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摘要: 针对海域超大范围外部重力场快速赋值的特殊需求，分析了3种传统扰动引力赋值模型的适用性和局限性，分别提出了直接积分改进模型、点质量改进模型和直接积分与点质量混合模型。利用数值计算验证了3组改进模型的合理性和有效性，为实际工程应用奠定了必要的理论基础。Abstract: In accordance with the special requirement of determining the external gravity field quickly in ultra-large sea area, a detail analysis is made on the applicability and limitations of the three traditional models, i.e. spherical harmonic expansion model, direct integral model and point mass model, for computing disturbing gravity. And then three modified computational models, i.e. modified direct integral model, modified point mass model and mixed model of direct integral and point mass, are proposed one by one. A numerical test has been made to prove the reasonableness and validity of the suggested models. It is shown that the singularity in three traditional models have been eliminated in the solutions of the modified models. They can satisfy the practical needs of determining the local gravity field quickly in ultra-large sea areas and full height. The accuracy of the modified point mass model is estimated to be about ±1mGal in smooth sea areas, and to be less than ±3mGal in rugged sea areas. The obtained conclusions are valuable to the practical engineering projects.
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Keywords:
- external gravity field /
- disturbing gravity /
- model construction /
- ultra-large area
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表 1 地面重力异常统计结果/ (10-5m·s-2)
Table 1 Statistic of Anomalies from EGM2008/(10-5m·s-2)
数据块 最小值 最大值 平均值 均方根 2′×2′ -343.4 559.3 -0.05 37.9 5′×5′ -341.6 495.9 -0.05 37.6 20′×20′ -313.7 279.1 -0.04 34.5 1°×1° -234.8 161.7 -0.04 26.4 
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表 2 海沟区P1计算点比对结果/ (10-5 m·s-2)
Table 2 Comparison of the Calculated Results at Point P1 in Oceanic Trench/(10-5 m·s-2)
高度/km 0 0.02 1 3 5 10 30 50 100 300 模型1 Δδgr 0.02 -0.00 -0.38 -1.01 -1.56 -0.22 -0.17 -0.19 -0.17 -0.06 Δδgφ -0.28 -0.36 -1.41 -3.63 -6.03 -5.73 -4.66 -3.77 -2.16 -0.23 Δδgλ 0.45 0.42 0.33 0.30 0.47 0.46 0.40 0.31 0.09 -0.17 模型2 Δδgr -0.01 -0.02 -0.18 -0.27 -0.35 -0.46 -0.36 -0.18 0.08 0.15 Δδgφ -3.31 -3.30 -3.03 -2.68 -2.44 -2.03 -1.21 -0.81 -0.37 -0.02 Δδgλ 0.29 0.29 0.27 0.18 0.07 -0.15 -0.45 -0.46 -0.38 -0.32 模型3 Δδgr -1.37 -1.33 -0.84 -0.89 -0.94 -1.05 -1.36 -1.53 -1.52 -0.71 Δδgφ -3.98 -3.97 -3.86 -3.77 -3.69 -3.49 -2.83 -2.32 -1.40 -0.15 Δδgλ 1.89 1.89 1.83 1.83 1.82 1.80 1.63 1.36 0.69 -0.10
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表 3 边缘区P2计算点比对结果/ (10-5m·s-2)
Table 3 Comparison of the Calculated Results at Point P2 in Border Area/(10-5m·s-2)
高度/km 0 0.02 1 3 5 10 30 50 100 300 模型1 Δδgr -0.01 0.00 0.09 0.19 0.10 0.09 0.05 0.03 0.02 0.10 Δδgφ -0.20 -0.22 -0.50 -1.30 -2.31 -2.16 -1.70 -1.38 -0.91 -0.43 Δδgλ -0.01 -0.02 -0.05 -0.05 -0.15 -0.14 -0.12 -0.10 -0.04 -0.01 模型2 Δδgr -1.64 -1.61 -0.93 -0.53 -0.42 -0.32 -0.14 -0.09 -0.05 -0.06 Δδgφ -2.53 -2.53 -2.37 -2.15 -2.00 -1.71 -1.07 -0.69 -0.14 0.38 Δδgλ 0.21 0.21 0.18 0.16 0.15 0.13 0.10 0.09 0.06 0.02 模型3 Δδgr -2.47 -2.43 -1.56 -1.24 -1.12 -0.86 -0.30 -0.10 0.01 0.10 Δδgφ -3.67 -3.67 -3.60 -3.41 -3.23 -2.89 -2.13 -1.69 -1.06 -0.44 Δδgλ 0.50 0.50 0.47 0.42 0.38 0.31 0.15 0.08 0.02 -0.00
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[1] Moritz H. The Computation of the External Gravity Field and the Geodetic Boundary-Value Problem[M]//Orlin H. Extension of Gravity Anomalies to Unsurveyed Areas, Geophysical Monograph Series. Washington D C, USA: American Geophysical Union, 1966
[2] Moritz H. Physical Geodesy[M]. Wien, Austia:Springer, 2005
[3] 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 Huang Motao, Zhai Guojun, Guan Zheng, et al. The Determination and Application of Marine Gravity Field[M]. Beijing:Surveying and Mapping Press, 2005
[4] 陆仲连, 吴晓平, 丁行斌, 等.弹道导弹重力学[M].北京:八一出版社, 1993 Lu Zhonglian, Wu Xiaoping, Ding Xingbin, et al. Gravimetry in Ballistic Missile[M]. Beijing:Bayi Press, 1993
[5] 王建强, 李建成, 王正涛, 等.球谐函数变换快速计算扰动引力[J].武汉大学学报·信息科学版, 2013, 38(9):1039-1043 http://ch.whu.edu.cn/CN/abstract/abstract2741.shtml Wang Jianqiang, Li Jiancheng, Wang Zhengtao, et al. Pole Transform of Spherical Harmonic Function to Quickly Calculate the Disturbing Gravity on Earth-Orbiting Satellites[J]. Geomatics and Information Science of Wuhan University, 2013, 38(9):1039-1043 http://ch.whu.edu.cn/CN/abstract/abstract2741.shtml
[6] 吴晓平.在推求地球外部扰动重力场中数据的采用[J].解放军测绘学院学报, 1992(4):1-10 Wu Xiaoping. Application of Data in the Determination of the External Disturbing Gravity Field Outside the Earth[J]. Journal of PLA Institute of Surveying and Mapping, 1992(4):1-10
[7] Bjerhammar A. Discrete Physical Geodesy[R]. The Ohio State University, Ohio, USA, 1987
[8] 吴晓平.局部重力场的点质量模型[J].测绘学报, 1984, 13(4):249-258 http://kns.cnki.net/KCMS/detail/detail.aspx?filename=chxb198404001&dbname=CJFD&dbcode=CJFQ Wu Xiaoping. Point-Mass Model of Local Gravity Field[J]. Acta Geodaetica et Cartographica Sinica, 1984, 13(4):249-258 http://kns.cnki.net/KCMS/detail/detail.aspx?filename=chxb198404001&dbname=CJFD&dbcode=CJFQ
[9] 黄谟涛. 潜地战略导弹弹道扰动引力计算与研究[D]. 郑州: 解放军测绘学院, 1991 Huang Motao. Calculation and Study of Gravity Disturbances in Ballistic Computation for Strategic Submarine Missile[D]. Zhengzhou: Institute of Surveying and Mapping, 1991
[10] 黄金水, 朱灼文.外部扰动重力场的频谱响应质点模型[J].地球物理学报, 1995, 38(2):182-188 http://kns.cnki.net/KCMS/detail/detail.aspx?filename=dqwx502.005&dbname=CJFD&dbcode=CJFQ Huang Jinshui, Zhu Zhuowen. Frequency Response Point Masses Model of Exterior Disturbing Gravity Field[J]. Acta Geophysica Sinica, 1995, 38(2):182-188 http://kns.cnki.net/KCMS/detail/detail.aspx?filename=dqwx502.005&dbname=CJFD&dbcode=CJFQ
[11] 赵东明, 吴晓平.扰动引力快速确定的替代算法[J].解放军测绘学院学报, 2001, 18(B09):11-13 http://www.cqvip.com/QK/98086B/2001B09/5677567.html Zhao Dongming, Wu Xiaoping. A Substitute Method for Fast Determination of Disturbing Gravity[J]. Journal of PLA Institute of Surveying and Mapping, 2001, 18(B09):11-13 http://www.cqvip.com/QK/98086B/2001B09/5677567.html
[12] 张嗥. 快速逼近弹道扰动引力的算法研究[D]. 郑州: 信息工程大学, 2007 http://cdmd.cnki.com.cn/article/cdmd-90008-2008044481.htm Zhang Hao. A Study on Fast Computation of Trajectory Disturbing Gravity[D]. Zhengzhou: Information Engineering University, 2007 http://cdmd.cnki.com.cn/article/cdmd-90008-2008044481.htm
[13] 郑伟, 钱山, 汤国建.弹道导弹制导计算中扰动引力的快速赋值[J].飞行力学, 2007, 25(3):42-44 http://d.old.wanfangdata.com.cn/Periodical/fxlx200703011 Zheng Wei, Qian Shan, Tang Guojian. Fast Computation of Disturbing Gravity in Ballistic Missile Guidance[J]. Flying Mechanic, 2007, 25(3):42-44 http://d.old.wanfangdata.com.cn/Periodical/fxlx200703011
[14] 江东, 王庆宾, 赵东明.空中扰动引力快速赋值算法的效能分析[J].测绘科学技术学报, 2011, 28(6):411-415 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=chxyxb201106006 Jiang Dong, Wang Qingbin, Zhao Dongming. Analysis on Efficiency of the Methods for Fast Computing Disturbing Gravity[J]. Journal of Geomatics Science and Technology, 2011, 28(6):411-415 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=chxyxb201106006
[15] 陈国强.异常重力场中飞行器动力学[M].长沙:国防科技大学出版社, 1982 Chen Guoqiang. Spacecraft Dynamics in Gravity Anomaly Field[M]. Changsha:National University of Defense Technology Press, 1982
[16] 贾沛然, 陈克俊, 何力.远程火箭弹道学[M].长沙:国防科技大学出版社, 1993 Jia Peiran, Chen Kejun, He Li. Long Range Rocket Ballistics[M]. Changsha:National University of Defense Technology Press, 1993
[17] 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 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
[18] 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 http://ch.whu.edu.cn/CN/abstract/abstract3180.shtml Huang Motao, Ouyang Yongzhong, Liu Min, et al. Regulation of Point Mass Model for Multi-Source Gravity Data Fusion Processing[J]. Geomatics and Information Science of Wuhan University, 2015, 40(2):170-175 http://ch.whu.edu.cn/CN/abstract/abstract3180.shtml
[19] 黄谟涛, 管铮.扰动点质量模型构制与检验[J].武汉测绘科技大学学报, 1994, 19(4):304-309 Huang Motao, Guan Zheng. Test and Construction of Disturbing Point Mass Model[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1994, 19(4):304-309
[20] 黄谟涛, 管铮, 欧阳永忠.中国地区1°×1°点质量解算与精度分析[J].武汉测绘科技大学学报, 1995, 20(3):257-262 http://kns.cnki.net/KCMS/detail/detail.aspx?filename=whch503.014&dbname=CJFD&dbcode=CJFQ Huang Motao, Guan Zheng, Ouyang Yongzhong. Accuracy Analysis and Calculation of 1°×1°point Masses in the Area of China[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1995, 20(3):257-262 http://kns.cnki.net/KCMS/detail/detail.aspx?filename=whch503.014&dbname=CJFD&dbcode=CJFQ
[21] 黄谟涛.扰动质点赋值模式结构优化及序贯解法[J].测绘学报, 1994, 23(2):81-89 http://www.cqvip.com/QK/90069X/199402/1299349.html Huang Motao. Configuration Optimization of the Disturbing Point Masses Model and Its Sequential Solution[J]. Acta Geodaetica et Cartographica Sinica, 1994, 23(2):81-89 http://www.cqvip.com/QK/90069X/199402/1299349.html
[22] 冯康.数值计算方法[M].北京:国防工业出版社, 1978 Feng Kang. Method of Numerical Computation[M]. Beijing:National Defence Industry Press, 1978
[23] Zhang Chuanding, Lu Zhonglian, Wu Xiaoping. Truncation Error Formulae for the Disturbing Gravity Vector[J]. Journal of Geodesy, 1998, 72(3):119-123 doi: 10.1007/s001900050153
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