海域流动点外部扰动引力无奇异计算模型
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摘要
针对海域重力场变化特征和远程飞行器机动发射保障应用需求,本文分析研究了地球外部空间扰动引力三类传统计算模型的技术特点及其适用性,指出了采用表层法作为海域流动点扰动引力计算模型的合理性及需要解决的关键问题,分析论证了空中扰动引力计算对地面观测数据的分辨率和精度要求,提出通过引入局部积分域恒等式变换、局域泰勒级数展开和非网格点内插方法,消除表层法计算模型积分奇异性固有缺陷的研究思路,进而推出了适合于海域流动点应用的扰动引力无奇异计算模型,较好地满足了全海域和全高度段对局部扰动重力场快速赋值的实际需求.以超高阶全球位模型EGM2008作为标准场,通过数值计算验证了无奇异计算模型的可行性和有效性,在重力场变化比较剧烈的海沟区,该模型的计算精度优于2×10~(-5)m·s~(-2).
In accordance with the variation characteristics of the marine gravity field and the special support requirement of launching a long range spacecraft at a mobile point,this paper presents a detail analysis on the applicability and distinguishing features of the three traditional models for computing disturbing gravity.Then the reasonability of using the surface layer method to compute the disturbing gravity in sea areas and the key problems to be resolved are pointed out.The surveying resolution and accuracy requirement of gravity anomalies on the earth′surface for calculating the external disturbing gravity field is discussed.A new study approach is suggested to modify theoriginal surface layer model,in which a transformation of identical equation with a local integration field,Taylor series expansion in the local area and an interpolation method for non-grid point are introduced to eliminate the singularity drawback inherent in the surface layer model.And a nonsingular modified model of computing the external gravity field at a mobile point in a sea area is proposed for application,which can satisfy the practical needs of determining the local gravity field quickly in all sea areas and full height.A numerical test using a synthetic gravity data set from the ultra-high-degree geopotential model EGM2008 proves the feasibility and validity of the suggested model.The approximation accuracy of the modified model is superior to 2×10-5 m·s-2 in rugged oceanic trench areas with intense variations of the gravity field.
In accordance with the variation characteristics of the marine gravity field and the special support requirement of launching a long range spacecraft at a mobile point,this paper presents a detail analysis on the applicability and distinguishing features of the three traditional models for computing disturbing gravity.Then the reasonability of using the surface layer method to compute the disturbing gravity in sea areas and the key problems to be resolved are pointed out.The surveying resolution and accuracy requirement of gravity anomalies on the earth′surface for calculating the external disturbing gravity field is discussed.A new study approach is suggested to modify theoriginal surface layer model,in which a transformation of identical equation with a local integration field,Taylor series expansion in the local area and an interpolation method for non-grid point are introduced to eliminate the singularity drawback inherent in the surface layer model.And a nonsingular modified model of computing the external gravity field at a mobile point in a sea area is proposed for application,which can satisfy the practical needs of determining the local gravity field quickly in all sea areas and full height.A numerical test using a synthetic gravity data set from the ultra-high-degree geopotential model EGM2008 proves the feasibility and validity of the suggested model.The approximation accuracy of the modified model is superior to 2×10-5 m·s-2 in rugged oceanic trench areas with intense variations of the gravity field.
引文
Bian S.1997.Some cubature formulas for singular integrals in physical geodesy.Journal of Geodesy,71(8):443-453.
Bjerhammar A.1964.A New Theory of Geodetic Gravity.Stockholm:Tekniska Hogskolan.
Bjerhammar A.1987.Discrete Physical Geodesy.Dept.of Geodetic Science and Surveying.Report 380.Columbus,Ohio:The Ohio State University.
Cao H S,Zhu Z W,Wang X L.1985.Digital realization of the theory of repre-senting the Earth′s gravity field by fictitious single-layer density.Acta Geodaetica et Cartographica Sinica(in Chinese),14(4):262-273.
Chen G Q.1982.Spacecraft Dynamics in Gravity Anomaly Field(in Chinese).Changsha:National University of Defense Technology Press.
Chen X.2016.Research on refined processing of marine gravity measurement data[Ph.D.Thesis](in Chinese).Dalian:Dalian Naval Academy.
Guo D M,Xu H Z.2011.Research on the singular integral of local terrain correction computation.Chinese Journal of Geophysics(in Chinese),54(4):977-983,doi:10.3969/j.issn.0001-5733.2011.04.012.
Heiskanen W A,Moritz H.1967.Physical Geodesy.San Francisco:Freeman and Company.
Huang J S,Zhu Z W.1995.Frequency response point masses model of exterior disturbing gravity field.Acta Geophysica Sinica(in Chinese),38(2):182-188.
Huang M T,Zhai G J,Guan Z,et al.2005.Determination and Application of Marine Gravity Field(in Chinese).Beijing:Surveying and Mapping Press.
Huang M T,Liu M,Ouyang Y Z,et al.2016.Effect of external disturbing gravity field on spacecraft guidance and surveying line layout for marine gravity survey.Acta Geodaetica et Cartographica Sinica(in Chinese),45(11):1261-1269.
Hwang C.1998.Inverse Vening Meinesz formula and deflectiongeoid formula:applications to the predictions of gravity and geoid over the South China Sea.Journal of Geodesy,72(5):304-312.
Li J C,Chen J Y,Ning J S,et al.2003.Theory of the Earth′s Gravity Field Approximation and Determination of China Quasi-Geoid 2000(in Chinese).Wuhan:Wuhan University Press.
Liu C H.2016.Improved Direct Integral Methods Calculating Exterior Disturbing Gravity in Low-altitude Airspace[Ph.M.Thesis](in Chinese).Zhengzhou:PLA Information Engineering University.
Lu Z L,Wu X P,Ding X B,et al.1993.Gravimetry in Ballistic Missile(in Chinese).Beijing:Bayi Press.
Lu Z L.1996.Theory and Method of the Earth′s Gravity Field(in Chinese).Beijing:PLA Publishing House.
Moritz H.1966.The computation of the external gravity field and the geodetic boundary-value problem.∥Orlin H ed.Gravity Anomalies:Unsurveyed Areas.Washington D C:American Geophysical Union,9:127-136.
Shu C F,Li F,Li M F,et al.2011.Determination of GPS/gravity quasi-geoid using the Bjerhammar method.Chinese Journal of Geophysics(in Chinese),54(10):2503-2509,doi:10.3969/j.issn.0001-5733.2011.10.008.
Sunkel H.1983.The generation of a mass point model from surface gravity data.Columbus,Ohio:Ohio State University.
Wang J Q,Li J C,Zhao G Q,et al.2010.The construction and analysis for three-tier point mass model of gravity.Acta Geodaetica et Cartographica Sinica(in Chinese),39(5):503-507,515.
Wu X P.1984.Point-mass model of local gravity field.Acta Geodaetica et Cartographica Sinica(in Chinese),13(4):249-258.
Wu X P.1992.Applications of data in the determination of the external disturbing gravity field outside the earth.Journal of PLA Institute of Surveying and Mapping(in Chinese),(4):1-10.
Xu H Z,Zhu Z W.1984.Representation of gravity field outside the earth using fictitious single layer density.Scientia Sinica(Series B),27(9):985-992.
Zhang C D,Lu Z L,Wu X P.1998.Truncation error formulae for the disturbing gravity vector.Journal of Geodesy,72(3):119-123.
操华胜,朱灼文,王晓岚.1985.地球重力场的虚拟单层密度表示理论的数字实现.测绘学报,14(4):262-273.
陈国强.1982.异常重力场中飞行器动力学.长沙:国防科技大学出版社.
陈欣.2016.海域重力测量数据的精化处理研究[博士论文].大连:海军大连舰艇学院.
郭东美,许厚泽.2011.局部地形改正的奇异积分研究.地球物理学报,54(4):977-983,doi:10.3969/j.issn.0001-5733.2011.04.012.
黄金水,朱灼文.1995.外部扰动重力场的频谱响应质点模型.地球物理学报,38(2):182-188.
黄谟涛,翟国君,管铮等.2005.海洋重力场测定及其应用.北京:测绘出版社.
黄谟涛,刘敏,欧阳永忠等.2016.重力场对飞行器制导的影响及海洋重力测线布设.测绘学报,45(11):1261-1269.
李建成,陈俊勇,宁津生等.2003.地球重力场逼近理论与中国2000似大地水准面的确定.武汉:武汉大学出版社.
刘长弘.2016.改进的直接积分方法计算低空扰动引力[硕士论文].郑州:解放军信息工程大学.
陆仲连,吴晓平,丁行斌等.1993.弹道导弹重力学.北京:八一出版社.
陆仲连.1996.地球重力场理论与方法.北京:解放军出版社.
束蝉方,李斐,李明峰等.2011.应用Bjerhammar方法确定GPS重力似大地水准面.地球物理学报,54(10):2503-2509,doi:10.3969/j.issn.0001-5733.2011.10.008.
王建强,李建成,赵国强等.2010.重力三层点质量模型的构造与分析.测绘学报,39(5):503-507,515.
吴晓平.1984.局部重力场的点质量模型.测绘学报,13(4):249-258.
吴晓平.1992.在推求地球外部扰动重力场中数据的采用.解放军测绘学院学报,(4):1-10.
许厚泽,朱灼文.1984.地球外部重力场的虚拟单层密度表示.中国科学(B辑),17(6):575-580.
Bjerhammar A.1964.A New Theory of Geodetic Gravity.Stockholm:Tekniska Hogskolan.
Bjerhammar A.1987.Discrete Physical Geodesy.Dept.of Geodetic Science and Surveying.Report 380.Columbus,Ohio:The Ohio State University.
Cao H S,Zhu Z W,Wang X L.1985.Digital realization of the theory of repre-senting the Earth′s gravity field by fictitious single-layer density.Acta Geodaetica et Cartographica Sinica(in Chinese),14(4):262-273.
Chen G Q.1982.Spacecraft Dynamics in Gravity Anomaly Field(in Chinese).Changsha:National University of Defense Technology Press.
Chen X.2016.Research on refined processing of marine gravity measurement data[Ph.D.Thesis](in Chinese).Dalian:Dalian Naval Academy.
Guo D M,Xu H Z.2011.Research on the singular integral of local terrain correction computation.Chinese Journal of Geophysics(in Chinese),54(4):977-983,doi:10.3969/j.issn.0001-5733.2011.04.012.
Heiskanen W A,Moritz H.1967.Physical Geodesy.San Francisco:Freeman and Company.
Huang J S,Zhu Z W.1995.Frequency response point masses model of exterior disturbing gravity field.Acta Geophysica Sinica(in Chinese),38(2):182-188.
Huang M T,Zhai G J,Guan Z,et al.2005.Determination and Application of Marine Gravity Field(in Chinese).Beijing:Surveying and Mapping Press.
Huang M T,Liu M,Ouyang Y Z,et al.2016.Effect of external disturbing gravity field on spacecraft guidance and surveying line layout for marine gravity survey.Acta Geodaetica et Cartographica Sinica(in Chinese),45(11):1261-1269.
Hwang C.1998.Inverse Vening Meinesz formula and deflectiongeoid formula:applications to the predictions of gravity and geoid over the South China Sea.Journal of Geodesy,72(5):304-312.
Li J C,Chen J Y,Ning J S,et al.2003.Theory of the Earth′s Gravity Field Approximation and Determination of China Quasi-Geoid 2000(in Chinese).Wuhan:Wuhan University Press.
Liu C H.2016.Improved Direct Integral Methods Calculating Exterior Disturbing Gravity in Low-altitude Airspace[Ph.M.Thesis](in Chinese).Zhengzhou:PLA Information Engineering University.
Lu Z L,Wu X P,Ding X B,et al.1993.Gravimetry in Ballistic Missile(in Chinese).Beijing:Bayi Press.
Lu Z L.1996.Theory and Method of the Earth′s Gravity Field(in Chinese).Beijing:PLA Publishing House.
Moritz H.1966.The computation of the external gravity field and the geodetic boundary-value problem.∥Orlin H ed.Gravity Anomalies:Unsurveyed Areas.Washington D C:American Geophysical Union,9:127-136.
Shu C F,Li F,Li M F,et al.2011.Determination of GPS/gravity quasi-geoid using the Bjerhammar method.Chinese Journal of Geophysics(in Chinese),54(10):2503-2509,doi:10.3969/j.issn.0001-5733.2011.10.008.
Sunkel H.1983.The generation of a mass point model from surface gravity data.Columbus,Ohio:Ohio State University.
Wang J Q,Li J C,Zhao G Q,et al.2010.The construction and analysis for three-tier point mass model of gravity.Acta Geodaetica et Cartographica Sinica(in Chinese),39(5):503-507,515.
Wu X P.1984.Point-mass model of local gravity field.Acta Geodaetica et Cartographica Sinica(in Chinese),13(4):249-258.
Wu X P.1992.Applications of data in the determination of the external disturbing gravity field outside the earth.Journal of PLA Institute of Surveying and Mapping(in Chinese),(4):1-10.
Xu H Z,Zhu Z W.1984.Representation of gravity field outside the earth using fictitious single layer density.Scientia Sinica(Series B),27(9):985-992.
Zhang C D,Lu Z L,Wu X P.1998.Truncation error formulae for the disturbing gravity vector.Journal of Geodesy,72(3):119-123.
操华胜,朱灼文,王晓岚.1985.地球重力场的虚拟单层密度表示理论的数字实现.测绘学报,14(4):262-273.
陈国强.1982.异常重力场中飞行器动力学.长沙:国防科技大学出版社.
陈欣.2016.海域重力测量数据的精化处理研究[博士论文].大连:海军大连舰艇学院.
郭东美,许厚泽.2011.局部地形改正的奇异积分研究.地球物理学报,54(4):977-983,doi:10.3969/j.issn.0001-5733.2011.04.012.
黄金水,朱灼文.1995.外部扰动重力场的频谱响应质点模型.地球物理学报,38(2):182-188.
黄谟涛,翟国君,管铮等.2005.海洋重力场测定及其应用.北京:测绘出版社.
黄谟涛,刘敏,欧阳永忠等.2016.重力场对飞行器制导的影响及海洋重力测线布设.测绘学报,45(11):1261-1269.
李建成,陈俊勇,宁津生等.2003.地球重力场逼近理论与中国2000似大地水准面的确定.武汉:武汉大学出版社.
刘长弘.2016.改进的直接积分方法计算低空扰动引力[硕士论文].郑州:解放军信息工程大学.
陆仲连,吴晓平,丁行斌等.1993.弹道导弹重力学.北京:八一出版社.
陆仲连.1996.地球重力场理论与方法.北京:解放军出版社.
束蝉方,李斐,李明峰等.2011.应用Bjerhammar方法确定GPS重力似大地水准面.地球物理学报,54(10):2503-2509,doi:10.3969/j.issn.0001-5733.2011.10.008.
王建强,李建成,赵国强等.2010.重力三层点质量模型的构造与分析.测绘学报,39(5):503-507,515.
吴晓平.1984.局部重力场的点质量模型.测绘学报,13(4):249-258.
吴晓平.1992.在推求地球外部扰动重力场中数据的采用.解放军测绘学院学报,(4):1-10.
许厚泽,朱灼文.1984.地球外部重力场的虚拟单层密度表示.中国科学(B辑),17(6):575-580.
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