市级大地水准面精化的研究与应用
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摘要
柑化大地水准面是大地测量的重要研究内容之一,也是一项重要的基础测绘项目。随着全球地球重力场模型、地面的实测重力数据、GPS水准数据和数字地而模型等数据的丰富,为确定厘米级大地水准面提供了必要条件。确定区域高精度大地水准面的目的,一方面是大地测量学科发展的需要,另一方面是用GPS测量手段代替低等级的水准测量,在用GPS确定平面位置的同时,也能获得正常高,可以大幅度减少外业工作量和降低生产成本,加快成图周期,具有特别重要的科学意义和经济效益。
本文介绍了我国的高程系统及其相互关系,认真研究了精化大地水准面的几种方法,主要包括几何水准法、重力法以及组合法。基于厘米级似大地水准面的精度要求,系统的分析了似大地水准面精化过程中的数据融合、精度评定等问题,以及各种误差的影响以及控制方法,主要包括GPS水准测量的误差和重力数据误差(位系数精度、地形改正误差和重力异常误差等)。
本文利用全球重力位模型、胶州市地面重力观测数据、胶州市GPS水准数据和数字地面模型(DTM)采用组合法应用移去-恢复技术计算剩余大地水准面,并与地球位模型计算的高程异常进行拟合,得到该地区重力似大地水准面,再和布测、计算得到的GPS/水准所构成的几何大地水准面拟合,利用多项式拟合完成系统改正,获得最终的大地水准面结果及相关的精度信息。
Refinement of local geoid is one of the importing issue of the geodesy, and same time, it also is an import basic surveying project. Along with a large numbers of the earth gravity field model, gravity data in the earth surface, GPS/leveling data, digital terrain model and other related data, the refinement of centimeter order geoid has been provided with necessary conditions. The purpose of refining high accuracy local geoid, one is to develop physical geodesy, the other is to solve the problem that replace the low accuracy leveling by GPS surveying. Thus in using GPS determines the plane position while also determines normal height to cut the field work and the production cost and has important scientific significance and economic benefits.
At first the article describes the national geodetic reference systems and the relationship of each other, researches principle of several kind methods of geoid refinement systematically, mainly include geometric leveling method, gravimetric method and combination method. Then in view of the precision demand of centimeter order quasi-geoid, the data assimilation and precision assess in quasi-geoid refinement were systematically analyzed. Analyze the influence from all kinds of error and the methods to control them. The error mainly includes GPS/leveling measurement and the gravity data such as potential coefficient error, terrain correction error and gravity anomaly error.
Based on the above theory the article chooses combination method (Molodensky theory) using the remove-restore technique to compute remainder geoid. We supplied available data which come from the Whole World Gravity Field Model, the gravity data in Jiaozhou, the GPS/leveling data in Jiaozhou and the digital terrain model. We determined the local gravity geoid by fitting the remainder geoid with height anomaly which was computed by the Whole World Gravity Field Model. Then the local gravity geoid is combined with geometric geoid obtained from GPS leveling and systematically corrected by the least square collocation method. Then we gained the result of this regional geoid and the information about its precision.
本文介绍了我国的高程系统及其相互关系,认真研究了精化大地水准面的几种方法,主要包括几何水准法、重力法以及组合法。基于厘米级似大地水准面的精度要求,系统的分析了似大地水准面精化过程中的数据融合、精度评定等问题,以及各种误差的影响以及控制方法,主要包括GPS水准测量的误差和重力数据误差(位系数精度、地形改正误差和重力异常误差等)。
本文利用全球重力位模型、胶州市地面重力观测数据、胶州市GPS水准数据和数字地面模型(DTM)采用组合法应用移去-恢复技术计算剩余大地水准面,并与地球位模型计算的高程异常进行拟合,得到该地区重力似大地水准面,再和布测、计算得到的GPS/水准所构成的几何大地水准面拟合,利用多项式拟合完成系统改正,获得最终的大地水准面结果及相关的精度信息。
Refinement of local geoid is one of the importing issue of the geodesy, and same time, it also is an import basic surveying project. Along with a large numbers of the earth gravity field model, gravity data in the earth surface, GPS/leveling data, digital terrain model and other related data, the refinement of centimeter order geoid has been provided with necessary conditions. The purpose of refining high accuracy local geoid, one is to develop physical geodesy, the other is to solve the problem that replace the low accuracy leveling by GPS surveying. Thus in using GPS determines the plane position while also determines normal height to cut the field work and the production cost and has important scientific significance and economic benefits.
At first the article describes the national geodetic reference systems and the relationship of each other, researches principle of several kind methods of geoid refinement systematically, mainly include geometric leveling method, gravimetric method and combination method. Then in view of the precision demand of centimeter order quasi-geoid, the data assimilation and precision assess in quasi-geoid refinement were systematically analyzed. Analyze the influence from all kinds of error and the methods to control them. The error mainly includes GPS/leveling measurement and the gravity data such as potential coefficient error, terrain correction error and gravity anomaly error.
Based on the above theory the article chooses combination method (Molodensky theory) using the remove-restore technique to compute remainder geoid. We supplied available data which come from the Whole World Gravity Field Model, the gravity data in Jiaozhou, the GPS/leveling data in Jiaozhou and the digital terrain model. We determined the local gravity geoid by fitting the remainder geoid with height anomaly which was computed by the Whole World Gravity Field Model. Then the local gravity geoid is combined with geometric geoid obtained from GPS leveling and systematically corrected by the least square collocation method. Then we gained the result of this regional geoid and the information about its precision.
引文
1.张风举,张华海,赵长胜等.控制测量学[M].北京：煤炭工业出版社,1999,6-7
2.李建成,陈俊勇,宁津生等.地球重力场逼近理论与中国2000似大地水准面的确定[M].武汉：武汉大学出版社,2005,76-82
3.宁津生,邱卫根,陶本藻.地球重力场模型理论[M].武汉：武汉测绘科技大学出版社,1990,49-52
4.许厚泽,陆仲连.中国地球重力场与大地水准面[M].北京：解放军出版社,1997,18-23
5.宁津生,李建成,晁定波等.WDM94 360阶地球重力场模型研究[J],武汉测绘科技大学学报,1994,19(4)：283-291
6.陈俊勇.高精度局域大地水准面对布测GPS水准和重力的要求[J],测绘学报,2001,30(3)：189-191
7.陈俊勇,文汉江,程鹏飞.中国大地测量学发展的若干问题[J],武汉大学学报信息科学版,2001,26(6)：475-482
8.胡明城。现代大地测量学的理论及其应用[M].北京：测绘出版社,2003,84-99
9.管泽霖,李建成,晁定波,等.WZD94中国大地水准面研究[J],武汉测绘科技大学学报,1994,29(4)：292-297
10.管泽霖等。地球形状及外部重力场[M].北京：测绘出版社,1980,87-92
11.陈俊勇等.迈入新千年的大地测量学-第22届IUGG大会有关大地测量部分的技术总结[J],测绘学报,2000,24(1)：96-101
12.罗志才,陈永奇,宁津生.地形对确定高精度局部大地水准面的影响[J],武汉大学学报(信息科学版),2003,28(3)：340-344
13.马林波等.利用重力成果解算GPS网点正常高[J],东北测绘.2001,24(4)：5-6
14.陈俊勇,李建成.推算我国高精度和高分辨率似大地水准面的若干技术问题[J],武汉测绘科技大学学报,1998,23(2)：95-99
15.宁津生,刘经南,陈俊勇等.现代大地测量理论与技术[M].武汉：武汉大学出版社,2006,46-59
16.宁津生,罗志才,李建成.我国省市级大地水准面精化的现状及技术模式[J],大地测量与地球动力学,2004,24(1)：4-8
17.陈俊勇。高程异常控制网中利用重力数据进行估的精度评定[J],测绘学报，1995,(3)： 96-99
18.汤国安,刘学军,闾国年。数字高程模型及地学分析的原理与方法[M].北京：科学出版社,2005,57-62
19.魏子卿,王刚.用地球位模型和GPS/水准数据确定我国大陆似大地水准面[J],测绘学报,2003,32(1)：1-5
20.许才军.地球重力场和大地水准面精确求定新进展[J],武汉测绘科技大学学报,1996,12(3)：45-47
21.陈俊勇,李建成,宁津生等.中国新一代高精度、高分辨率大地水准面的研究和实施[J],武汉大学学报(信息科学版),2001,26(4)：283-289
22.章传银,党亚民,晁定波等.似大地水准面的误差分析与抑制技术[J],测绘科学,2006,31(6)：27-29
23.畅毅,姜卫平.局部似大地水准面精化技术及其应用现状分析[J],物探装备,2006,16(4)：255-260
24.张全德,张燕平,张鹏等。精化区域大地水准面若干问题的探讨[J],武汉大学学报(信息科学版),2003,28(Special Issue):94-96
25.周兴华,姚艺强,赵吉先.DEM内插方法与精度评定[J],测绘科学,2005,30(5)：86-88
26.周忠谟,易杰军,周琪.GPS卫星测量原理与应用[M].北京：测绘出版社.2004,226-237
27.邹贤才,李建成.最小二乘配置方法确定局部大地水准面的研究[J],武汉大学学报(信息科学版).2004,29(3)：218-221
28. Ellipsoidal Geoidal Undulations(Ellipsoidal Bruns Formula):Case Studies/Ardalan A A,Grafarend E W//Journal of Geodesy.-2001,75(9/10),544-552
26. An Improved Local Geoid in the Mt.Everest Area/Chen J Y...//ZfV,1999(11):362-363
27. National Height Datum,the Gauss-Listing Geoid Level Value Wg and its Time ariation(Baltic Sea Level Project:Epochs 1990.8,1997.4)/Ardalan A Grafarend E,Kakkuri J//Journal of Geodesy,2002,76(1):1-28
28.Determination of active units with different kinematic property and their activity pattern in North China based on the data from GPS remeasurements:Acta Seismologica Sinica,2001,(1):2-28
29. GPS measurement of surface deformation around Soufriere Hills volcano, Montserrat from October 1995 to July 1996 Mattioli, Glen S.;Dixon,Timothy H.;Farina,Fredric; Howell,Ellen S.;Jansma,Pamela E.;Smith,Alan LGeophysical Research Letters,1998,25(18): 3417-3420
30. G Strang van Hees. Precision of the geoid, computed from terrestrial gravity measure-ments [J]. manuscripta geodaetica,1986, (11):1-14
31.GPS estimate of relative motion between North and SouthAmerica.Dixon,Timothy;Mao, Ailin.Geophysical.Research Letters,-1997,24(5):535-538
32.Smith DA and Roman DR.GEOID99and G99SSS:1-arcminute Geoid Models for the United States [J].Journal ofGeodesy,2001,75:469-490
33. CHEN Jun-yong. Accuracy Evaluation for the Height Anomaly Prediction means of Gravity Data in a Height Anomaly Control Network [J]. Acta Geod et Carto Sinica 1995,24 (3):161-167
34. State Bureau of Surveying and Mapping. Atlas of Geodesy in China [M].Beijing:State Bureau of Surveying and Mapping,1986
35. Bjerhammar A.(1974) Discrete approach to the solution of the boundary value problem in physical geodesy. Internation School of Geodesy Eriche 1974
36. HEISKANEN W.A.MORITZ Physical Publishing House of Surveying & Mapping,1967
37. Moritz H.Local geoid determination in mountainous areas [R].Report No.353. Department of Geodetic Science and Surveying, The Ohio State University,1983
38. Engelis T, Rapp R.H, Bock Y(1985). Measuring orthometric height differences with GPS and gravity data. Manuscripta Geodaetica, vol.10, PP.187-194 Featherston W(2000). Refinement of gravimetric geoid using GPS and levelling data. Journal og Surveying Engineering, vol.126, no.2, May 2000, pp.27-56
39. Forsberg R.(1984) A study of terrain reductions, density anomalies and geophysical inverseion methods in gravity field modelling, Reports of the Department of Geodetic Science and Surveying, NO.335, The Ohio State Univeristy, Columbus, Ohio
40. Fotopoulos G.(2003). An Analysis on the Optimal Combination of Geoid, Orthometricand Ellipsoidal Height Data, UCGE Report No.20185. Department of Geomatics Engineering, University of Galgary
41. Grafarend E.W., Ardalan A.A., Sideris M.(1999) The ellipsoidal fixed-free two-boundary value problem for geoid determination (the ellipsoidal Bruns transform). Journal of Geodesy 73:513-533
42. Helmut Moritz. (1976) Covariance Functions in Least-Squares Collocation. Report of the Department of Geodetic Science Report No.240 OSU
43. Jekeli C.(1981) The downward continuation to the earth's surface of truncated spherical and ellipsoidal harmonic series of the gravity and height anomalies. Report 323, Ohio State Univeristy Department of Geodeic Science and Surveying, Columbus Ohio 1981
44. Jiang Z., Duquenne H(1996). On the combined adjustment of a gravimerically determined geoid and GPS levelling stations. Journal of Geodesy, vol.70, pp.505-514
45. Martinec Z. (1988a) Boundary-value problem for gravimetric determination of a precise geoid. Springer Verlag, Berlin 1998
46. Omang O.C.D, Forsberg R.(2000) How to handle topography in practical geoid determination:three examples. Journal of Geodesy 74:458-466
47. Rappa R. (1992) Use of potenial coefficients models for geoid undulation determinations using a spherical harmonic representation of height anomaly/geoid undulation difference. Journal of Geodesy 71:282-289
48. Rummel.D, Teunissen. P.J.G, Van Gelderen.M,(1989) Uniquenly and over determined geodetic boundary value problems by lease squares. Bull. Geod,63,1-33
49. Sjoeberg L.E. (1998) The external Airy/Heiskanen topographic-isostatic gravity potenial, anomaly and the effect of analytical continuation. Journal of Geodesy 11:654-662
50. Sj o eberg L.E. (2000) Topographic effect by the Stokes-Helmert method of geoid and quai-geoid determinations. Journal of Geodesy 74:255-268
51. Tshcherning C.C., Rapp R.H., Goad C.(1983) A comparison of methods for computing gravimetric quantities from hight degree spherical harmonic expansions. Manuscripta geodaetica 8:249-272
52. Tshcherning C.C.(2001). Computation of spherical harmonic coefficients and their error estimates using least-squares collocation,.Journal of Geodesy, vol.75, pp.12-18
53. Vanicek P., Featherstone W.E.(1998). Performance of three types of Stokes's kernel in the combined solution for the geoid. Journal of Geodesy 72:684-697
54. Vanicek etc., Determination of the boundary values for the Stokes-Helmert problem, Journal of Geodesy,1999,73:180-192
55. W.E. Featherstone, A comparison of gravimetric geoid models over Western Australia, computed using modified forms of Stokes's integral, Journal of the Royal Society of Western Australia,1999,82(4):137-145
2.李建成,陈俊勇,宁津生等.地球重力场逼近理论与中国2000似大地水准面的确定[M].武汉：武汉大学出版社,2005,76-82
3.宁津生,邱卫根,陶本藻.地球重力场模型理论[M].武汉：武汉测绘科技大学出版社,1990,49-52
4.许厚泽,陆仲连.中国地球重力场与大地水准面[M].北京：解放军出版社,1997,18-23
5.宁津生,李建成,晁定波等.WDM94 360阶地球重力场模型研究[J],武汉测绘科技大学学报,1994,19(4)：283-291
6.陈俊勇.高精度局域大地水准面对布测GPS水准和重力的要求[J],测绘学报,2001,30(3)：189-191
7.陈俊勇,文汉江,程鹏飞.中国大地测量学发展的若干问题[J],武汉大学学报信息科学版,2001,26(6)：475-482
8.胡明城。现代大地测量学的理论及其应用[M].北京：测绘出版社,2003,84-99
9.管泽霖,李建成,晁定波,等.WZD94中国大地水准面研究[J],武汉测绘科技大学学报,1994,29(4)：292-297
10.管泽霖等。地球形状及外部重力场[M].北京：测绘出版社,1980,87-92
11.陈俊勇等.迈入新千年的大地测量学-第22届IUGG大会有关大地测量部分的技术总结[J],测绘学报,2000,24(1)：96-101
12.罗志才,陈永奇,宁津生.地形对确定高精度局部大地水准面的影响[J],武汉大学学报(信息科学版),2003,28(3)：340-344
13.马林波等.利用重力成果解算GPS网点正常高[J],东北测绘.2001,24(4)：5-6
14.陈俊勇,李建成.推算我国高精度和高分辨率似大地水准面的若干技术问题[J],武汉测绘科技大学学报,1998,23(2)：95-99
15.宁津生,刘经南,陈俊勇等.现代大地测量理论与技术[M].武汉：武汉大学出版社,2006,46-59
16.宁津生,罗志才,李建成.我国省市级大地水准面精化的现状及技术模式[J],大地测量与地球动力学,2004,24(1)：4-8
17.陈俊勇。高程异常控制网中利用重力数据进行估的精度评定[J],测绘学报，1995,(3)： 96-99
18.汤国安,刘学军,闾国年。数字高程模型及地学分析的原理与方法[M].北京：科学出版社,2005,57-62
19.魏子卿,王刚.用地球位模型和GPS/水准数据确定我国大陆似大地水准面[J],测绘学报,2003,32(1)：1-5
20.许才军.地球重力场和大地水准面精确求定新进展[J],武汉测绘科技大学学报,1996,12(3)：45-47
21.陈俊勇,李建成,宁津生等.中国新一代高精度、高分辨率大地水准面的研究和实施[J],武汉大学学报(信息科学版),2001,26(4)：283-289
22.章传银,党亚民,晁定波等.似大地水准面的误差分析与抑制技术[J],测绘科学,2006,31(6)：27-29
23.畅毅,姜卫平.局部似大地水准面精化技术及其应用现状分析[J],物探装备,2006,16(4)：255-260
24.张全德,张燕平,张鹏等。精化区域大地水准面若干问题的探讨[J],武汉大学学报(信息科学版),2003,28(Special Issue):94-96
25.周兴华,姚艺强,赵吉先.DEM内插方法与精度评定[J],测绘科学,2005,30(5)：86-88
26.周忠谟,易杰军,周琪.GPS卫星测量原理与应用[M].北京：测绘出版社.2004,226-237
27.邹贤才,李建成.最小二乘配置方法确定局部大地水准面的研究[J],武汉大学学报(信息科学版).2004,29(3)：218-221
28. Ellipsoidal Geoidal Undulations(Ellipsoidal Bruns Formula):Case Studies/Ardalan A A,Grafarend E W//Journal of Geodesy.-2001,75(9/10),544-552
26. An Improved Local Geoid in the Mt.Everest Area/Chen J Y...//ZfV,1999(11):362-363
27. National Height Datum,the Gauss-Listing Geoid Level Value Wg and its Time ariation(Baltic Sea Level Project:Epochs 1990.8,1997.4)/Ardalan A Grafarend E,Kakkuri J//Journal of Geodesy,2002,76(1):1-28
28.Determination of active units with different kinematic property and their activity pattern in North China based on the data from GPS remeasurements:Acta Seismologica Sinica,2001,(1):2-28
29. GPS measurement of surface deformation around Soufriere Hills volcano, Montserrat from October 1995 to July 1996 Mattioli, Glen S.;Dixon,Timothy H.;Farina,Fredric; Howell,Ellen S.;Jansma,Pamela E.;Smith,Alan LGeophysical Research Letters,1998,25(18): 3417-3420
30. G Strang van Hees. Precision of the geoid, computed from terrestrial gravity measure-ments [J]. manuscripta geodaetica,1986, (11):1-14
31.GPS estimate of relative motion between North and SouthAmerica.Dixon,Timothy;Mao, Ailin.Geophysical.Research Letters,-1997,24(5):535-538
32.Smith DA and Roman DR.GEOID99and G99SSS:1-arcminute Geoid Models for the United States [J].Journal ofGeodesy,2001,75:469-490
33. CHEN Jun-yong. Accuracy Evaluation for the Height Anomaly Prediction means of Gravity Data in a Height Anomaly Control Network [J]. Acta Geod et Carto Sinica 1995,24 (3):161-167
34. State Bureau of Surveying and Mapping. Atlas of Geodesy in China [M].Beijing:State Bureau of Surveying and Mapping,1986
35. Bjerhammar A.(1974) Discrete approach to the solution of the boundary value problem in physical geodesy. Internation School of Geodesy Eriche 1974
36. HEISKANEN W.A.MORITZ Physical Publishing House of Surveying & Mapping,1967
37. Moritz H.Local geoid determination in mountainous areas [R].Report No.353. Department of Geodetic Science and Surveying, The Ohio State University,1983
38. Engelis T, Rapp R.H, Bock Y(1985). Measuring orthometric height differences with GPS and gravity data. Manuscripta Geodaetica, vol.10, PP.187-194 Featherston W(2000). Refinement of gravimetric geoid using GPS and levelling data. Journal og Surveying Engineering, vol.126, no.2, May 2000, pp.27-56
39. Forsberg R.(1984) A study of terrain reductions, density anomalies and geophysical inverseion methods in gravity field modelling, Reports of the Department of Geodetic Science and Surveying, NO.335, The Ohio State Univeristy, Columbus, Ohio
40. Fotopoulos G.(2003). An Analysis on the Optimal Combination of Geoid, Orthometricand Ellipsoidal Height Data, UCGE Report No.20185. Department of Geomatics Engineering, University of Galgary
41. Grafarend E.W., Ardalan A.A., Sideris M.(1999) The ellipsoidal fixed-free two-boundary value problem for geoid determination (the ellipsoidal Bruns transform). Journal of Geodesy 73:513-533
42. Helmut Moritz. (1976) Covariance Functions in Least-Squares Collocation. Report of the Department of Geodetic Science Report No.240 OSU
43. Jekeli C.(1981) The downward continuation to the earth's surface of truncated spherical and ellipsoidal harmonic series of the gravity and height anomalies. Report 323, Ohio State Univeristy Department of Geodeic Science and Surveying, Columbus Ohio 1981
44. Jiang Z., Duquenne H(1996). On the combined adjustment of a gravimerically determined geoid and GPS levelling stations. Journal of Geodesy, vol.70, pp.505-514
45. Martinec Z. (1988a) Boundary-value problem for gravimetric determination of a precise geoid. Springer Verlag, Berlin 1998
46. Omang O.C.D, Forsberg R.(2000) How to handle topography in practical geoid determination:three examples. Journal of Geodesy 74:458-466
47. Rappa R. (1992) Use of potenial coefficients models for geoid undulation determinations using a spherical harmonic representation of height anomaly/geoid undulation difference. Journal of Geodesy 71:282-289
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