| 用于势场反演的特殊解法 |
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| 引用本文： | 闻则刚,何璟琳.用于势场反演的特殊解法[J].CT理论与应用研究,2001,10(2):11-18. |
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| 作者姓名： | 闻则刚 何璟琳 |
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| 作者单位： | 广东省地震局, |
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| 摘 要： | 本文以无旋场的积分路径为射线，以边界上已知的势值为输入、输出量、利用反拉东变换求一个梯度场的势函数，用反演的方法求解可以化为拉普拉斯方程的一类二阶偏微分方程。其思路新颖，原理独特，运算正确，边界条件处理方便，数值实现容易，在重力场和地电场的研究中可能得到应用。
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| 关 键 词： | 天旋场 射线 拉普拉斯方程 反演 重力场 地电场 势场 边界条件 |
| 修稿时间： | 2001年1月18日 |
The Particular Solution Method for Potential value Inversion |
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| Wen Zegang,He Jinglin.The Particular Solution Method for Potential value Inversion[J].Computerized Tomography Theory and Applications,2001,10(2):11-18. |
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| Authors: | Wen Zegang He Jinglin |
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| Abstract: | In this paper the integral routes of irrotational field are treated as rays, the potential values of the boundary points which be passed by the ray are treated as input and output, then Laplace Equation can be solved by inverse method. This method is innovatory and applicable, the results are precise and the boundary conditions are easy to be coped with. This is a useful numerical method for a kind of second-order partial differential equations that can be transformed to Laplace Equation. The most of control equations in engineering and physics are Laplace Equation or Poisson Equation, and the analytical solution of the two kinds of equations cannot be gotten generally, so they often be solved by differential method and finite element method. It is too complex to cope with the boundary conditions by differential method and its grids must be square and same size when calculated. We measure the input and output from different directions with instrument through which we can get the total attenuation of every my. It means that we need some rays and detecting instrument. In this paper the integral routes of irrotational field are treated as rays, the potential values of the boundary points that rays pass by are treated as input and output, then a kind of secondorder partial differential equations that can be transformed to Laplace Equation which can be solved by inverse method. This theory is particular and simple, the results are precise and the boundary conditions are easy to be coped with. So we think it has wide applications in physics, numerical mathematics, and specially, may be used in the research of gravity and geoelectric fields. |
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| Keywords: | Inverse Method Laplace Equation Ray Potential value |
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