| 关于Stokes公式的球面卷积和平面卷积的注记 |
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| 引用本文： | 晁定波.关于Stokes公式的球面卷积和平面卷积的注记[J].武汉大学学报(信息科学版),2003,28(6):651-654. |
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| 作者姓名： | 晁定波 |
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| 作者单位： | 武汉大学测绘学院,武汉市珞喻路129号,430079 |
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| 基金项目： | 国家自然科学基金资助项目 ( 4 0 1740 0 4),国家教育部博士点专项基金资助项目 ( 2 0 0 10 4860 13 ) |
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| 摘 要： | 讨论了Stokes公式球面卷积和平面卷积形式的近似性和严密性问题,分析了Stokes函数球面卷积形式和平面卷积形式的关系,推导了其间的差值表达式,估算了最大差值及其对计算大地水准面差距的误差影响。同时指出,将顾及Stokes函数全项的平面卷积公式称为严密公式的提法,仅仅是相对仅顾及Stokes函数首项的简单平面卷积公式而言,认为更合理的提法应该是“高精度Stokes平面近似卷积公式”。理论分析表明,球面卷积不可能严格转化为等效的平面卷积。
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| 关 键 词： | Stokes公式 球面卷积 平面卷积 重力数据 |
| 文章编号： | 1671-8860(2003)06-0651-04 |
| 修稿时间： | 2003年9月14日 |
A Note on Stokes Formula in the Form of Spherical and Planar Convolution |
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| CHAO Dingbo.A Note on Stokes Formula in the Form of Spherical and Planar Convolution[J].Geomatics and Information Science of Wuhan University,2003,28(6):651-654. |
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| Authors: | CHAO Dingbo |
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| Institution: | CHAO Dingbo 1 |
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| Abstract: | This paper discusses the rigidity and approximation of Stokes formula expressed by spherical and planar convolution the difference between the spherical and planar expression derived. The maximal difference value and the induced error effect on geoid undulation computation are then estimated. It is pointed out that the planar convolution form of Stokes formula taking account of all terms of Stokes function is referred to as "rigorous formula" only in the sense of this formula versus the simple planar convolution form of Stokes formula taking account of the first term of Stokes function which is commonly used in local geoid computation, and that the accurate statement of the so-called "rigorous formula" should be "a high accuracy Stokes convolution formula in planar approximation". In theory, the spherical convolution can not rigorously be converted to any equivalent planar convolution. |
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| Keywords: | Stokes formula spherical convolution planar convolution |
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