| 基于球面边值问题的点质量调和分析方法 |
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| 引用本文： | 吴星,张传定,赵东明.基于球面边值问题的点质量调和分析方法[J].地球物理学报,2009,52(12):2993-3000. |
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| 作者姓名： | 吴星 张传定 赵东明 |
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| 作者单位： | 1.信息工程大学测绘学院, 郑州 450052;2.北京特种工程设计研究院, 北京 100028 |
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| 基金项目： | 国家自然科学基金，全国优秀博士论文专项基金，解放军信息工程大学博士生创新基金，中国科学院动力大地测量学重点实验验开放基金 |
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| 摘 要： | 对全球扰动点质量模型而言，可以假定虚拟扰动质点系位于地球内部同一Bjerhamar球面上，同时把边值界面视为球面.本文针对这一假设下所形成的线性方程组的系数阵，运用快速傅里叶变换的方法，得到了点质量模型解算中利用分块循环矩阵分解大型线性方程组的新方法.全球30′×30′扰动点质量模型259200阶方程组的解算分解为720个360阶方程组的解算，解决了点质量模型构建中大型线性方程组的稳定解算问题.推导了全球点质量模型与球谐位系数模型的转换关系，得到了一种基于球面边值问题的点质量调和分析方法.数值模拟试验表明，在适当选取点质量埋深度的情况下，本文的点质量调和分析方法较传统的调和分析方法精度更高.
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| 关 键 词： | 扰动点质量模型 调和分析 Toeplitz循环矩阵 快速傅里叶变换 |
| 收稿时间： | 2009-4-9 |
| 修稿时间： | 2009-12-1 |
Point mass harmonic analysis method based on spherical boundary value problem |
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| WU Xing,ZHANG Chuan-Ding,ZHAO Dong-Ming.Point mass harmonic analysis method based on spherical boundary value problem[J].Chinese Journal of Geophysics,2009,52(12):2993-3000. |
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| Authors: | WU Xing ZHANG Chuan-Ding ZHAO Dong-Ming |
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| Institution: | 1.Institute of Surveying and Mapping，Information Engineering University，Zhengzhou 450052，China;2.Beijing Special Type Engineering Design and Reasearch Institute, Beijing 100028, China |
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| Abstract: | The global disturbing point mass model is based on the assumption that the virtual disturbing point mass are located on the same Bjerhamar sphere inside the earth and at the same time the boundary is a sphere surface. From the assumption linear equations has to be solved for the point masses. The paper is aimed at the solution of point masses by decomposing huge linear equations in terms of blocked circular matrix using the Fast Fourier Transform method. For global 30'×30' point masses, the solution was completed by decomposing a 259200-order linear equations into 720 360-order equations. The method solves the stability problem that occurs in the solution of huge linear equations for point mass modeling. The conversion from global pointmass model to spherical harmonic coefficient was made and a point mass harmonic analysis method based on spherical boundary value problem was derived. Numerical simulation proves that the proposed method is more accurate than conventional harmonic analysis method. |
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| Keywords: | Disturbing point mass model Harmonic analysis Toeplitz circular matrix Fast Fourier transform |
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