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
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摘要
本文研究了联合卫星观测数据和重力异常数据确定超高阶重力场模型的理论方法,并使用EGM2008模型重力异常和GOCE(gravity field and ocean circulation explorer)观测数据构建了重力场模型SGG-UGM-1。重点研究了由球面格网重力异常快速构建超高阶重力场模型的块对角最小二乘方法,将OpenMP技术引入到块对角最小二乘中以提高计算效率,并基于模拟数据验证了方法及算法和软件模块的正确性。采用本文制定的联合解算策略,利用GOCE重力卫星观测数据构建的220阶次法方程和EGM2008模型重力异常构建的2159阶次块对角法方程,联合求解了2159阶次的重力场模型SGG-UGM-1。将SGG-UGM-1与EGM2008、EIGEN-6C2、EIGEN-6C4等超高阶模型在频谱域内进行了比较分析,结果表明SGG-UGM-1相对参考模型的系数误差较小,且在220阶次内的系数精度相比EGM2008模型有了提高。采用中国与美国的GPS/水准数据和毛乌素测区的航空重力观测数据对这些模型进行了外符合精度的检验。检核结果表明,在中国区域,SGG-UGM-1模型大地水准面的精度在EIGEN-6C2和EIGEN-6C4两个模型之间,优于GOSG-EGM模型和EGM2008模型,与美国区域几个模型的精度相当。利用毛乌素测区的航空重力数据对几个模型进行了检核,结果表明SGG-UGM-1模型计算的重力扰动精度与EGM2008、EIGEN-6C4模型相当,优于GOSG-EGM模型和EIGEN-6C2模型。
The theory and methods of the determination of an ultra-high gravity field model by combination of satellite observation data and gravity anomaly data are studied.And an ultra-high gravity field model named SGGUGM-1 is computed using EGM2008 derived gravity anomaly and GOCE observation data.The block-diagonal least squares(BDLS)method for quickly estimating an ultra-high gravity field model is researched and the corresponding software module is validated by numerical experiments.OpenMP technique is introduced into the BDLS program,which improves computing efficiency dramatically.An ultra-high gravity model SGG-UGM-1 complete to degree and order 2159 is derived using the proposed calculation strategies.The fully occupied normal equation system up to degree and order 220 formed by GOCE satellite data and the block-diagonal normal equation system up to degree and order 2159 formed by EGM2008 gravity anomaly data are used for the combination.Comparison among the models SGG-UGM-1 and EGM2008,EIGEN-6C2,EIGEN-6C4,GOSG-EGM in frequency domain has been done,which shows that SGG-UGM-1 is close to the reference models and that the coefficients lower than degree 220 of SGG-UGM-1 are more accurate than that of EGM2008.The models are also validated by GPS-leveling data in China and America and airborne gravity data in Maowusu surveying area.The results show that in China the accuracy level of SGG-UGM-1 derived geoid is between EIGEN-6C2 and EIGEN-6C4,and better than GOSG-EGM and EGM2008,while in America theyarealmostthesame.InMaowusuarea the accuracy level of SGG-UGM-1 derived gravity disturbance is almost at the same accuracy level with EGM2008 and EIGEN-6C4 and better than GOSG-EGM and EIGEN-6C2.
The theory and methods of the determination of an ultra-high gravity field model by combination of satellite observation data and gravity anomaly data are studied.And an ultra-high gravity field model named SGGUGM-1 is computed using EGM2008 derived gravity anomaly and GOCE observation data.The block-diagonal least squares(BDLS)method for quickly estimating an ultra-high gravity field model is researched and the corresponding software module is validated by numerical experiments.OpenMP technique is introduced into the BDLS program,which improves computing efficiency dramatically.An ultra-high gravity model SGG-UGM-1 complete to degree and order 2159 is derived using the proposed calculation strategies.The fully occupied normal equation system up to degree and order 220 formed by GOCE satellite data and the block-diagonal normal equation system up to degree and order 2159 formed by EGM2008 gravity anomaly data are used for the combination.Comparison among the models SGG-UGM-1 and EGM2008,EIGEN-6C2,EIGEN-6C4,GOSG-EGM in frequency domain has been done,which shows that SGG-UGM-1 is close to the reference models and that the coefficients lower than degree 220 of SGG-UGM-1 are more accurate than that of EGM2008.The models are also validated by GPS-leveling data in China and America and airborne gravity data in Maowusu surveying area.The results show that in China the accuracy level of SGG-UGM-1 derived geoid is between EIGEN-6C2 and EIGEN-6C4,and better than GOSG-EGM and EGM2008,while in America theyarealmostthesame.InMaowusuarea the accuracy level of SGG-UGM-1 derived gravity disturbance is almost at the same accuracy level with EGM2008 and EIGEN-6C4 and better than GOSG-EGM and EIGEN-6C2.
引文
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[20]陈国良.并行计算:结构·算法·编程[M].3版.北京:高等教育出版社,2011.CHEN Guoliang.Parallel Computing:Architecture,Algorithm and Programming[M].3rd ed.Beijing:Higher Education Press,2011.
[21]邹贤才,李建成,汪海洪,等.OpenMP并行计算在卫星重力数据处理中的应用[J].测绘学报,2010,39(6):636-641.ZOU Xiancai,LI Jiancheng,WANG Haihong,et al.Application of Parallel Computing with OpenMP in Data Processing for Satellite Gravity[J].Acta Geodaetica et Cartographica Sinica,2010,39(6):636-641.
[22]FOERSTE C,BRUINSMA S L,FLECHTNER F,et al.A Preliminary Update of the Direct Approach GOCE Processing and a New Release of EIGEN-6C[C]//Proceedings of American Geophysical Union 2012 Fall Meeting.San Francisco,USA:American Geophysical Union,2012.
[23]LI Jiancheng,JIANG Weiping,ZOU Xiancai,et al.Evaluation of Recent GRACE and GOCE Satellite Gravity Models and Combined Models Using GPS/leveling and Gravity Data in China[M]//MARTI U.Gravity,Geoid and Height Systems.Cham,Switzerland:Springer,2014:67-74.
[24]MILBERT D G.Documentation for the GPS Benchmark Data Set of 23-July-98[R].Milan:IGeS International Geoid Service,1998:29-42.
[25]RUMMEL R,YI Weiyong,STUMMER C.GOCE Gravitational Gradiometry[J].Journal of Geodesy,2011,85(11):777-790.
[2]PAIL R,GOIGINGER H,SCHUH W D,et al.Combined Satellite Gravity Field Model GOCO01S Derived from GOCE and GRACE[J].Geophysical Research Letters,2010,37(20):L20314.
[3]FEATHERSTONE W E.GNSS-based Heighting in Australia:Current,Emerging and Future Issues[J].Journal of Spatial Science,2008,53(2):115-133.
[4]RUMMEL R.Height Unification Using GOCE[J].Journal of Geodetic Science,2012,2(4):355-362.
[5]MCKENZIE D,YI Weiyong,RUMMEL R.Estimates of Tefrom GOCE Data[J].Earth and Planetary Science Letters,2014,399(2):116-127.
[6]PAVLIS N K.Modeling and Estimation of a Low Degree Geopotential Model from Terrestrial Gravity Data[R].Report No.386.Columbus:The Ohio State University,1988.
[7]LEMONIE F G,KENYON S C,FACTOR J K,et al.The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency(NIMA)Geopotential Model EGM96[R].Greenbelt:NASA Goddard Space Flight Center,1998.
[8]PAVLIS N K,HOLMES S A,KENYON S C,et al.The Development and Evaluation of the Earth Gravitational Model 2008(EGM2008)[J].Journal of Geophysical Research,2012,117(3):205-213.
[9]FORSTE C,BRUINSMA S L,ABRIKOSOV O,et al.EIGEN-6C4the Latest Combined Global Gravity Field Model Including GOCE Data up to Degree and Order 2190of GFZ Potsdam and GRGS Toulouse[EB/OL].http://doi.org/10.5880/icgem.2015.1.
[10]李新星,吴晓平,李姗姗,等.块对角最小二乘方法在确定全球重力场模型中的应用[J].测绘学报,2014,43(8):778-785.DOI:10.13485/j.cnki.11-2089.2014.0110.LI Xinxing,WU Xiaoping,LI Shanshan,et al.The Application of Block-diagonal Least-squares Methods in Geopotential Model Determination[J].Acta Geodaetica et Cartographica Sinica,2014,43(8):778-785.DOI:10.13485/j.cnki.11-2089.2014.0110.
[11]GILARDONI M,REGUZZONI M,SAMPIETRO D.GECO:A Global Gravity Model by Locally Combining GOCE Data and EGM2008[J].Studia Geophysica et Geodaetica,2016,60(2):228-247.
[12]FECHER T,PAIL R,GRUBER T,et al.GOCO05c:A New Combined Gravity Field Model Based on Full Normal Equations and Regionally Varying Weighting[J].Surveys in Geophysics,2017,38(3):571-590.
[13]王正涛,党亚民,晁定波.超高阶地球重力位模型确定的理论与方法[M].北京:测绘出版社,2011.WANG Zhengtao,DANG Yamin,CHAO Dingbo.Theory and Methodology of Ultra-high-degree Geopotential Model Determination[M].Beijing:Surveying and Mapping Press,2011.
[14]李新星.超高阶地球重力场模型的构建[D].郑州:信息工程大学,2013.LI Xinxing.Building of an Ultra-high-degree Geopotential Model[D].Zhengzhou:Information Engineering University,2013.
[15]海斯卡涅W A,莫里兹H.物理大地测量学[M].卢福康,胡国理,译.北京:测绘出版社,1979.HEISKANEN W A,MORITZ H.Physical Geodesy[M].LU Fukang,HU Guoli,trans.Beijing:Surveying and Mapping Press,1979.
[16]COLOMBO O L.Numerical Methods for Harmonic Analysis on the Sphere[R].Columbus:The Ohio State University,1981.
[17]LIANG Wei,LI Jiancheng,XU Xinyu,et al.Analysis of the Impact on the Gravity Field Determination from the Data with the Ununiform Noise Distribution Using Blockdiagonal Least Squares Method[J].Geodesy and Geodynamics,2016,7(3):194-201.
[18]XU Xinyu,ZHAO Yongqi,REUBELT T,et al.A GOCE Only Gravity Model GOSG01S and the Validation of GOCE Related Satellite Gravity Models[J].Geodesy and Geodynamics,2017,8(4):260-272.
[19]钟波,宁津生,罗志才,等.联合GOCE卫星轨道和重力梯度数据严密求解重力场的模拟研究[J].武汉大学学报(信息科学版),2012,37(10):1215-1220.ZHONG Bo,NING Jinsheng,LUO Zhicai,et al.Simulation Study of Rigorous Gravity Field Recovery by Combining GOCE Satellite Orbit and Gravity Gradient Data[J].Geomatics and Information Science of Wuhan University,2012,37(10):1215-1220.
[20]陈国良.并行计算:结构·算法·编程[M].3版.北京:高等教育出版社,2011.CHEN Guoliang.Parallel Computing:Architecture,Algorithm and Programming[M].3rd ed.Beijing:Higher Education Press,2011.
[21]邹贤才,李建成,汪海洪,等.OpenMP并行计算在卫星重力数据处理中的应用[J].测绘学报,2010,39(6):636-641.ZOU Xiancai,LI Jiancheng,WANG Haihong,et al.Application of Parallel Computing with OpenMP in Data Processing for Satellite Gravity[J].Acta Geodaetica et Cartographica Sinica,2010,39(6):636-641.
[22]FOERSTE C,BRUINSMA S L,FLECHTNER F,et al.A Preliminary Update of the Direct Approach GOCE Processing and a New Release of EIGEN-6C[C]//Proceedings of American Geophysical Union 2012 Fall Meeting.San Francisco,USA:American Geophysical Union,2012.
[23]LI Jiancheng,JIANG Weiping,ZOU Xiancai,et al.Evaluation of Recent GRACE and GOCE Satellite Gravity Models and Combined Models Using GPS/leveling and Gravity Data in China[M]//MARTI U.Gravity,Geoid and Height Systems.Cham,Switzerland:Springer,2014:67-74.
[24]MILBERT D G.Documentation for the GPS Benchmark Data Set of 23-July-98[R].Milan:IGeS International Geoid Service,1998:29-42.
[25]RUMMEL R,YI Weiyong,STUMMER C.GOCE Gravitational Gradiometry[J].Journal of Geodesy,2011,85(11):777-790.