基于改进径向导数的解析向下延拓优化算法  

Optimization algorithm for analytical downward continuation based on improved radial derivative

作　　者：马健 翟振和[1,2] 冯长强 管斌 王云鹏[1,2] 李端 MA Jian;ZHAI Zhenhe;FENG Changqiang;GUAN Bin;WANG Yunpeng;LI Duan(Xi’an Research Institute of Surveying and Mapping,Xi’an 710054,China;State Key Laboratory of Geo-Information Engineering,Xi’an 710054,China;School of Architecture and Urban Planning,Shenzhen University,Shenzhen 518060,China)

机构地区：[1]西安测绘研究所,陕西西安710054 [2]地理信息工程国家重点实验室,陕西西安710054 [3]深圳大学建筑与城市规划学院,广东深圳518060

出　　处：《测绘学报》2023年第10期1650-1660,共11页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(42204002);中国博士后科学基金(2022M712162)。

摘　　要：解析延拓算法是一种重要的位场延拓方法。与Poisson延拓算法相比,解析延拓算法具有算法简单、运算速度快等特点,在基于第二或第三大地边值理论构建(似)大地水准面或垂线偏差模型的实践中具有重要的应用价值。径向导数的计算是解析延拓算法的关键,而传统解析延拓算法中径向导数的计算存在一定程度的近似误差。本文提出了一种径向导数的改进方法,在此基础上实现了解析延拓算法的优化。本文利用球谐方法从理论上证明了改进径向导数比传统径向导数更接近理论严密的径向导数,并通过绘制经度剖面和纬度剖面图直观地印证了这一结论。在我国中部地形起伏较大的区域进行的试验表明,改进径向导数精度较传统径向导数精度提高了32.45%。在1、2、3、4 mGal的误差条件下,改进径向导数的解析延拓算法较传统解析延拓算法向下延拓精度分别提高了29.04%、19.48%、10.12%、2.65%。本文通过理论分析和算法试验证明了基于改进径向导数的解析向下延拓优化算法的有效性,该方法在大地边值解算中具有一定的应用价值。Analytical continuation algorithm is an important continuation method for the potential field,which has important application value in the construction of the(quasi-)geoid or vertical deflection models based on the second or third geodetic boundary-value theory.Compared with Poisson continuation,the analytical continuation algorithm is simpler and faster.The calculation of the radial derivative is crucial for the analytical continuation algorithm.However,the traditional method for the radial derivative of the analytical continuation introduces a certain approximation error.An improved method for radial derivative is proposed in this paper.The optimization of the analytical continuation algorithm is then realized.In this research,it is proved by spherical harmonic method that the improved radial derivative is closer to the theoretically true radial derivative than the traditional one.The conclusion is displayed by the longitude and latitude profiles.The test of a large mountainous area conducted in central China shows that the accuracy of the improved radial derivative is 32.45%higher than that of the traditional radial derivative.When the errors contained in the gravity data are 1,2,3 and 4 mGal,the downward continuation accuracies of analytical continuation based on the improved radial derivative is 29.04%,19.48%,10.12%and 2.65%higher than that of the traditional analytical continuation,respectively.Theoretical analysis and test proves the effectiveness of the analytical downward continuation based on the improved radial derivative,which is useful in the geodetic boundary-value problem.

关 键 词：解析延拓算法 传统径向导数 改进径向导数 向下延拓 球谐方法 

分 类 号：P223[天文地球—大地测量学与测量工程]