Molodensky-Poisson核函数应用于重力异常向下延拓分析
|
摘要
分析标准Poisson核函数和Molodensky-Poisson核函数特性,并计算其远区效应的截断误差,获取与延拓高度、积分半径和截断阶次的关系。分析认为,Molodensky-Poisson核函数能够抑制远区的影响,当延拓高度不高于3km,积分半径至少0.5°时,其截断误差在1mGal以内;当积分半径为1°时,其截断误差在10μGal量级,可满足计算1cm大地水准面目标的要求。
This paper attempts to achieve accurate results for the downward-continuation.In the paper the detailed characters of the standard Poisson kernel and the Molodensky-Poisson kernel are analyzed.The truncation error of the far-zone contribution is estimated.The relations of the height,the truncation radius and degree are analyzed in the downward-continuation of the gravity anomalies.The results suggest that the Molodensky-Poisson kernel can reduce the far-zone contribution.The height is less than 3km and the truncation radius is more than 0.5°.The truncation error estimated at less than 1mGal;when the truncation radius reaches 1°,the truncation error estimate achieves an accuracy of 10μGal.Hence it ensures the accuracy of the geoid reach to the 1cm level.
This paper attempts to achieve accurate results for the downward-continuation.In the paper the detailed characters of the standard Poisson kernel and the Molodensky-Poisson kernel are analyzed.The truncation error of the far-zone contribution is estimated.The relations of the height,the truncation radius and degree are analyzed in the downward-continuation of the gravity anomalies.The results suggest that the Molodensky-Poisson kernel can reduce the far-zone contribution.The height is less than 3km and the truncation radius is more than 0.5°.The truncation error estimated at less than 1mGal;when the truncation radius reaches 1°,the truncation error estimate achieves an accuracy of 10μGal.Hence it ensures the accuracy of the geoid reach to the 1cm level.
引文
[1]陆仲连.地球重力场理论与方法[M].北京:解放军出版社,1996(Lu Zhonglian.Theory and Method of Earth’s Gravity[M].Beijing:PLA Press,1996)
[2]魏子卿.大地水准面短议[J].地理空间信息,2009,7(1):1-3(Wei Ziqing.Brief Introduction to the Geoid[J].Geospatial Information,2009,7(1):1-3)
[3]Hofmann-Wellenhof B,Moritz H.Physical Geodesy[M].Springer Wien,2006
[4]李建成.最新中国陆地数字高程基准模型:重力似大地水准面CNGG2011[J].测绘学报,2012,41(5):651-660(Li Jiancheng.The Recent Chinese Terrestrial Digital Height Datum Model:Gravimetric Quasi Geoid CNGG2011[J].Acta Geo- daetica et Cartographica Sinica,2012,41(5):651-660)
[5]李建成.我国现代高程测定关键技术若干问题的研究及进展[J].武汉大学学报:信息科学版,2007,32(11):980-987(Li Jiancheng.Study and Progress in Theories and Crucial Techniques of Modern Height Measurement in China[J].Geomatics and Information Science of Wuhan University,2007,32(11):980-987)
[6]欧阳永忠,邓凯亮,黄谟涛,等.重力异常延拓计算积分半径的选择及远区效应[J].海洋测绘,2011,31(4):5-7(Ouyang Yongzhong,Deng Kailiang,Huang Motao,et al.The Choice of Integral Radius and Its Far-Zone Effects in the Continuation of the Gravity Anomaly[J].Hydrographic Surveying and Charting,2011,31(4):5-7)
[7]荣敏,周巍,陈春旺.重力场模型EGM2008和EGM96在中国地区的比较与评价[J].大地测量与地球动力学,2009(6):123-125(Rong Min,Zhou Wei,Chen Chunwang.Evaluation of Gravity Field Models EGM2008and Applied in Chinese Area[J].Journal of Geodesy and Geodynamics,2009(6):123-125)
[8]周巍,荣敏.多类地球重力场模型精度分析[J].海洋测绘.2014,34(3):5-8(Zhou Wei,Rong Min.Accuracy Analysis of Gravity Field Models[J].Hydrographic Surveying and Charting,2014,34(3):5-8)
[9]Huang Jianliang.Computational Methods for the Discrete Downward Continuation of the Earth Gravity and Effects of Lateral Topographical Mass Density Variation of Gravity and Geoid[R].University of New Brunswick,2002
[10]Huang J,Veronneau M.Applications of Downward-Continuation in Gravimetric Geoid Modeling:Case Studies in Western Canada[J].Journal of Geodesy,2005,79:135-145
[11]Vanicek P,Sun W,Ong P,et al.Downward Continuation of Helmert’s Gravity[J].Journal of Geodesy,1996,71:21-34
[12]Featherstone W E,Evans J D,Olliver J G.A Meissl-Modified Vanicek and Kleusberg Kernel to Reduce the Truncation Error in Gravimetric Geoid Computations[J].Journal of Geodesy,1998,72:154-160
[13]Sun W,Vanicek P.On Some Problems of the Downward Continuation of the 5′×5′Mean Helmert Gravity Disturbance[J].Journal of Geodesy,1998,72:411-420
[14]Sjberg L E.On the Error of Analytical Continuation in Physical Geodesy[J].Journal of Geodesy,1996,70:724-730
[15]Nahavandchi H.The Direct Topographical Correction in Gravimetric Geoid Determination by the Stokes-Helmert Method[J].Journal of Geodesy,2000,74:488-496
[16]Kern M.An Analysis of the Combination and Downward Continuation of Satellite,Airborne and Terrestrial Gravity Data[R].University of Calgary,2003
[2]魏子卿.大地水准面短议[J].地理空间信息,2009,7(1):1-3(Wei Ziqing.Brief Introduction to the Geoid[J].Geospatial Information,2009,7(1):1-3)
[3]Hofmann-Wellenhof B,Moritz H.Physical Geodesy[M].Springer Wien,2006
[4]李建成.最新中国陆地数字高程基准模型:重力似大地水准面CNGG2011[J].测绘学报,2012,41(5):651-660(Li Jiancheng.The Recent Chinese Terrestrial Digital Height Datum Model:Gravimetric Quasi Geoid CNGG2011[J].Acta Geo- daetica et Cartographica Sinica,2012,41(5):651-660)
[5]李建成.我国现代高程测定关键技术若干问题的研究及进展[J].武汉大学学报:信息科学版,2007,32(11):980-987(Li Jiancheng.Study and Progress in Theories and Crucial Techniques of Modern Height Measurement in China[J].Geomatics and Information Science of Wuhan University,2007,32(11):980-987)
[6]欧阳永忠,邓凯亮,黄谟涛,等.重力异常延拓计算积分半径的选择及远区效应[J].海洋测绘,2011,31(4):5-7(Ouyang Yongzhong,Deng Kailiang,Huang Motao,et al.The Choice of Integral Radius and Its Far-Zone Effects in the Continuation of the Gravity Anomaly[J].Hydrographic Surveying and Charting,2011,31(4):5-7)
[7]荣敏,周巍,陈春旺.重力场模型EGM2008和EGM96在中国地区的比较与评价[J].大地测量与地球动力学,2009(6):123-125(Rong Min,Zhou Wei,Chen Chunwang.Evaluation of Gravity Field Models EGM2008and Applied in Chinese Area[J].Journal of Geodesy and Geodynamics,2009(6):123-125)
[8]周巍,荣敏.多类地球重力场模型精度分析[J].海洋测绘.2014,34(3):5-8(Zhou Wei,Rong Min.Accuracy Analysis of Gravity Field Models[J].Hydrographic Surveying and Charting,2014,34(3):5-8)
[9]Huang Jianliang.Computational Methods for the Discrete Downward Continuation of the Earth Gravity and Effects of Lateral Topographical Mass Density Variation of Gravity and Geoid[R].University of New Brunswick,2002
[10]Huang J,Veronneau M.Applications of Downward-Continuation in Gravimetric Geoid Modeling:Case Studies in Western Canada[J].Journal of Geodesy,2005,79:135-145
[11]Vanicek P,Sun W,Ong P,et al.Downward Continuation of Helmert’s Gravity[J].Journal of Geodesy,1996,71:21-34
[12]Featherstone W E,Evans J D,Olliver J G.A Meissl-Modified Vanicek and Kleusberg Kernel to Reduce the Truncation Error in Gravimetric Geoid Computations[J].Journal of Geodesy,1998,72:154-160
[13]Sun W,Vanicek P.On Some Problems of the Downward Continuation of the 5′×5′Mean Helmert Gravity Disturbance[J].Journal of Geodesy,1998,72:411-420
[14]Sjberg L E.On the Error of Analytical Continuation in Physical Geodesy[J].Journal of Geodesy,1996,70:724-730
[15]Nahavandchi H.The Direct Topographical Correction in Gravimetric Geoid Determination by the Stokes-Helmert Method[J].Journal of Geodesy,2000,74:488-496
[16]Kern M.An Analysis of the Combination and Downward Continuation of Satellite,Airborne and Terrestrial Gravity Data[R].University of Calgary,2003