| 电阻率成像的混合正则化反演算法 |
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| 引用本文： | 韩波,窦以鑫,丁亮.电阻率成像的混合正则化反演算法[J].地球物理学报,2012,55(3):970-980. |
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| 作者姓名： | 韩波 窦以鑫 丁亮 |
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| 作者单位： | 1. 哈尔滨工业大学数学系, 哈尔滨 150001;
2. 哈尔滨工业大学航天学院航天工程与力学系, 哈尔滨 150001;
3. 东北林业大学数学系, 哈尔滨 150001 |
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| 摘 要： | 利用混合正则化方法对二维分片常值电阻率进行反演研究,该方法结合了全变差正则化方法(total variation regularization)和经典吉洪诺夫正则化方法(classical Tikhonov regularization)的优点. 全变差正则化能够有效地重构分片常值电阻率和识别边界,而经典吉洪诺夫正则化方法则能有效地重构光滑的电阻率,从数值算例中可以看出,将这两种方法有效地结合到一起能够改进重构效果.
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| 关 键 词： | 电阻率成像 经典吉洪诺夫正则化 全变差正则化方法 混和正则化方法 |
| 收稿时间： | 2011-09-15 |
Electrical resistivity tomography by using a hybrid regularization |
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| HAN Bo
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DOU Yi-Xin
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DING Liang.Electrical resistivity tomography by using a hybrid regularization[J].Chinese Journal of Geophysics,2012,55(3):970-980. |
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| Authors: | HAN Bo DOU Yi-Xin DING Liang |
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| Institution: | 1. Department of Mathematics, Harbin Institute of Technology, Harbin 150001,China;
2. Astronautical Engineering and Mechanics,School of Astronautics,Harbin Institute of Technology, Harbin 150001,China;
3. Department of Mathematics, Northeast Forest University, Harbin 150001,China |
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| Abstract: | In this paper,we investigate the reconstruction of a piecewise constant resistivity in 2D by using a hybrid regularization.This hybrid regularization integrates a total variation(TV) regularization with a classical Tikhonov regularization.A TV regularization can reconstruct a piecewise constant resistivity as well as detect jump boundaries,and a classical Tikhonov regularization has the ability to reconstruct a smooth resistivity.Combining a classical Tikhonov regularization with a TV regularization,we can see that the hybrid regularization improves the results of numerical experiments. |
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| Keywords: | Electrical resistivity tomography Classical Tikhonov regularization Total variation regularization Hybrid regularization |
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