| 沿球面大圆的积分逆变换及其应用 |
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| 引用本文： | 徐果明.沿球面大圆的积分逆变换及其应用[J].地球物理学报,1989,32(2):153-162. |
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| 作者姓名： | 徐果明 |
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| 作者单位： | 中国科技大学地球和空间科学系 合肥 |
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| 摘 要： | 本文给出了从沿球面上大圆的积分值直接反推球面上函数分布的关系式,即得到了球面上大圆的积分变换和反变换对。如利用的是整个大圆的积分,得到的是球面上任何点及其对蹠点上函数的平均值,或者说得到的是球面上函数的偶对称部分。如果进行积分的球面域小于半球面,反演将是唯一的。所得结果可应用于从地震表面波资料反演三维地球内部构造的地球物理问题。
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| 关 键 词： | 雷当变换 层析成象 反演理论 |
| 收稿时间： | 1987-01-19 |
INTEGRAL INVERSE TRANSFORM ALONG A GREAT CIRCLE ON SPHERICAL SURFACE AND ITS APPLICATION |
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| Xu GuO-MING.INTEGRAL INVERSE TRANSFORM ALONG A GREAT CIRCLE ON SPHERICAL SURFACE AND ITS APPLICATION[J].Chinese Journal of Geophysics,1989,32(2):153-162. |
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| Authors: | Xu GuO-MING |
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| Institution: | Depart, of Earth and Space Sciences, Univ. of Science and Technology of China, Hefei |
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| Abstract: | Formula for the distribution of function directly obtained from the integral value along a. great circle on the spherical surface has been derived and the integral transform and its inverse transform are obtained. If the whole integrals on the great circle are used, the average of the function values for any point and its antipodal can be obtained. If the integrated area is less than half spherical surface, inversion will be unique. The results can be applied in geophysics, used in 3-D earth's structure inversion from the seismic surface waves data. |
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| Keywords: | Radon transform Tomography Inverse theory |
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