,宁津生. 地球形状及外部重力场[M].北京:测绘出版社,1981)
[2] Lu Zhonglian. Theory and Method of the Earth’s Gravity Field[M].Beijing: PLA Publishing House,1996(陆仲连. 地球重力场理论与方法[M].北京:解放军出版社,1996)
[3] Li Jiancheng, Chen Junyong, Ning Jinsheng, et al. Theory of the Earth’s Gravity Field Approximation and Determination of China Quasi-Geoid 2000[M]. Wuhan: Wuhan University Press, 2003(李建成,陈俊勇,宁津生,等. 地球重力场逼近理论与中国2000似大地水准面的确定[M]. 武汉:武汉大学出版社,2003)
[4] Shi Pan, Wang Mengzhao, Wang Ruirong. Design of the Surveying Line for Marine Gravimetry [J]. Military Surveying and Mapping, 1980(4): 15-22(石磐,王孟昭,王瑞榕. 海洋重力测量的测线布设[J]. 军事测绘,1980(4): 15-22)
[5] Chen Yue. Discussion on the Space of Surveying Line for Marine Gravimetry[J]. Hydrographic Surveying and Charting, 1983,3(1):9-13(陈跃. 海洋重力测线布设间距的讨论[J]. 海洋测绘,1983,3(1):9-13)
[6] Huang Motao. On the Design of Surveying Line for Marine Gravimetry[J]. Hydrographic Surveying and Charting, 1988,8(4):31-35(黄谟涛. 论海洋重力测线布设[J]. 海洋测绘,1988,8(4):31-35)
[7] Heiskanen W A, Moritz H. Physical Geodesy [M]. San Francisco: Freeman W H and Company, 1967
[8] Moritz H. Advanced Physical Geodesy[M]. England: Abacus Press, 1980
[9] Tscherning C C,Rubek F,Forsberg R. Combining Airborne and Ground Gravity Using Collocation[C]. International Association of Geodesy Symposia,Rio de Janeiro, Brazil, 1998
[10] Zou Xiancai, Li Jiancheng. Determination of Local Geoid Using Least-Squares Collocation[J].Geomatics and Information Science of Wuhan University, 2004, 29(3): 218-222(邹贤才,李建成. 最小二乘配置方法确定局部大地水准面的研究[J].武汉大学学报·信息科学版,2004,29(3): 218-222)
[11] Zhang Chuanyin, Ding Jian, Chao Dingbo. General Expression of Least Squares Collocation in Local Gravity Filed[J]. Geomatics and Information Science of Wuhan University, 2007, 32(5):431-434(章传银,丁剑,晁定波. 局部重力场最小二乘配置通用表示技术[J]. 武汉大学学报·信息科学版,2007, 32(5): 431-434)
[12] Ouyang Yongzhong, Deng Kailiang, Huang Motao, et al. The Tikhonov-Least Squares Collocation Method for Determining Geoid[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(6): 804-810(欧阳永忠,邓凯亮,黄谟涛,等. 确定大地水准面的Tikhonov最小二乘配置法[J].测绘学报,2012,41(6):804-810)
[13] Huang Motao, Ouyang Yongzhong, Zhai Guojun, et al. Tikhonov Regularization Collocation for Multi-source Gravity Data Fusion Processing[J]. Hydrographic Surveying and Charting, 2013,33(3):6-12(黄谟涛,欧阳永忠,翟国君,等. 融合多源重力数据的Tikhonov正则化配置法[J]. 海洋测绘,2013,33(3):6-12)
[14] Hirvonen R A. On the Statistical Analysis of Gravity Anomalies[R]. Publication Isostatic Institute of IAG, Helsinki, Finland, 1962
[15] Tscherning C C,Rapp R H. Closed Covariance Expressions for Gravity Anomalies, Geoid Undulations, and Deflections of the Vertical Implied by Anomaly Degree Variance Models [R]. Dep of Geod Sci, Ohio State Univ, Ohio, USA, 1974
[16] Shi Pan, Wang Mengzhao, Wang Ruirong. Statistical Analysis of the Marine Gravity Anomalies[J]. Military Surveying and Mapping, 1980(4): 23-29(石磐,王孟昭,王瑞榕. 海洋重力异常的统计分析[J]. 军事测绘,1980(4): 23-29)
[17] Ding Xingbin. Several Experienced Formulas for Calculating the Commission Error of Free Air Anomalies[J]. Military Surveying and Mapping, 1980(4): 30-37(丁行斌.估算空间重力异常代表误差的几种经验公式[J]. 军事测绘,1980(4): 30-37)
[18] Ding Xingbin. Calculation of the Commission Error of Free Air Anomalies[J]. Military Surveying and Mapping, 1981(6): 22-25(丁行斌.重力异常代表误差及其计算[J]. 军事测绘,1981(6): 22-25)
[19] Xia Zheren, Lin Li. Approximations of Local Covariance Functions of Gravity Anomaly[J]. Acta Geodaetica et Cartographica Sinica, 1995,24(1):23-27(夏哲仁,林丽. 局部重力异常协方差函数的逼近[J]. 测绘学报,1995,24(1):23-27)
[20] Li Shanshan, Wu Xiaoping, Zhang Chuanding, et al. Calculation and Analysis of the New Statistical Character Parameters of Gravity Field in China[J]. Chinese Journal of Geophysics, 2010, 53(5):1 099-1 108(李姗姗,吴晓平,张传定,等. 我国重力场新的统计特征参数的计算分析[J]. 地球物理学报,2010,53(5):1 099-1 108)
[21] Huang Motao, Zhai Guojun, Guan Zheng, et al. The Determination and Application of Marine Gravity Field[M]. Beijing: Surveying and Mapping Press, 2005(黄谟涛,翟国君,管铮,等. 海洋重力场测定及其应用[M]. 北京:测绘出版社,2005)
[22] Zhai Zhenhe. Researches on Theories and Algorithms of Data Processing and Application in Alti-metry Satellite [D]. Zhengzhou: Information Engineering University, 2015(翟振和. 海洋测高卫星数据处理理论及应用方法研究[D].郑州:信息工程大学,2015)
[23] Andersen O B, Knudsen P. The DNSC08GRA Global Marine Gravity Field from Double Retracked Satellite Altimetry [J]. J Geod,2010,84:191-199
[24] Huang Motao, Liu Min, Sun Lan, et al. Compensation and Analysis of Dynamic Environment Effect on Marine Gravimetry[J]. Hydrographic Surve-ying and Charting, 2015,35(1):1-6(黄谟涛,刘敏,孙岚,等. 海洋重力测量动态环境效应分析与补偿[J]. 海洋测绘,2015,35(1):1-6)
[25] Huang Weibin. Theory and Application of Modern Adjustment[M]. Beijing: PLA Publishing House,1992(黄维彬. 近代平差理论及其应用[M].北京:解放军出版社,1992)
[26] The Headquarters of General Equipment. Specification for Marine Gravity Survey: GJB 890A-2008[S]. Beijing: Military Standard Press of the Headquarters of General Equipment, 2008(总装备部. 海洋重力测量规范: GJB 890A-2008[S].北京:总装备部军标出版发行部,2008)
[27] Amante C, Eakins B W. ETOPO1 1 Arcminute Global Relief Model: Procedures, Data Sources and Analysis[R]. NOAA Technical Memorandum NESDIS NGDC-24, National Centers for Environmental Information, USA, 2009
[28] Guan Zheng. Discussion on the Bouguer Gravity Anomaly[J]. Hydrographic Surveying and Charting, 1987,7(4):14-18(管铮. 关于布格重力异常的讨论[J]. 海洋测绘,1987,7(4):14-18)
[2] Lu Zhonglian. Theory and Method of the Earth’s Gravity Field[M].Beijing: PLA Publishing House,1996(陆仲连. 地球重力场理论与方法[M].北京:解放军出版社,1996)
[3] Li Jiancheng, Chen Junyong, Ning Jinsheng, et al. Theory of the Earth’s Gravity Field Approximation and Determination of China Quasi-Geoid 2000[M]. Wuhan: Wuhan University Press, 2003(李建成,陈俊勇,宁津生,等. 地球重力场逼近理论与中国2000似大地水准面的确定[M]. 武汉:武汉大学出版社,2003)
[4] Shi Pan, Wang Mengzhao, Wang Ruirong. Design of the Surveying Line for Marine Gravimetry [J]. Military Surveying and Mapping, 1980(4): 15-22(石磐,王孟昭,王瑞榕. 海洋重力测量的测线布设[J]. 军事测绘,1980(4): 15-22)
[5] Chen Yue. Discussion on the Space of Surveying Line for Marine Gravimetry[J]. Hydrographic Surveying and Charting, 1983,3(1):9-13(陈跃. 海洋重力测线布设间距的讨论[J]. 海洋测绘,1983,3(1):9-13)
[6] Huang Motao. On the Design of Surveying Line for Marine Gravimetry[J]. Hydrographic Surveying and Charting, 1988,8(4):31-35(黄谟涛. 论海洋重力测线布设[J]. 海洋测绘,1988,8(4):31-35)
[7] Heiskanen W A, Moritz H. Physical Geodesy [M]. San Francisco: Freeman W H and Company, 1967
[8] Moritz H. Advanced Physical Geodesy[M]. England: Abacus Press, 1980
[9] Tscherning C C,Rubek F,Forsberg R. Combining Airborne and Ground Gravity Using Collocation[C]. International Association of Geodesy Symposia,Rio de Janeiro, Brazil, 1998
[10] Zou Xiancai, Li Jiancheng. Determination of Local Geoid Using Least-Squares Collocation[J].Geomatics and Information Science of Wuhan University, 2004, 29(3): 218-222(邹贤才,李建成. 最小二乘配置方法确定局部大地水准面的研究[J].武汉大学学报·信息科学版,2004,29(3): 218-222)
[11] Zhang Chuanyin, Ding Jian, Chao Dingbo. General Expression of Least Squares Collocation in Local Gravity Filed[J]. Geomatics and Information Science of Wuhan University, 2007, 32(5):431-434(章传银,丁剑,晁定波. 局部重力场最小二乘配置通用表示技术[J]. 武汉大学学报·信息科学版,2007, 32(5): 431-434)
[12] Ouyang Yongzhong, Deng Kailiang, Huang Motao, et al. The Tikhonov-Least Squares Collocation Method for Determining Geoid[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(6): 804-810(欧阳永忠,邓凯亮,黄谟涛,等. 确定大地水准面的Tikhonov最小二乘配置法[J].测绘学报,2012,41(6):804-810)
[13] Huang Motao, Ouyang Yongzhong, Zhai Guojun, et al. Tikhonov Regularization Collocation for Multi-source Gravity Data Fusion Processing[J]. Hydrographic Surveying and Charting, 2013,33(3):6-12(黄谟涛,欧阳永忠,翟国君,等. 融合多源重力数据的Tikhonov正则化配置法[J]. 海洋测绘,2013,33(3):6-12)
[14] Hirvonen R A. On the Statistical Analysis of Gravity Anomalies[R]. Publication Isostatic Institute of IAG, Helsinki, Finland, 1962
[15] Tscherning C C,Rapp R H. Closed Covariance Expressions for Gravity Anomalies, Geoid Undulations, and Deflections of the Vertical Implied by Anomaly Degree Variance Models [R]. Dep of Geod Sci, Ohio State Univ, Ohio, USA, 1974
[16] Shi Pan, Wang Mengzhao, Wang Ruirong. Statistical Analysis of the Marine Gravity Anomalies[J]. Military Surveying and Mapping, 1980(4): 23-29(石磐,王孟昭,王瑞榕. 海洋重力异常的统计分析[J]. 军事测绘,1980(4): 23-29)
[17] Ding Xingbin. Several Experienced Formulas for Calculating the Commission Error of Free Air Anomalies[J]. Military Surveying and Mapping, 1980(4): 30-37(丁行斌.估算空间重力异常代表误差的几种经验公式[J]. 军事测绘,1980(4): 30-37)
[18] Ding Xingbin. Calculation of the Commission Error of Free Air Anomalies[J]. Military Surveying and Mapping, 1981(6): 22-25(丁行斌.重力异常代表误差及其计算[J]. 军事测绘,1981(6): 22-25)
[19] Xia Zheren, Lin Li. Approximations of Local Covariance Functions of Gravity Anomaly[J]. Acta Geodaetica et Cartographica Sinica, 1995,24(1):23-27(夏哲仁,林丽. 局部重力异常协方差函数的逼近[J]. 测绘学报,1995,24(1):23-27)
[20] Li Shanshan, Wu Xiaoping, Zhang Chuanding, et al. Calculation and Analysis of the New Statistical Character Parameters of Gravity Field in China[J]. Chinese Journal of Geophysics, 2010, 53(5):1 099-1 108(李姗姗,吴晓平,张传定,等. 我国重力场新的统计特征参数的计算分析[J]. 地球物理学报,2010,53(5):1 099-1 108)
[21] Huang Motao, Zhai Guojun, Guan Zheng, et al. The Determination and Application of Marine Gravity Field[M]. Beijing: Surveying and Mapping Press, 2005(黄谟涛,翟国君,管铮,等. 海洋重力场测定及其应用[M]. 北京:测绘出版社,2005)
[22] Zhai Zhenhe. Researches on Theories and Algorithms of Data Processing and Application in Alti-metry Satellite [D]. Zhengzhou: Information Engineering University, 2015(翟振和. 海洋测高卫星数据处理理论及应用方法研究[D].郑州:信息工程大学,2015)
[23] Andersen O B, Knudsen P. The DNSC08GRA Global Marine Gravity Field from Double Retracked Satellite Altimetry [J]. J Geod,2010,84:191-199
[24] Huang Motao, Liu Min, Sun Lan, et al. Compensation and Analysis of Dynamic Environment Effect on Marine Gravimetry[J]. Hydrographic Surve-ying and Charting, 2015,35(1):1-6(黄谟涛,刘敏,孙岚,等. 海洋重力测量动态环境效应分析与补偿[J]. 海洋测绘,2015,35(1):1-6)
[25] Huang Weibin. Theory and Application of Modern Adjustment[M]. Beijing: PLA Publishing House,1992(黄维彬. 近代平差理论及其应用[M].北京:解放军出版社,1992)
[26] The Headquarters of General Equipment. Specification for Marine Gravity Survey: GJB 890A-2008[S]. Beijing: Military Standard Press of the Headquarters of General Equipment, 2008(总装备部. 海洋重力测量规范: GJB 890A-2008[S].北京:总装备部军标出版发行部,2008)
[27] Amante C, Eakins B W. ETOPO1 1 Arcminute Global Relief Model: Procedures, Data Sources and Analysis[R]. NOAA Technical Memorandum NESDIS NGDC-24, National Centers for Environmental Information, USA, 2009
[28] Guan Zheng. Discussion on the Bouguer Gravity Anomaly[J]. Hydrographic Surveying and Charting, 1987,7(4):14-18(管铮. 关于布格重力异常的讨论[J]. 海洋测绘,1987,7(4):14-18)
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