| 基于Clenshaw求和法的重力场元计算 |
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| 引用本文： | 赵德军,吴晓平.基于Clenshaw求和法的重力场元计算[J].海洋测绘,2004,24(6):13-15,26. |
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| 作者姓名： | 赵德军 吴晓平 |
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| 作者单位： | 解放军信息工程大学,测绘学院,河南,郑州,450052 |
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| 基金项目： | 全国博士学位论文作者专项资金资助项目(200344)，河南省杰出人才创新基金资助项目(0321000100)。 |
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| 摘 要： | 重力场计算中，经常需要计算以有限阶球谐级数表示的重力场元。常规计算中除需存储(N 1)^2个系数值外，还需迭代计算出(N 2)(N 1)／2个完全正常化勒让德函数值。Clenshaw求和法不需要计算单个球谐函数值而直接计算级数和，因而计算速度上有所提高。总结了球谐函数的零阶导数级数和，并推导了一阶导数级数和。通过数值试验，对于任意点的重力场元，使用C1enshaw求和法计算零阶导数球谐函数和比常规方法节省一半的时间，一阶导数球谐函数之和的计算速度提高幅度不大，并分析了其中的原因。
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| 关 键 词： | 重力测量 重力场 Clenshaw 球谐函数 重力场元 |
| 文章编号： | 1671-3044(2004)06-0013-03 |
| 修稿时间： | 2004年9月6日 |
Computations of Gravity Quantities Based on Clenshaw Summation Method |
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| ZHAO De-jun,WU Xiao-ping.Computations of Gravity Quantities Based on Clenshaw Summation Method[J].Hydrographic Surveying and Charting,2004,24(6):13-15,26. |
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| Authors: | ZHAO De-jun WU Xiao-ping |
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| Abstract: | There are many gravity quantities expressed by finite spherical harmonic series expansions in the computing for geopotential.It need store(N+1)~2 coefficients and compute(N+2)(N+1)/2 fully normalized associated Legendre functions with the use of normal method.But,it only need compute the summation of spherical harmonic expansions rather than single spherical harmonic for Clenshaw summation,so it speeds up the computing.This paper summarizes the computing for the sum of the spherical harmonics,and deduced first derivative with respect to latitude for the sum of the spherical harmonics.According to the numerical test,it spends only 50% time in computing the sum of spherical harmonics of arbitrary point by Clenshaw summation in contrast with normal method.But it speeds up little for the sum of first derivative,the question is analyzed.In a word,this method is suitable to compute the sum of gravimetric quantities. |
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| Keywords: | gravimetry gravity field clenshaw summation sphere harmonics gravimetric quantity |
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