不同地形条件下超高阶重力场模型精度比较分析
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摘要
超高阶高精度的重力场模型在地球动力学、地球物理学、大地测量学、地震学、海洋学等诸多领域具有非常重要的研究意义。本文主要从大地水准面阶误差和累积误差两个方面研究了EGM2008、EIGEN-6C4、GECO等三种2190阶次的超高阶重力场模型的内符合精度;以新疆地区为例,选取37个均匀分布、地形多样的测区共971个实测GNSS水准点数据分别检核了三种模型的外符合精度。计算结果表明,EIGEN-6C4模型在内符合精度方面优于其他两种模型;三种超高阶重力场模型的外符合精度从高到低依次为EIGEN-6C4、EGM2008、GECO,精度分别为0.136m,0.146m、0.190m。故推荐使用EIGEN-6C4模型进行似大地水准面精化、重力异常、垂线偏差等重力场元计算。
The ultra-high-degree gravity field model has very important research significance in many fields such as geodynamics, geophysics, geodesy, seismology, oceanography, etc. In this paper, the internal coincidence accuracy of three 2190-order ultra-high-order gravity field models, EGM2008, EIGEN-6 C4 and GECO, is mainly studied from two aspects of geoid order error and cumulative error. Taking Xinjiang as an example, 971 measured GNSS benchmark data from 37 evenly distributed survey areas with diverse topography were selected to check the external coincidence accuracy of the three models respectively. The calculation results show that the EIGEN-6 C4 model is superior to the other two models in terms of internal coincidence accuracy. The external accuracy from high to low of the three ultra-high-order gravity field models is EIGEN-6 C4, EGM2008 and GECO, with the precision of 0.136 m, 0.146 m and 0.190 m respectively. Therefore, EIGEN-6 C4 model is recommended for gravity field element calculation such as quasi-geoid refinement, gravity anomaly and vertical deviation.
The ultra-high-degree gravity field model has very important research significance in many fields such as geodynamics, geophysics, geodesy, seismology, oceanography, etc. In this paper, the internal coincidence accuracy of three 2190-order ultra-high-order gravity field models, EGM2008, EIGEN-6 C4 and GECO, is mainly studied from two aspects of geoid order error and cumulative error. Taking Xinjiang as an example, 971 measured GNSS benchmark data from 37 evenly distributed survey areas with diverse topography were selected to check the external coincidence accuracy of the three models respectively. The calculation results show that the EIGEN-6 C4 model is superior to the other two models in terms of internal coincidence accuracy. The external accuracy from high to low of the three ultra-high-order gravity field models is EIGEN-6 C4, EGM2008 and GECO, with the precision of 0.136 m, 0.146 m and 0.190 m respectively. Therefore, EIGEN-6 C4 model is recommended for gravity field element calculation such as quasi-geoid refinement, gravity anomaly and vertical deviation.
引文
[1] 章传银,郭春喜,陈俊勇等.EGM2008地球重力场模型在中国大陆适用性分析[J].测绘学报,2009,(4):283～289.Zhang Chanyin,Guo Chunxi,Chen Junyong et al.EGM2008 and its application analysis in Chinese mainland[J].Acta Geodaetica et Cartographica Sinica,2009,38(4):283～289.(in Chinese)
[2] 赵德军,张敏利,王强等.EIGEN-6C2重力场模型在中国大陆的精度分析[J].大地测量与地球动力学,2014,34(5):21～24.Zhao Dejun,Zhang Minli,Wangqiang et al.Accuracy analyses of EIGEN-6C2 geopotential model in China mainland[J].Journal of Geodesy and Geodynamics,2014,34(5):21～24.(in Chinese)
[3] 冯进凯,王庆宾,黄佳喜等.多个超高阶重力场模型精度分析[J].测绘科学技术学报,2017,34(4):358～363.Feng Jinkai,Wang Qingbin,Huang Jiaxi et al.The accuracy analysis of multiple ultra-high-degree gravity field models[J].Journal of Geomatics Science and Technology,2017,34(4):358～363.(in Chinese)
[4] Pavlis N K,Holmes S A,Kenyon S C et al.An earth gravitational model to degree 2160.EGM2008 The General Assembly of the European Geosciences Union.2008.
[5] F?rste,Christoph;Bruinsma,Sean.L;Abrikosov,Oleg;Lemoine,Jean-Michel;Marty,Jean Charles;Flechtner,Frank;Balmino,G.;Barthelmes,F.;Biancale,R.EIGEN-6C4 The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse,2014.
[6] 谭衍涛,黄健鹏,黄国荣等.重力场模型及GNSS/水准的区域似大地水准面精化[J].测绘科学,2016,41(4):5～9.Tan Yantao,Huang Jianpeng,Huang Guorong et al.Refinement of local quasi-geoid based on earth gravity field models and GNSS/leveling[J].Science of Surveying and Mapping,2016,41(4):5～9.(in Chinese)
[7] Maddalena Gilardoni,Mirko Reguzzoni,Daniele Sampietro.GECO:a global gravity model by locally combining GOCE data and EGM2008[J].Studia Geophysica et Geodaetica,2016,60(2).
[8] 张兴福,李博峰,魏德宏等.多类重力场模型的精度分析及联合确定GPS点正常高的方法[J].测绘学报,2013,(1):6～12.Zhang Xingfu,Li Bofeng,Wei Dehong et al.The accuracy analysis of multiple earth gravity field models and normal height determination of GPS points based on combination method[J].Acta Geodaetica et Cartographica Sinica,2013,(1):6～12.(in Chinese)
[9] 赵德军,徐新强,陈永祥等.GOCE重力场模型的精度评估[J].大地测量与地球动力学,2015,(2):322～325.Zhao Dejun,Xu Xinqiang,Chen Yongxiang et al.Evaluations of the recent GOCE-based gravity field models[J].Journal of Geodesy and Geodynamics,2015,(2):322～325.(in Chinese)
[10] 许双安.基于EGM2008模型的GPS高程转换方法研究[J].铁道勘察,2012,(5):31～34Xu Shuang’an.Study on the method of GPS height transformation using the earth gravity model 2008[J].Railway Investigation and Surveying,2012,(5):31～34.(in Chinese)
[11] 张敏利,赵德军,陈永祥.利用Wenzel加权谱组合法拓展GOCE重力场模型[J].大地测量与地球动力学,2015,35(3):481～484.Zhang Minli,Zhao Dejun,Chen Yongxiang.Extending GOCE geopotential model using Wenzel’s weighted spectral combination[J].Journal of Geodesy and Geodynamics,2015,35(3):481～484.(in Chinese)
[12] 梁伟,徐新禹,李建成等.联合EGM2008模型重力异常和GOCE观测数据构建超高阶地球重力场模型SGG-UGM-1[J].测绘学报,2018,(4):425～434.Liang Wei,Xu Xinyu,Li Jiancheng et al.The determination of an ultra-high gravity field model SGG-UGM-1 by combining EGM2008 gravity anomaly and GOCE observation data[J].Acta Geodaetica et Cartographica Sinica,2018,(4):425～434.(in Chinese)
[13] 罗陶荣,王中元,梁宁等.利用EGM2008模型与加权组合模型进行高程异常拟合[J].测绘通报,2018,(1):28～32.Luo Taorong,Wang Zhongyuan,Liang Ning et al.Height anomaly fitting based on EGM2008 model and weighted composite model[J].Bulletin of Surveying and Mapping,2018,(1):28～32.(in Chinese)
[14] 冯国正,曹磊,马耀昌等.EGM 2008模型的无验潮测深技术[J].测绘科学,2018,43(1):26～30.Feng Guozheng,Cao Lei,Ma Yaochang et al.Non-tidal sounding technology based on EGM 2008 model[J].Science of Surveying and Mapping,2018,43(1):26～30.(in Chinese)
[15] 李建成,褚永海,徐新禹.区域与全球高程基准差异的确定[J].测绘学报,2017,46(10):1262～1273.Li Jiancheng,Chu Yonghai,Xu Xinyu.Determination of vertical datum offset between the regional and the global height datum[J].Acta Geodaetica et Cartographica Sinica,2017,46(10):1262～1273 (in Chinese).
[16] 胡品,王建强,张飞.超高阶重力场模型的研究与实现[J].测绘与空间地理信息,2017,40(12):57～59,63.Hu Pin,Wang Jianqiang,Zhang Fei.Research and realization of ultra-high degree gravity field model[J].Geomatics & Spatial Information Technology,2017,40(12):57～59,63.(in Chinese)
[2] 赵德军,张敏利,王强等.EIGEN-6C2重力场模型在中国大陆的精度分析[J].大地测量与地球动力学,2014,34(5):21～24.Zhao Dejun,Zhang Minli,Wangqiang et al.Accuracy analyses of EIGEN-6C2 geopotential model in China mainland[J].Journal of Geodesy and Geodynamics,2014,34(5):21～24.(in Chinese)
[3] 冯进凯,王庆宾,黄佳喜等.多个超高阶重力场模型精度分析[J].测绘科学技术学报,2017,34(4):358～363.Feng Jinkai,Wang Qingbin,Huang Jiaxi et al.The accuracy analysis of multiple ultra-high-degree gravity field models[J].Journal of Geomatics Science and Technology,2017,34(4):358～363.(in Chinese)
[4] Pavlis N K,Holmes S A,Kenyon S C et al.An earth gravitational model to degree 2160.EGM2008 The General Assembly of the European Geosciences Union.2008.
[5] F?rste,Christoph;Bruinsma,Sean.L;Abrikosov,Oleg;Lemoine,Jean-Michel;Marty,Jean Charles;Flechtner,Frank;Balmino,G.;Barthelmes,F.;Biancale,R.EIGEN-6C4 The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse,2014.
[6] 谭衍涛,黄健鹏,黄国荣等.重力场模型及GNSS/水准的区域似大地水准面精化[J].测绘科学,2016,41(4):5～9.Tan Yantao,Huang Jianpeng,Huang Guorong et al.Refinement of local quasi-geoid based on earth gravity field models and GNSS/leveling[J].Science of Surveying and Mapping,2016,41(4):5～9.(in Chinese)
[7] Maddalena Gilardoni,Mirko Reguzzoni,Daniele Sampietro.GECO:a global gravity model by locally combining GOCE data and EGM2008[J].Studia Geophysica et Geodaetica,2016,60(2).
[8] 张兴福,李博峰,魏德宏等.多类重力场模型的精度分析及联合确定GPS点正常高的方法[J].测绘学报,2013,(1):6～12.Zhang Xingfu,Li Bofeng,Wei Dehong et al.The accuracy analysis of multiple earth gravity field models and normal height determination of GPS points based on combination method[J].Acta Geodaetica et Cartographica Sinica,2013,(1):6～12.(in Chinese)
[9] 赵德军,徐新强,陈永祥等.GOCE重力场模型的精度评估[J].大地测量与地球动力学,2015,(2):322～325.Zhao Dejun,Xu Xinqiang,Chen Yongxiang et al.Evaluations of the recent GOCE-based gravity field models[J].Journal of Geodesy and Geodynamics,2015,(2):322～325.(in Chinese)
[10] 许双安.基于EGM2008模型的GPS高程转换方法研究[J].铁道勘察,2012,(5):31～34Xu Shuang’an.Study on the method of GPS height transformation using the earth gravity model 2008[J].Railway Investigation and Surveying,2012,(5):31～34.(in Chinese)
[11] 张敏利,赵德军,陈永祥.利用Wenzel加权谱组合法拓展GOCE重力场模型[J].大地测量与地球动力学,2015,35(3):481～484.Zhang Minli,Zhao Dejun,Chen Yongxiang.Extending GOCE geopotential model using Wenzel’s weighted spectral combination[J].Journal of Geodesy and Geodynamics,2015,35(3):481～484.(in Chinese)
[12] 梁伟,徐新禹,李建成等.联合EGM2008模型重力异常和GOCE观测数据构建超高阶地球重力场模型SGG-UGM-1[J].测绘学报,2018,(4):425～434.Liang Wei,Xu Xinyu,Li Jiancheng et al.The determination of an ultra-high gravity field model SGG-UGM-1 by combining EGM2008 gravity anomaly and GOCE observation data[J].Acta Geodaetica et Cartographica Sinica,2018,(4):425～434.(in Chinese)
[13] 罗陶荣,王中元,梁宁等.利用EGM2008模型与加权组合模型进行高程异常拟合[J].测绘通报,2018,(1):28～32.Luo Taorong,Wang Zhongyuan,Liang Ning et al.Height anomaly fitting based on EGM2008 model and weighted composite model[J].Bulletin of Surveying and Mapping,2018,(1):28～32.(in Chinese)
[14] 冯国正,曹磊,马耀昌等.EGM 2008模型的无验潮测深技术[J].测绘科学,2018,43(1):26～30.Feng Guozheng,Cao Lei,Ma Yaochang et al.Non-tidal sounding technology based on EGM 2008 model[J].Science of Surveying and Mapping,2018,43(1):26～30.(in Chinese)
[15] 李建成,褚永海,徐新禹.区域与全球高程基准差异的确定[J].测绘学报,2017,46(10):1262～1273.Li Jiancheng,Chu Yonghai,Xu Xinyu.Determination of vertical datum offset between the regional and the global height datum[J].Acta Geodaetica et Cartographica Sinica,2017,46(10):1262～1273 (in Chinese).
[16] 胡品,王建强,张飞.超高阶重力场模型的研究与实现[J].测绘与空间地理信息,2017,40(12):57～59,63.Hu Pin,Wang Jianqiang,Zhang Fei.Research and realization of ultra-high degree gravity field model[J].Geomatics & Spatial Information Technology,2017,40(12):57～59,63.(in Chinese)