利用大地边值问题方法统一全球高程基准
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摘要
为解决世界各国高程基准差异的问题,提出联合卫星重力场模型、地面重力数据、GNSS大地高、局部高程基准的正高或正常高,按大地边值问题法确定局部高程基准重力位差的方法。首先推导了利用传统地面"有偏"重力异常确定高程基准重力位差的方法;接着利用改化Stokes核函数削弱"有偏"重力异常的影响,并联合卫星重力场模型和地面"有偏"重力数据,得到独立于任何局部高程基准的重力水准面,以此来确定局部高程基准重力位差;最后利用GNSS+水准数据和重力大地水准面确定了美国高程基准与全球高程基准W0的重力位差为-4.82±0.05 m~2s~(-2)。
In order to unify height datums in different countries,an algorithm based on geodetic boundary value problems( GBVP) is presented,which utilizes satellite gravity field models,terrestrial gravimetric data,GNSS geodetic heights,orthometric heights or normal heights.First of all,the algorithm to determinate height datum geopotential difference using conventional terrestrial "biased"gravity anomalies is deduced.Secondly,the indirect biased term is neglected by using modified Stokes kernel function.A geoid that is not related to any local vertical datums is obtained by combining satellite-only gravity field models and terrestrial"biased"gravity anomalies.That independent geoid is then adapted to determinate height datum geopotential difference. At last,the geopotential difference between US vertical datum( NAVD88) and world geoidal geopotential W0 is determined through GBVP by combining GNSS/leveling benchmark data and gravity geoid,which is about-4.82±0.05 m2 s-2.
In order to unify height datums in different countries,an algorithm based on geodetic boundary value problems( GBVP) is presented,which utilizes satellite gravity field models,terrestrial gravimetric data,GNSS geodetic heights,orthometric heights or normal heights.First of all,the algorithm to determinate height datum geopotential difference using conventional terrestrial "biased"gravity anomalies is deduced.Secondly,the indirect biased term is neglected by using modified Stokes kernel function.A geoid that is not related to any local vertical datums is obtained by combining satellite-only gravity field models and terrestrial"biased"gravity anomalies.That independent geoid is then adapted to determinate height datum geopotential difference. At last,the geopotential difference between US vertical datum( NAVD88) and world geoidal geopotential W0 is determined through GBVP by combining GNSS/leveling benchmark data and gravity geoid,which is about-4.82±0.05 m2 s-2.
引文
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[2]WOODWORTH P,HUGHES C W,BINGHAM R J.Towards Worldwide Height System Unification Using Ocean Information[J].Journal of Geodetic Science,2012,2(4):302-318.DOI:10.2478/v10156-012-0004-8.
[3]焦文海,魏子卿,马欣,等.1985国家高程基准相对于大地水准面的垂直偏差[J].测绘学报,2002,31(3):196-200.
[4]郭海荣,焦文海,杨元喜.1985国家高程基准的系统差[J].武汉大学学报(信息科学版),2004,29(8):715-717.
[5]翟振和,魏子卿,吴富梅.利用EGM2008位模型计算中国高程基准与大地水准面间的垂直偏差[J].大地测量与地球动力学,2011,31(4):116-118.
[6]赫林,李建成.褚永海.1985国家高程基准与全球高程基准之间的垂直偏差[J].测绘学报,2016,45(7):768-774.DOI:10.11947/j.AGCS.2016.20160029.
[7]吴富梅,魏子卿.利用GNSS和EGM2008模型进行跨海高程传递[J].武汉大学学报(信息科学版),2016,41(5):698-703.DOI:10.13203/j.whugis20140392.
[8]KOTSAKIS C.Estimation of the Zero-height Geopotential Level WLVD0 in a Local Vertical Datum From Inversion of Co-located GPS,Leveling and Geoid Heights:A Case Study in the Hellenic Islands[J].Journal of Geodesy,2012,86(6):423-439.DOI:10.1007/s00190-011-0530-7.
[9]RUMMEL R,TEUNISSEN P.Height Datum Definition,Height Datum Connection and the Role of the Geodetic Boundary Value Problem[J].Bulletin Géodésique,1988,62(4):477-498.
[10]SANSO F,USAI S.Height Datum and Local Geodetic Datums in the Theory of Geodetic Boundary Value Problems[J].Allgemeine Vermessung Nachrichten,1995,102:343-355.
[11]PAN M,SJOBERG L E.Unification of Vertical Datums by GPS and Gravimetric Geoid Models With Application to Fennoscandia[J].Journal of Geodesy,1998,72(2):64-70.
[12]莫登沅.高程基准统一问题的研究[D].郑州:信息工程大学,2000.
[13]徐菊生,王建华,赖锡安,等.垂直基准定义及联接[J].地壳形变与地震,2001,21(1):24-34.
[14]AMOS M J,FEATHERSTONE W E.Unification of New Zealand’s Local Vertical Datums:Iterative Gravimetric Quasigeoid Computations[J].Journal of Geodesy,2009,83(1):57-68.
[15]GERLACH C,RUMMEL R.Global Height System Unification with GOCE:A Simulation Study on the Indirect Bias Term in the GBVP Approach[J].Journal of Geodesy,2013,87(1):57-67.DOI:10.1007/s00190-012-0579-y.
[16]GATTI A,REGUZZONI M,VENUTI G.The Height Datum Problem and the Role of Satellite Gravity Models[J].Journal of Geodesy,2013,87(1):15-22.DOI:10.1007/s00190-012-0574-3.
[17]ZHANG L,LI F,CHEN W,et al.Height Datum Unification Between Shenzhen and Hong Kong Using the Solution of the Linearized Fixed-gravimetric Boundary Value Problem[J].Journal of Geodesy,2008,83(5):411-417.DOI:10.1007/s00190-008-0234-9.
[18]JEKELI C.Heights,the Geopotential,and Vertical Datums[C]∥Report 459.[S.l.]:The Ohio State University,2000.
[19]XU P.A Quality Investigation of Global Vertical Datum Connection[J].Geophysical Journal International,1992,110(2):361-370.DOI:10.1111/j.1365-246X.1992.tb00880.x.
[20]傅露,褚永海.区域大地水准面确定中Stokes核函数的应用[J].大地测量与地球动力学,2013,33(2):110-113.
[21]赫林,李建成.褚永海.1985国家高程基准与全球高程基准之间的垂直偏差[J].测绘学报,2016,45(7):768-774.DOI:10.11947/j.AGCS.2016.20160029.
[22]赵德军.GOCE重力场模型的精度评估[J].大地测量与地球动力学,2015,35(2):21-25.
[23]HUANG J,VERONNEAU M.Canadian Gravimetric Geoid Model 2010[J].Journal of Geodesy,2013,87(8):771-790.
[2]WOODWORTH P,HUGHES C W,BINGHAM R J.Towards Worldwide Height System Unification Using Ocean Information[J].Journal of Geodetic Science,2012,2(4):302-318.DOI:10.2478/v10156-012-0004-8.
[3]焦文海,魏子卿,马欣,等.1985国家高程基准相对于大地水准面的垂直偏差[J].测绘学报,2002,31(3):196-200.
[4]郭海荣,焦文海,杨元喜.1985国家高程基准的系统差[J].武汉大学学报(信息科学版),2004,29(8):715-717.
[5]翟振和,魏子卿,吴富梅.利用EGM2008位模型计算中国高程基准与大地水准面间的垂直偏差[J].大地测量与地球动力学,2011,31(4):116-118.
[6]赫林,李建成.褚永海.1985国家高程基准与全球高程基准之间的垂直偏差[J].测绘学报,2016,45(7):768-774.DOI:10.11947/j.AGCS.2016.20160029.
[7]吴富梅,魏子卿.利用GNSS和EGM2008模型进行跨海高程传递[J].武汉大学学报(信息科学版),2016,41(5):698-703.DOI:10.13203/j.whugis20140392.
[8]KOTSAKIS C.Estimation of the Zero-height Geopotential Level WLVD0 in a Local Vertical Datum From Inversion of Co-located GPS,Leveling and Geoid Heights:A Case Study in the Hellenic Islands[J].Journal of Geodesy,2012,86(6):423-439.DOI:10.1007/s00190-011-0530-7.
[9]RUMMEL R,TEUNISSEN P.Height Datum Definition,Height Datum Connection and the Role of the Geodetic Boundary Value Problem[J].Bulletin Géodésique,1988,62(4):477-498.
[10]SANSO F,USAI S.Height Datum and Local Geodetic Datums in the Theory of Geodetic Boundary Value Problems[J].Allgemeine Vermessung Nachrichten,1995,102:343-355.
[11]PAN M,SJOBERG L E.Unification of Vertical Datums by GPS and Gravimetric Geoid Models With Application to Fennoscandia[J].Journal of Geodesy,1998,72(2):64-70.
[12]莫登沅.高程基准统一问题的研究[D].郑州:信息工程大学,2000.
[13]徐菊生,王建华,赖锡安,等.垂直基准定义及联接[J].地壳形变与地震,2001,21(1):24-34.
[14]AMOS M J,FEATHERSTONE W E.Unification of New Zealand’s Local Vertical Datums:Iterative Gravimetric Quasigeoid Computations[J].Journal of Geodesy,2009,83(1):57-68.
[15]GERLACH C,RUMMEL R.Global Height System Unification with GOCE:A Simulation Study on the Indirect Bias Term in the GBVP Approach[J].Journal of Geodesy,2013,87(1):57-67.DOI:10.1007/s00190-012-0579-y.
[16]GATTI A,REGUZZONI M,VENUTI G.The Height Datum Problem and the Role of Satellite Gravity Models[J].Journal of Geodesy,2013,87(1):15-22.DOI:10.1007/s00190-012-0574-3.
[17]ZHANG L,LI F,CHEN W,et al.Height Datum Unification Between Shenzhen and Hong Kong Using the Solution of the Linearized Fixed-gravimetric Boundary Value Problem[J].Journal of Geodesy,2008,83(5):411-417.DOI:10.1007/s00190-008-0234-9.
[18]JEKELI C.Heights,the Geopotential,and Vertical Datums[C]∥Report 459.[S.l.]:The Ohio State University,2000.
[19]XU P.A Quality Investigation of Global Vertical Datum Connection[J].Geophysical Journal International,1992,110(2):361-370.DOI:10.1111/j.1365-246X.1992.tb00880.x.
[20]傅露,褚永海.区域大地水准面确定中Stokes核函数的应用[J].大地测量与地球动力学,2013,33(2):110-113.
[21]赫林,李建成.褚永海.1985国家高程基准与全球高程基准之间的垂直偏差[J].测绘学报,2016,45(7):768-774.DOI:10.11947/j.AGCS.2016.20160029.
[22]赵德军.GOCE重力场模型的精度评估[J].大地测量与地球动力学,2015,35(2):21-25.
[23]HUANG J,VERONNEAU M.Canadian Gravimetric Geoid Model 2010[J].Journal of Geodesy,2013,87(8):771-790.