| 山体表面重构数值反演的同伦算法 |
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| 引用本文： | 窦以鑫,韩波.山体表面重构数值反演的同伦算法[J].地球物理学报,2011,54(7):1893-1899. |
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| 作者姓名： | 窦以鑫 韩波 |
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| 作者单位： | 哈尔滨工业大学数学系, 哈尔滨 150001 |
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| 基金项目： | 中央高校基本科研业务费专项资金项目 |
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| 摘 要： | 本文主要研究山体表面重构过程.山体表而重构主要包括地球内部热流变化和地球表面运动规律两个过程,是三维对流扩散方程和二维山体表面运动方程的耦合,求解十分困难.为了模拟山体表面重构过程,还要对耦合方程进行反演研究,是一个大尺度非线性优化问题.为了克服对于初值的强烈依赖和非线性优化中存在的多极值难点,我们将同伦反演算法应用到...
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| 关 键 词： | 山体表面重构 热传导模型 山体表面运动模型 反问题 同伦算法 |
| 收稿时间： | 2010-05-05 |
Numerical inversion of reconstruction of mountain surface by homotopy method |
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| DOU Yi Xin,Han Bo.Numerical inversion of reconstruction of mountain surface by homotopy method[J].Chinese Journal of Geophysics,2011,54(7):1893-1899. |
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| Authors: | DOU Yi Xin Han Bo |
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| Institution: | Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China |
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| Abstract: | In this paper, we focus on the reconstruction of a mountain surface with time span of millions of years. Reconstruction of a mountain surface consists of two processes. One is the heat transport process model in three dimensional spatial domain, which describes the change of temperature of rocks, and the other is the surface process model in two dimensional spatial domain, which explains the evolution of mountain surface. This is a large scale nonlinear optimization for reconstruction of a mountain surface back to millions of years. To overcome the strong dependency on initial guess value and multiple local minima, we apply a homotopy method to restore the mountain surface. Numerical results show that our algorithm has a good convergent property for given initial guess values and is robust. |
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| Keywords: | Reconstruction of a mountain surface Heat transport process model Surface process model Inverse problem Homotopy algorithm |
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