地球重力场模型在工程控制网中的应用
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摘要
GPS技术已经广泛应用于大地测量、工程测量、摄影测量与遥感、地壳运动监测、工程变形监测、地球动力学等多学科领域,它可同时精确测定三维大地坐标,并且通过精密似大地水准面,可将GPS点的大地高转换为正常高,从而代替普通水准测量。地球重力场模型和大地水准面的确定是重力卫星研究的主要内容,因此重力卫星研究的成就是继GPS技术之后的又一次革命性突破,它不仅带动了现代大地测量学的变革,还推动了其他相关学科的发展。在精密工程测量中,将高分辨率的地球重力场模型与高精度的GPS相结合,可以提高GPS高程转换精度。
不同地球重力场模型的优选及不同拟合方法的合理选择是GPS高程转换所需考虑的关键问题。随着以卫星重力梯度为主要观测值的GOCE重力卫星的发射成功及其相关重力场模型的推出,使得地球重力场模型的精度及分辨率有了较大提高,有必要将其应用于GPS高程转换的研究；现在精密工程测量中GPS与全站仪的共用是普遍存在的事实,这必然存在法线系统与垂线系统的转换问题,以往由于重力场模型精度较低,未能充分顾及到这种差别,而利用现有最新的地球重力场模型,能较精确地计算垂线偏差并将其应用于精密工程测量。
针对以上问题,本文提出了用目前具有较高精度的EGM2008和SGG地球重力场模型来代替以往较低精度地球重力场模型的策略,计算分析了这两种模型解算全球高程异常的精度,并将这两种模型应用于“移去-拟合-恢复”法的GPS高程转换中,可较好地移去高程异常的系统偏差,在此基础上分析了平面法、二次曲面法、正双曲面法、倒双曲面法及样条函数法用于高程异常拟合的精度,并通过某实际隧道工程算例验证了各种方法的精度。针对精密工程测量的特点,本文提出了顾及垂线偏差的GPS与全站仪的精密数据处理方法,通过“三差改正”将全站仪观测值转化为法线系统下的观测值,与GPS数据统一处理,利用某隧道算例验证了地球重力场模型对平面控制网数据处理的影响不容忽视。
In current days, GPS technology has been widely used in geodesy, engineering surveying, photogrammetry and remote sensing, crustal movement monitoring, deformation monitoring, geodynamics, and other research areas, it can simultaneous determine precise three-dimensional geodetic coordinate. Once the local geoid is determined, the ellipsoidal height of GPS point can be easily transformed to quasi-geoid height through precise quasi-geoid to replace the geometric leveling. The Earth gravity model and the determination of geoid is the main research area of gravity satellite, and the achievement of the gravity satellite research is another revolutionary breakthrough after GPS technology, which not only led to change in modern geodesy but also promote the development of other related disciplines. In precise engineering surveying, by combining high resolution gravity model with high precise GPS surveying, it is possible to improve the accuracy of GPS height transformation.
The key problem of transferring GPS leveling is to get an optimal combination of different gravity models and a reasonable selection of different fitting methods. Along with the successful launching of GOCE gravity satellite which takes gravity gradient as main observations and its related production of gravity model which greatly improves the accuracy and resolution of the Earth gravity model, and it is necessary to apply it to GPS leveling transformation. It is common to use both of GPS and total station in current precise engineering survey, which leads to the transformation problem between normal and vertical system. Because of the low precision of gravity model in the past, the effect of the problem is ignored. But now, with the latest available gravity field model, it is possible to calculate the vertical deflection and apply it to precise engineering survey.
Considering the problems mentioned above, the thesis proposes the method of using the latest higher precise EGM2008 and SGG gravity model to replace the gravity model in the past and analyzes the precision of height anomaly calculated respectively by two models. The thesis also applies the two models to the method of recovery - fitting- restore of GPS leveling transformation which can effectively remove the system error caused by height anomaly. Based on this the thesis analyzes the fitting accuracy of plane method. quadratic surface method, two-surface method, inverted double surface method and spline function method that is used to height anomaly fitting and validates the precision respectively by actual data of a actual tunnel project. According to the characteristic of precise engineering survey, the thesis proposes the precise GPS and total station data processing method taking the vertical deflection into account. The method first transform the total station observation data from normal to vertical system and then process data together with GPS data. According the actual tunnel project example, the result shows that the effect of the earth gravity model on plane control network can not be ignored.
不同地球重力场模型的优选及不同拟合方法的合理选择是GPS高程转换所需考虑的关键问题。随着以卫星重力梯度为主要观测值的GOCE重力卫星的发射成功及其相关重力场模型的推出,使得地球重力场模型的精度及分辨率有了较大提高,有必要将其应用于GPS高程转换的研究；现在精密工程测量中GPS与全站仪的共用是普遍存在的事实,这必然存在法线系统与垂线系统的转换问题,以往由于重力场模型精度较低,未能充分顾及到这种差别,而利用现有最新的地球重力场模型,能较精确地计算垂线偏差并将其应用于精密工程测量。
针对以上问题,本文提出了用目前具有较高精度的EGM2008和SGG地球重力场模型来代替以往较低精度地球重力场模型的策略,计算分析了这两种模型解算全球高程异常的精度,并将这两种模型应用于“移去-拟合-恢复”法的GPS高程转换中,可较好地移去高程异常的系统偏差,在此基础上分析了平面法、二次曲面法、正双曲面法、倒双曲面法及样条函数法用于高程异常拟合的精度,并通过某实际隧道工程算例验证了各种方法的精度。针对精密工程测量的特点,本文提出了顾及垂线偏差的GPS与全站仪的精密数据处理方法,通过“三差改正”将全站仪观测值转化为法线系统下的观测值,与GPS数据统一处理,利用某隧道算例验证了地球重力场模型对平面控制网数据处理的影响不容忽视。
In current days, GPS technology has been widely used in geodesy, engineering surveying, photogrammetry and remote sensing, crustal movement monitoring, deformation monitoring, geodynamics, and other research areas, it can simultaneous determine precise three-dimensional geodetic coordinate. Once the local geoid is determined, the ellipsoidal height of GPS point can be easily transformed to quasi-geoid height through precise quasi-geoid to replace the geometric leveling. The Earth gravity model and the determination of geoid is the main research area of gravity satellite, and the achievement of the gravity satellite research is another revolutionary breakthrough after GPS technology, which not only led to change in modern geodesy but also promote the development of other related disciplines. In precise engineering surveying, by combining high resolution gravity model with high precise GPS surveying, it is possible to improve the accuracy of GPS height transformation.
The key problem of transferring GPS leveling is to get an optimal combination of different gravity models and a reasonable selection of different fitting methods. Along with the successful launching of GOCE gravity satellite which takes gravity gradient as main observations and its related production of gravity model which greatly improves the accuracy and resolution of the Earth gravity model, and it is necessary to apply it to GPS leveling transformation. It is common to use both of GPS and total station in current precise engineering survey, which leads to the transformation problem between normal and vertical system. Because of the low precision of gravity model in the past, the effect of the problem is ignored. But now, with the latest available gravity field model, it is possible to calculate the vertical deflection and apply it to precise engineering survey.
Considering the problems mentioned above, the thesis proposes the method of using the latest higher precise EGM2008 and SGG gravity model to replace the gravity model in the past and analyzes the precision of height anomaly calculated respectively by two models. The thesis also applies the two models to the method of recovery - fitting- restore of GPS leveling transformation which can effectively remove the system error caused by height anomaly. Based on this the thesis analyzes the fitting accuracy of plane method. quadratic surface method, two-surface method, inverted double surface method and spline function method that is used to height anomaly fitting and validates the precision respectively by actual data of a actual tunnel project. According to the characteristic of precise engineering survey, the thesis proposes the precise GPS and total station data processing method taking the vertical deflection into account. The method first transform the total station observation data from normal to vertical system and then process data together with GPS data. According the actual tunnel project example, the result shows that the effect of the earth gravity model on plane control network can not be ignored.
引文
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[30]杨丹,奚以成.多面函数法在GPS高程拟合中的应用[J].辽宁省交通高等专科学校学报,2009,11(1)：40-42.
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[33]刘晓刚,刘雁雨,曹纪东,王丽红,庞振兴,陈少明.GPS采用移去恢复技术拟合大地水准面方法的研究[J].测绘工程,2008,17(3)：70-73.
[34]芮小平,余志伟,郁福梅.一种基于超曲面样条函数的三维空间插值方法[J].地理与地理信息科学,2006,22(6)：21-23.
[35]Sanburi J, Angelakis N, Jaeger R, Illner M, Jackson P. Height measurement of Kilimanjaro [J]. Survey Review,2000,35(278):552-556.
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[39]路伯祥,岑敏仪,卢健康.地球重力场模型在线路GPS高程转换中的应用[J].工程勘察,2004,(2).
[40]冯林刚,赵军,赵锁志.EGM2008模型在GPS高程转换中的应用研究[J].测绘信息与工程,2009,34(5)：6-8.
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[2]郑伟,许厚泽,钟敏,员美娟,彭碧波,周旭华.地球重力场模型研究进展和现状[J].大地测量学与地球动力学,2010,30(4)：83-91.
[3]Reigber Ch, et al. CHAMP phase-B executive summary[R]. G. F. Z., STR96/13, 1996.
[4]GRACE(1998)-Gravity Recovery and Climate Experiment:Science and mission requirements document, revision A[R]. JPLD-15928, NADA's Earth System Science Pathfinder Program.
[5]SA. Gravity field and steady-state ocean circulation mission (GOCE), Report for mission selection:The Four Candidate Earth Explorer core Mission[R]. ESA SP-1233/1, July,1999.
[6]宁津生.地球重力场模型及其应用[J].冶金测绘,1994,3(2).
[7]孙文科.低轨道人造卫星(CHAMP、GRACE、GOCE)与高精度地球重力场[J].大地测量与地球动力学,2002,22(1)：92-100.
[8]李克行,彭冬菊,黄碱,冯初刚.GOCE卫星重力计划及其应用[J].天文学进展,2005,23(1).
[9]陆仲连,吴晓平.人造地球卫星与地球重力场[M].北京：测绘出版社,1994：30-71.
[10]胡明成.现代大地测量学的理论及其应用[M].北京：测绘出版社,2003：84-101.
[11]钟波.基于GOCE卫星重力测量技术确定地球重力场的研究[D].武汉大学博士学位论文,2010,1-10.
[12]Muller J, Wermut M. GOCE gradients in various reference frames and their accuracies [J]. Advances in Geosciences,2003, (1).
[13]Zheng W, LuXL, XuHZ, et al. Simulation of Earth's gravitational field recovery from GRACE using the energy balance approach [J]. Progress in Natural Science, 2005,15(7).
[14]Reigber Ch, et al. The CHAMP-only Earth gravity field model EIGEN-2[J]. Advances in Space Research,2003,31(8).
[15]Featherstone W E. Refinement of Gravimetric geoid using GPS and leveling data [J]. Journal of Survey Engineering,2000,126(2):27-56.
[16]钟波,罗志才.GPS水准综合模型的应用研究[J].测绘通报,2007,(6).
[17]国家测绘局职业技能鉴定指导中心.测绘综合能力[M].北京：测绘出版社,2009：41-45.
[18]张勤,李家权等.GPS测量原理及应用[M].北京：科学出版社,2005：214-219.
[19]吴灵芳.几种GPS高程曲面拟合方法的比较与分析[J].山西建筑,2009,35(8)： 358-359.
[20]田建波,曾志林.利用GPS高求取正常高的几种拟合方法[J].海洋测绘,2004,24(2)：15-18.
[21]金时华.多面函数拟合法转换GPS高程[J].测绘与空间地理信启、,2005,28(6)：44-47.
[22]Sjoberg L E. A discussion on the approximations made in the practical implementation of the remove-compute-restore technique in regional geoid modeling[J]. J Geod, 2005,8(3):645-653.
[23]H. A. Abd-Elmotaall, N. Kulhtreiber2. Geoid determination using adapted reference field, seismic Moho depths and variable density contrast[J]. Journal of Geodesy, 2003,77(5).
[24]Heiskanen W A and Moritz H. Physical Geodesy[M]. Freeman W H and Company, San Francisco, California and London, UK,1967.
[25]陶本藻.GPS水准似大地水准面拟合和正常高计算[J].测绘通报,1992,(4)：14-18.
[26]陶本藻.论多面函数推估与协方差推估[J].测绘通报,2002,(9)：4-6.
[27]Houseman G, England P. Crustal thickening versus lateral expulsion in the Indian-Asian continental collision[J]. J Geophys Res,1993,98:12233-12249.
[28]Fu Y, Zhu W, Wang X, et al. Present-day crustal deformation in China relative to ITRF97 kinematic plate mode[J]. Journal of Geodesy,2002,76:216-225.
[29]Liddle D A. Orthometric height determination by GPS[J]. Surveying and Mapping, 1999(1):54-59.
[30]杨丹,奚以成.多面函数法在GPS高程拟合中的应用[J].辽宁省交通高等专科学校学报,2009,11(1)：40-42.
[31]马洪滨,董仲宇.多面函数GPS水准高程拟合中光滑因子求定方法[J].东北大学学报(自然科学版),2008,29(8)：1176-1178.
[32]徐卫明,陆秀平,朱穆华,梁德清.利用地球重力场模型精化GPS水准[J].海洋测绘,2003,23(2)：5-8.
[33]刘晓刚,刘雁雨,曹纪东,王丽红,庞振兴,陈少明.GPS采用移去恢复技术拟合大地水准面方法的研究[J].测绘工程,2008,17(3)：70-73.
[34]芮小平,余志伟,郁福梅.一种基于超曲面样条函数的三维空间插值方法[J].地理与地理信息科学,2006,22(6)：21-23.
[35]Sanburi J, Angelakis N, Jaeger R, Illner M, Jackson P. Height measurement of Kilimanjaro [J]. Survey Review,2000,35(278):552-556.
[36]胡伍生,华锡生,张志伟.平坦地区转换GPS高程的混合转换方法[J].测绘学报,2002,31(2)：128～133.
[37]魏子卿,王刚.用地球位模型和GPS/水准数据确定我国大陆似水准面[J].测绘学报,2003,32(1).
[38]游为,范东明,付淑娟,龙小林,龚志强.GPS高程转换的新方法研究[J].工程 勘察,2009,(3).
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