| 引力场球谐综合的Walsh变换方法 |
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| 引用本文： | 孟嘉春,蔡喜楣,孟伟.引力场球谐综合的Walsh变换方法[J].地球物理学报,1999,42(Z1):85-92. |
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| 作者姓名： | 孟嘉春 蔡喜楣 孟伟 |
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| 作者单位： | 1. 中国科学院测量与地球物理研究所 武汉 430077;
2. 中国科学院武汉文献情报中心 武汉 430071 |
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| 基金项目： | 国家自然科学基金项目(49384003);;中国科学院院长基金特别支持项目(930156) |
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| 摘 要： | 提出直接在序率域内用Walsh变换实现引力场球谐综合的问题。给出球谐函数展开式的Walsh变换及快速算法,讨论了Walsh变换和Walsh-Fourier变换、Fourier变换之间的差异,分析了用地球重力场模型OSU81的位系数作出的Walsh变换和Fourier变换的结果。研究表明:Walsh变换与Walsh-Fourier变换、Fourier变换对应向量在数量方面的差值通常都小于士10~(-5);对于给定的阶数和飞行高度,3种方法求得的球谐综合值总是完全一致的;1°×1°等网格数据和Walsh函数形状相近。在重力场研究中Walsh级数会比Fourier级数收敛得更快;Walsh变换在计算速度、计算准确度、数据储存、收敛速度和方法简单方面都好于Fourier变换。
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| 关 键 词： | 引力场 球谐函数 Walsh变换 快速Walsh-Hadamard变换 |
| 收稿时间： | 1999-05-13 |
A WALSH TRANSFORM METHOD OF SPHERICAL HARMONIC SYNTHESIS FOR GRAVITATIONAL FIELD |
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| MENG JIA-CHUN CAI XI-MEI.A WALSH TRANSFORM METHOD OF SPHERICAL HARMONIC SYNTHESIS FOR GRAVITATIONAL FIELD[J].Chinese Journal of Geophysics,1999,42(Z1):85-92. |
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| Authors: | MENG JIA-CHUN CAI XI-MEI |
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| Institution: | 1. Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China;
2. Wuhan Documentation and Information Center. Chinese Academy of Sciences, Wuhan 430071, China |
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| Abstract: | The problem of spherical harmonic synthesis for the gravitational field realized directly by the Walsh transform in sequency domain is put forward in this paper. The Walsh transform of spherical harmonic expansion and fast algorithm is presented. The differences between the Walsh transform and the Walsh-Fourier transform, and the Fourier transform are discussed. The results of the Walsh transform and the Fourier transform made by the geopotential coefficients of the Earth's gravity field model OSU81 are analysed. The results of research show that the differences of corresponding vector between the Walsh transform and the Walsh-Fourier transform, and the Fourier transform are usually less than±10~(-5) in quantities. The values of spherical harmonic synthesis obtained by using three methods are always indentical for a given order and altitude. The data of grid for 1°×1°etc are similar to the Walsh functions in shape. The Walsh series will converge much faster than the Fourier series in research of gravity field. The Walsh transform can be better than the Fourier transform in computation speed, computational accuracy, data storage, convergence rate, and simplicity in method. |
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| Keywords: | Gravitationalfield Sphericalharmonics Walshtransform FastWalshHadamardtransform |
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