利用矩谐分析的局部大地水准面确定
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摘要
大地水准面是重力的等位面,建立高精度的大地水准面是大地测量学的重要任务之一。现阶段建立局部大地水准面多采用球谐分析以及球冠谐分析,但都无法获得高精度、小区域的大地水准面。针对这一研究现状,本文提出了采用矩谐分析确定局部大地水准面的方法。选取所研究区域中心点为坐标原点,建立直角坐标系,并在此坐标系下求解地球引力位Laplace方程;利用模拟的陆地重力及航空重力数据,对矩谐分析建模方法进行验证与分析;并针对影响矩谐分析精度的边界效应问题,采用扩展参数的方法提高精度,针对"龙格问题",进行了最佳截断阶数的研究。结果表明:由陆地重力和航空重力数据确定的2.5'×2.5'的大地水准面精度分别能达到4.2、4.3 cm;且对于航空重力数据,矩谐分析能同时实现向下延拓和解算两个重点、难点计算过程,将航空重力解算直接化、简单化。
The establishment of high-precision geoid is one of the important tasks of geodesy.At present,the spherical harmonic analysis and spherical crown analysis are used to establish the local geoid,but it can not get high precision,small area of the earth level.Aiming at the present situation of this study,so rectangular harmonic analysis( RHA) is proposed for regional geoid in this paper.By selecting the point of the regional for the origin to establish the Cartesian coordinate system,and solving the Laplace's equation of gravitational potential in it,then using the simulated terrestrial gravity and aerial gravity data,the method of rectangular harmonic analysis is validated and analyzed.Select the extended parameters,the best truncation method to improve the accuracy of the method. According to the numerical results,it is shown that the accuracy of the 2.5' × 2.5' geoid undulations computed from ground and airborne gravity data is 4.2 and 4.3 cm,and for the air neutral data,rectangular harmonic analysis can finish the downward extension and solution process,make the aviation gravity solution directly,and simply.
The establishment of high-precision geoid is one of the important tasks of geodesy.At present,the spherical harmonic analysis and spherical crown analysis are used to establish the local geoid,but it can not get high precision,small area of the earth level.Aiming at the present situation of this study,so rectangular harmonic analysis( RHA) is proposed for regional geoid in this paper.By selecting the point of the regional for the origin to establish the Cartesian coordinate system,and solving the Laplace's equation of gravitational potential in it,then using the simulated terrestrial gravity and aerial gravity data,the method of rectangular harmonic analysis is validated and analyzed.Select the extended parameters,the best truncation method to improve the accuracy of the method. According to the numerical results,it is shown that the accuracy of the 2.5' × 2.5' geoid undulations computed from ground and airborne gravity data is 4.2 and 4.3 cm,and for the air neutral data,rectangular harmonic analysis can finish the downward extension and solution process,make the aviation gravity solution directly,and simply.
引文
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[14]李伟.利用航空重力梯度数据恢复区域重力场[D].兰州:兰州交通大学,2014.
[15]KUSCHE J,KLEES R.Regularization of Gravity Field Estimation from Satellite Gravity Gradients[J].Journal of Geodesy,2002,76(6-7):359-368.
[2]蒋涛,李建成,党亚民,等.基于矩谐分析的区域重力场建模[J].中国科学:地球科学,2014,44(1):82-89.
[3]ALLDREDGE L R.Rectangular Harmonic Analysis Applied to the Geomagnetic Field[J].Journal of Geophysical Research,1981,86(B4):3021-3026.
[4]蒋涛,党亚民,章传银,等.基于矩谐分析的航空重力向下延拓[J].测绘学报,2013,42(4):475-480.
[5]王月华.MAGSAT卫星矢量磁异常的矩谐分析[J].地球物理学报,1992,35(5):654-660.
[6]安振昌,徐元芳,王月华.中国地区MAGSAT卫星标量和矢量磁异常图[J].空间科学学报,1992,12(2):123-128.
[7]徐文耀,朱岗昆.我国及邻近地区地磁场的矩谐分析[J].地球物理学报,1984(6):11-22.
[8]徐文耀.地磁学[M].北京:地震出版社,2003:170-192.
[9]MATSUSHITA S,XU W Y.Equivalent Ionospheric Current Systems Representing Lunar Daily Variations of the Polar Geomagnetic Field[J].Journal of Geophysical Research:Space Physics,1983,87(A10):8241-8254.
[10]赵建虎,刘辉,王胜平.局域海洋地磁场矩谐分析建模方法研究[J].大地测量与地球动力学,2009,29(2):82-87.
[11]朱岗崑,徐文耀.矩谐分析方法的数值检验及其与其他磁场分析方法的比较[J].地球物理学报,1986,29(6):540-546.
[12]边少锋.大地测量边值问题数值解法与地球重力场逼近[D].武汉:武汉测绘科技大学,1992.
[13]卢文祥,杜润生,赵星.测试信号频谱分析中的Gibbs现象[J].华中工学院学报(自然科学版),1985(5):65-70.
[14]李伟.利用航空重力梯度数据恢复区域重力场[D].兰州:兰州交通大学,2014.
[15]KUSCHE J,KLEES R.Regularization of Gravity Field Estimation from Satellite Gravity Gradients[J].Journal of Geodesy,2002,76(6-7):359-368.