基于相对高程异常差平差法的区域似大地水准面精化
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摘要
本文针对厘米级精度似大地水准面的工程应用需求,在现有数据的基础上,充分挖掘和利用重力数据中的高频信息,获得高精度的相对高程异常差,进而利用GPS/水准点进行严密的控制平差,将重力似大地水准面强制约束到GPS/水准似大地水准面上,最终获得了厘米级精度的局部似大地水准面格网数值模型。
本文的主要工作和创新点如下:
1.分析了精化(似)大地水准面的理论和方法,结合CGGM2000的建立研究了移去-恢复法和GPS/水准拟合法的具体应用。
2.研究了垂线偏差及其计算得到的高程异常差对地形高频信息的敏感性;推导了高程异常的重力异常改正项计算公式并对其进行了定量分析;分析了GPS/水准拟合法精化(似)大地水准面存在的不足。
3.提出了一种综合利用垂线偏差、重力异常、GPS/水准等数据的精化局部区域似大地水准面的方法——相对高程异常差平差法。
4.研究了针对高程异常差格网数据的平差计算方法,分析了传统的根据测段距离定权的参数平差方法在存有系统偏差的大型格网数据进行强约束平差中存在的问题,提出了两种适合于格网数据的参数平差方法:根据观测量(即高程异常差)到控制点的距离定权的格网平差法和根据路线控制的分步平差法。
5.分别在平原和山区地形条件下,计算分析了高程异常差平差法进行似大地水准面精化的相对精度和绝对精度。
Aiming at the requirements of engineering applications of cm-level quasi-geoid, the dissertation proposed a method for obtaining local cm-level quasi-geoid from known gravity anomalies and other data. Through making full use of the high-frequency information within gravity observations, firstly the relative difference of height anomaly was obtained with high accuracy, and then by making a strict controlled adjustment on GPS/leveling points, the gravimetrical quasi-geoid was mandatorily constrained to the GPS quasi-geoid, and finally the numerical grid model of cm-level local quasi-geoid was established. In the dissertation the following work has been completed.
1. The conventional theories and methods for the determination of geoid and/or quasi-geoid were discussed. Then taking the establishment of CGGM2000, the remove-and-restore technique for refining the quasi-geoid and the theory of GPS/leveling fitting were also researched.
2. The sensitivity of vertical deflections and height anomaly difference obtained using the former to the high frequency terrain information was studied. The formula of the gravity anomaly correction term for height anomaly was derived and analyzed quantitatively. The defects of the GPS/leveling fitting method were also analyzed.
3. A method was proposed for the refining of the local quasi-geoid using vertical deflections, gravity anomalies, GPS/leveling comprehensively, which was called relative height anomaly difference adjustment.
4. The adjustment method that deals with grid height anomaly difference was studied. The problems were analyzed in the application of the parametric adjustment in which weights are determined in terms of distances in strongly constrained adjustment of large grid where there exist systematic errors. Two parametric adjustment methods that apply to grid data were proposed. One is the grid adjustment method in which weights were determined in terms of the distance from the observed point to the control point; and the other is the step-wise adjustment method that relies on route.
5. The relative accuracy and absolute accuracy in the refining of quasi-geoid using the height anomaly difference adjustment were calculated and discussed for plains and mountainous areas respectively.
本文的主要工作和创新点如下:
1.分析了精化(似)大地水准面的理论和方法,结合CGGM2000的建立研究了移去-恢复法和GPS/水准拟合法的具体应用。
2.研究了垂线偏差及其计算得到的高程异常差对地形高频信息的敏感性;推导了高程异常的重力异常改正项计算公式并对其进行了定量分析;分析了GPS/水准拟合法精化(似)大地水准面存在的不足。
3.提出了一种综合利用垂线偏差、重力异常、GPS/水准等数据的精化局部区域似大地水准面的方法——相对高程异常差平差法。
4.研究了针对高程异常差格网数据的平差计算方法,分析了传统的根据测段距离定权的参数平差方法在存有系统偏差的大型格网数据进行强约束平差中存在的问题,提出了两种适合于格网数据的参数平差方法:根据观测量(即高程异常差)到控制点的距离定权的格网平差法和根据路线控制的分步平差法。
5.分别在平原和山区地形条件下,计算分析了高程异常差平差法进行似大地水准面精化的相对精度和绝对精度。
Aiming at the requirements of engineering applications of cm-level quasi-geoid, the dissertation proposed a method for obtaining local cm-level quasi-geoid from known gravity anomalies and other data. Through making full use of the high-frequency information within gravity observations, firstly the relative difference of height anomaly was obtained with high accuracy, and then by making a strict controlled adjustment on GPS/leveling points, the gravimetrical quasi-geoid was mandatorily constrained to the GPS quasi-geoid, and finally the numerical grid model of cm-level local quasi-geoid was established. In the dissertation the following work has been completed.
1. The conventional theories and methods for the determination of geoid and/or quasi-geoid were discussed. Then taking the establishment of CGGM2000, the remove-and-restore technique for refining the quasi-geoid and the theory of GPS/leveling fitting were also researched.
2. The sensitivity of vertical deflections and height anomaly difference obtained using the former to the high frequency terrain information was studied. The formula of the gravity anomaly correction term for height anomaly was derived and analyzed quantitatively. The defects of the GPS/leveling fitting method were also analyzed.
3. A method was proposed for the refining of the local quasi-geoid using vertical deflections, gravity anomalies, GPS/leveling comprehensively, which was called relative height anomaly difference adjustment.
4. The adjustment method that deals with grid height anomaly difference was studied. The problems were analyzed in the application of the parametric adjustment in which weights are determined in terms of distances in strongly constrained adjustment of large grid where there exist systematic errors. Two parametric adjustment methods that apply to grid data were proposed. One is the grid adjustment method in which weights were determined in terms of the distance from the observed point to the control point; and the other is the step-wise adjustment method that relies on route.
5. The relative accuracy and absolute accuracy in the refining of quasi-geoid using the height anomaly difference adjustment were calculated and discussed for plains and mountainous areas respectively.
引文
[1] W.A.海斯卡涅H.莫里斯,物理大地测量学,测绘出版社,1979
[2]陆仲连(1996).地球重力场理论与方法[M].北京:解放军出版社
[3]陆仲连,吴晓平(1994).人造地球卫星与地球重力场[M].北京:测绘出版社
[4]陆仲连,吴晓平等编著(1993).弹道导弹重力学[M].北京:八一出版社
[5]郭俊义(1994).物理大地测量学基础.武汉:武汉测绘科技大学出版社
[6]管泽霖,管铮,黄谟涛翟国君(1996).局部重力场逼近理论和方法.北京:测绘出版社
[7]李建成,陈俊勇,宁津生,晁定波(2003).地球重力场逼近理论与中国2000似大地水准面的确定.武汉:武汉大学出版社
[8]宁津生,刘经南,陈俊勇,淘本藻等(2006).现代大地测量理论与技术[M].武汉:武汉大学出版社
[9]许才军,申文斌,晁定波(2006).地球物理大地测量学原理与方法.武汉:武汉大学出版社
[10]党亚民,成英燕,薛树强(2010).大地坐标系统及其应用.北京:测绘出版社
[11]李征航,黄劲松(2005).GPS测量与数据处理.武汉:武汉大学出版社
[12]吴晓平,李姗姗,张传定(2003).扰动重力边值问题与实际数据处理的研究.武汉大学学报·信息科学版
[13]吴晓平,孙凤华,张传定.我国重力场与大地水准面的确定和改进.信息工程大学学报
[14]张传定(2000).卫星重力测量——基础、模型化方法与数据处理算法[博士论文].信息工程大学测绘学院,2004,5(2)
[15]边少锋(1992).大地测量边值问题数值解法与地球重力场逼近[博士论文].武汉测绘科技大学
[16]陆仲连(1988).球谐函数[M].北京:解放军出版社
[17]张嗥.快速逼近弹道扰动引力的算法研究[D] .郑州:解放军信息工程大学测绘学院.2007
[18]朱雷鸣吴晓平.高精度高分辨率的地球重力场模型EGM2008.军事测绘,2009,3
[19]刘长建吴洪举陈少明.GPS水准移动曲面法功能新探.全球定位系统,2006,1
[20]吴太旗黄谟涛欧阳永忠陆秀平.高精度海洋重力异常格网插值技术研究.测绘科学,2008,33(5)
[21]宁津生(1994).地球重力场模型及其应用[J].冶金测绘, 3(2):1-8
[22]宁津生(2001).跟踪世界发展动态、致力地球重力场研究[J].武汉大学学报·信息科学版,26(6):471-474
[23]宁津生,丘卫根,陶本藻(1990).地球重力场模型理论[M].武汉:武汉测绘科技大学出版社
[24]石磐(1994).利用局部重力数据改进重力场模型[J].测绘学报,23(4)
[25]许厚泽(1991).利用局部重力资料改善高阶地球重力场模型[J].动力大地测量学进展,地震出版社,1991
[26]许厚泽,陆仲连等(1997).中国地球重力场与大地水准面[M].北京,解放军出版社
[27]于锦海(1992).物理大地测量边值问题的理论[博士论文].中国科学院测量与地球物理研究所
[28]张传定(2004).地球重力场模型化理论与方法研究[博士后研究工作报告].中国科学院测量与地球物理研究所
[29]张传定,吴晓平,陆仲连(2000).全张量重力梯度数据的谱表示[J].测绘学报,29(4): 297-304
[30]赵东明(2004).卫星跟踪卫星任务的引力谱分析和状态估计方法[博士论文].信息工程大学测绘学院
[31] Pavlis, N.K., S.A. Holmes, S.C. Kenyon, and J.K. Factor, An Earth Gravitational Model to Degree 2160: EGM2008, presented at the 2008 General Assembly of the European Geosciences Union, Vienna, Austria, April 13-18, 2008.
[32] http://earth-info.nima.mil/GandG/
[33] Smith DA and Roman DR.GEOID99 and G99SSS:1-arcminute Geoid Models for the United States[j].Journal of Geodesy,2001,75:469—490
[34] D.R.Roman,Development of the North American Gravimetric Geoid: Adapting the Process to Determine a Unified Central American Geoid, USA National Geodetic Survey,2001
[35] Heiskanen W A,Moritz H.Physical Geodesy[M].San Francisco and London:W H Freeman Co,1967
[36] Vanicek P,ZHANG Changyou,Sjoberg L E.A comparison of Stokes and Hotine’s approaches to geoid computation[J].Manu.Geod,1992,17:29～35
[37] HAAGMANS R R N,de MINE,van GELDERENM.Fast Evaluation of Convolution Integrals on the Sphere Using 1-D FFT,and a Comparison with Existing Methods for Stokes’s Integral[J].Manuscr Geed,1993,(18):227~241
[38] Bjerhammar, A., A Review of Discrete Methods in Physical Geodesy, in Approximation Methods in Physical Geodesy, H.Moritz and H.Sunkel, Herbert Wichmann Verlag, Karisruhe,1978
[39] Cruz, J.Y. and P.Laskowski, Upward Continuation of Surface Gravity Anomalies, Report No.360,Dept. of Geodetic Science and Surveying , the Ohio State University ,December 1984
[40] Jekeli, C. The Downward Continuation to the Earth's Surface of Truncated Spherical and Ellipsoidal Harmonic Series of the Gravity and Height Anomalies, Report No.323, Dept. of Geodetic Science and Surveying , The Ohio State University , December 1981
[41] Moritz, H. Advanced Physical Geodesy, Herbert Wichmann Verlag, Karisruhe, 1980
[42] Rapp, R.H., Ellipsoidal Corrections for Geoid Undulation Computations, Report No.308, Dept. of Geodetic Science and Surveying ,The Ohio State University, March 1981
[43] Sjoberg, L., On the Discrete Boundary Value Problem of Physical Geodesy With Harmonic Reduction to an Internal Sphere, Division of Geodesy, The Royal Institute of Technology, Stockholm,1975
[44] Haines GV.Compute programs for Spherical cap harmonic analysis of potential and general fields[J].Compute Geosci.1988
[45] Haines GV,Torta JM.Determination of equivalent current sources from spherical cap harmonic of geomanetic field variations[J].Geophy J Int.1994
[46] Koch K R,Pope A J.Uniqueness and existence for the geodetic boundary value problem using the known surface of the Earth.Bull.Geod.,1972,46:167-176
[47] Bjerhammar A,Svensson L.On the geodetic boundary value problem for a fixed boundary surface-A satellite approach.Bull.Geod.,1983,57:382-393
[48] Migliaccio F, Sanso F(1989). The boundary value problem approach to the data reduction for a space borne gradiometer mission[A]. IAG Symposia 103[C]. Springer Verlag, Berlin, Heidleberg, NewYork.67～77
[49] KellerW(1994), HirschM. A boundary value approach to downward continuation [J]. Manuscripta Geodaetica , 19(2):101～118
[2]陆仲连(1996).地球重力场理论与方法[M].北京:解放军出版社
[3]陆仲连,吴晓平(1994).人造地球卫星与地球重力场[M].北京:测绘出版社
[4]陆仲连,吴晓平等编著(1993).弹道导弹重力学[M].北京:八一出版社
[5]郭俊义(1994).物理大地测量学基础.武汉:武汉测绘科技大学出版社
[6]管泽霖,管铮,黄谟涛翟国君(1996).局部重力场逼近理论和方法.北京:测绘出版社
[7]李建成,陈俊勇,宁津生,晁定波(2003).地球重力场逼近理论与中国2000似大地水准面的确定.武汉:武汉大学出版社
[8]宁津生,刘经南,陈俊勇,淘本藻等(2006).现代大地测量理论与技术[M].武汉:武汉大学出版社
[9]许才军,申文斌,晁定波(2006).地球物理大地测量学原理与方法.武汉:武汉大学出版社
[10]党亚民,成英燕,薛树强(2010).大地坐标系统及其应用.北京:测绘出版社
[11]李征航,黄劲松(2005).GPS测量与数据处理.武汉:武汉大学出版社
[12]吴晓平,李姗姗,张传定(2003).扰动重力边值问题与实际数据处理的研究.武汉大学学报·信息科学版
[13]吴晓平,孙凤华,张传定.我国重力场与大地水准面的确定和改进.信息工程大学学报
[14]张传定(2000).卫星重力测量——基础、模型化方法与数据处理算法[博士论文].信息工程大学测绘学院,2004,5(2)
[15]边少锋(1992).大地测量边值问题数值解法与地球重力场逼近[博士论文].武汉测绘科技大学
[16]陆仲连(1988).球谐函数[M].北京:解放军出版社
[17]张嗥.快速逼近弹道扰动引力的算法研究[D] .郑州:解放军信息工程大学测绘学院.2007
[18]朱雷鸣吴晓平.高精度高分辨率的地球重力场模型EGM2008.军事测绘,2009,3
[19]刘长建吴洪举陈少明.GPS水准移动曲面法功能新探.全球定位系统,2006,1
[20]吴太旗黄谟涛欧阳永忠陆秀平.高精度海洋重力异常格网插值技术研究.测绘科学,2008,33(5)
[21]宁津生(1994).地球重力场模型及其应用[J].冶金测绘, 3(2):1-8
[22]宁津生(2001).跟踪世界发展动态、致力地球重力场研究[J].武汉大学学报·信息科学版,26(6):471-474
[23]宁津生,丘卫根,陶本藻(1990).地球重力场模型理论[M].武汉:武汉测绘科技大学出版社
[24]石磐(1994).利用局部重力数据改进重力场模型[J].测绘学报,23(4)
[25]许厚泽(1991).利用局部重力资料改善高阶地球重力场模型[J].动力大地测量学进展,地震出版社,1991
[26]许厚泽,陆仲连等(1997).中国地球重力场与大地水准面[M].北京,解放军出版社
[27]于锦海(1992).物理大地测量边值问题的理论[博士论文].中国科学院测量与地球物理研究所
[28]张传定(2004).地球重力场模型化理论与方法研究[博士后研究工作报告].中国科学院测量与地球物理研究所
[29]张传定,吴晓平,陆仲连(2000).全张量重力梯度数据的谱表示[J].测绘学报,29(4): 297-304
[30]赵东明(2004).卫星跟踪卫星任务的引力谱分析和状态估计方法[博士论文].信息工程大学测绘学院
[31] Pavlis, N.K., S.A. Holmes, S.C. Kenyon, and J.K. Factor, An Earth Gravitational Model to Degree 2160: EGM2008, presented at the 2008 General Assembly of the European Geosciences Union, Vienna, Austria, April 13-18, 2008.
[32] http://earth-info.nima.mil/GandG/
[33] Smith DA and Roman DR.GEOID99 and G99SSS:1-arcminute Geoid Models for the United States[j].Journal of Geodesy,2001,75:469—490
[34] D.R.Roman,Development of the North American Gravimetric Geoid: Adapting the Process to Determine a Unified Central American Geoid, USA National Geodetic Survey,2001
[35] Heiskanen W A,Moritz H.Physical Geodesy[M].San Francisco and London:W H Freeman Co,1967
[36] Vanicek P,ZHANG Changyou,Sjoberg L E.A comparison of Stokes and Hotine’s approaches to geoid computation[J].Manu.Geod,1992,17:29～35
[37] HAAGMANS R R N,de MINE,van GELDERENM.Fast Evaluation of Convolution Integrals on the Sphere Using 1-D FFT,and a Comparison with Existing Methods for Stokes’s Integral[J].Manuscr Geed,1993,(18):227~241
[38] Bjerhammar, A., A Review of Discrete Methods in Physical Geodesy, in Approximation Methods in Physical Geodesy, H.Moritz and H.Sunkel, Herbert Wichmann Verlag, Karisruhe,1978
[39] Cruz, J.Y. and P.Laskowski, Upward Continuation of Surface Gravity Anomalies, Report No.360,Dept. of Geodetic Science and Surveying , the Ohio State University ,December 1984
[40] Jekeli, C. The Downward Continuation to the Earth's Surface of Truncated Spherical and Ellipsoidal Harmonic Series of the Gravity and Height Anomalies, Report No.323, Dept. of Geodetic Science and Surveying , The Ohio State University , December 1981
[41] Moritz, H. Advanced Physical Geodesy, Herbert Wichmann Verlag, Karisruhe, 1980
[42] Rapp, R.H., Ellipsoidal Corrections for Geoid Undulation Computations, Report No.308, Dept. of Geodetic Science and Surveying ,The Ohio State University, March 1981
[43] Sjoberg, L., On the Discrete Boundary Value Problem of Physical Geodesy With Harmonic Reduction to an Internal Sphere, Division of Geodesy, The Royal Institute of Technology, Stockholm,1975
[44] Haines GV.Compute programs for Spherical cap harmonic analysis of potential and general fields[J].Compute Geosci.1988
[45] Haines GV,Torta JM.Determination of equivalent current sources from spherical cap harmonic of geomanetic field variations[J].Geophy J Int.1994
[46] Koch K R,Pope A J.Uniqueness and existence for the geodetic boundary value problem using the known surface of the Earth.Bull.Geod.,1972,46:167-176
[47] Bjerhammar A,Svensson L.On the geodetic boundary value problem for a fixed boundary surface-A satellite approach.Bull.Geod.,1983,57:382-393
[48] Migliaccio F, Sanso F(1989). The boundary value problem approach to the data reduction for a space borne gradiometer mission[A]. IAG Symposia 103[C]. Springer Verlag, Berlin, Heidleberg, NewYork.67～77
[49] KellerW(1994), HirschM. A boundary value approach to downward continuation [J]. Manuscripta Geodaetica , 19(2):101～118