利用球谐函数计算重力场元

发布时间：2018-03-08 12:23

本文选题：球谐函数　切入点：重力场模型　出处：《东华理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：地球重力场模型是指地球引力位按球谐函数展开的一组位系数的集合,是对地球重力场的拟合或逼近。将重力场用球谐函数展开,对扰动函数施以简单的线性运算即可简单快速的导出重力异常、大地水准面差距和垂线偏差等具有重要应用价值的重力场元。因此,本文主要针对如何利用球谐函数快速准确的计算重力场元展开研究。主要的研究内容和成果如下:(1)计算球谐函数的一个关键问题是快速准确地递推缔合勒让德函数。从计算精度和计算速度两个方面探讨了四种常用缔合勒让德函数的适用性,实验表明,当阶数超高时,标准向前列和标准向前行的计算速度最快,但计算精度最差,跨阶次计算速度略快于beliokv,两者精度相当。通过插入比例因等方法改善递推过程不稳定的现象,但增加了运算次数,牺牲了计算速度。综合实验得到跨阶次递推算法更适宜作为超高阶缔合勒让德函数的递推算法。(2)利用球谐函数导出重力异常、大地水准面差距和垂线偏差等有重要应用的重力场元。通过三角函数的快速计算、先经行纬度循环再进行经度循环以及简化数组索引下标等方法提高计算速度,并通过实验验证了程序的正确性。结合Horner求和算法改善级数求和状况,并进一步提高计算效能。(3)以大地水准面精化为例,提出用QR矩阵分解法避免求解参数过程中的求逆过程,分析了光滑因子对多面函数的转换精度的影响。基于重力场模型比较分析了四种拟合模型的优劣以及采用最优的拟合算法分析不同重力场模型对转换精度的影响。综合实验得到采用二次曲面法更适用于大地水准面精化的拟合,并且超高阶的重力场模型在小工程区域内的区别不大。(4)根据上述的研究成果,使用ASP.NET(Csharp)编程语言实现了缔合勒让德的稳定性分析、重力场元的计算、重力场元的二维可视化以及高程转换等功能,采用webGL实现重力场元的三维可视化,设计开发了一个重力场计算平台。
[Abstract]:The gravity field model of the earth refers to the set of potential coefficients of the earth's gravitational potential expanded according to the spherical harmonic function, which is the fitting or approximation of the earth's gravity field. The gravity field is expanded with the spherical harmonic function. The gravitational field elements with important application value such as gravity anomaly, geoid difference and vertical deviation can be derived by simple linear operation on perturbation function. This paper mainly focuses on how to use spherical harmonic function to calculate gravitational field element quickly and accurately. The main research contents and results are as follows: 1) A key problem in the calculation of spherical harmonic function is the fast and accurate recursion association Legendre function. The applicability of four commonly used associative Legendre functions is discussed in terms of accuracy and speed. The experimental results show that when the order is high, the calculation speed of the standard moving forward to the front and the standard is the fastest, but the calculation accuracy is the worst. The calculation speed of cross-order is slightly faster than that of beliokv.The accuracy of the two methods is similar. The instability of the recursive process is improved by means of inserting proportional factors, but the number of operations is increased. At the expense of computational speed, it is found that the cross-order recursive algorithm is more suitable as a recursive algorithm for super-high order associating Legendre function.) the spherical harmonic function is used to derive gravity anomalies. The difference of geoid and the deviation of vertical line and other important applied gravity field elements. Through the fast calculation of trigonometric function, the longitude cycle is carried out first and then the longitude cycle is carried out, and the calculation speed is improved by simplifying the array index subscript, etc. The correctness of the program is verified by experiments. Combining with the Horner summation algorithm to improve the summation of series, and to further improve the computational efficiency, taking geoid refinement as an example, the QR matrix decomposition method is proposed to avoid the inverse process in the process of solving parameters. The influence of smoothing factor on the conversion accuracy of multi-plane function is analyzed. Based on the gravity field model, the advantages and disadvantages of the four fitting models are compared and the influence of different gravity field models on the conversion accuracy is analyzed by using the optimal fitting algorithm. Comprehensive experiments show that Quadric surface method is more suitable for geoid refinement. And the super high order gravity field model in the small engineering area is not different. (4) according to the above research results, the stability analysis of associating Legendre and the calculation of gravity field element are realized by using ASP. Net Csharp) programming language. The two-dimensional visualization and elevation conversion of gravity field elements are realized by using webGL. A gravity field computing platform is designed and developed.
【学位授予单位】：东华理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P223.0

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