| 一维声波方程声阻抗反演问题的稳定性分析 |
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| 引用本文： | 郝现军,朱本仁,张关泉. 一维声波方程声阻抗反演问题的稳定性分析[J]. 计算物理, 1998, 15(5): 559-567 |
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| 作者姓名： | 郝现军 朱本仁 张关泉 |
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| 作者单位： | 1. 中国科学院计算数学与科学工程计算研究所, 北京 100080;2. 山东大学数学系, 济南 250100;3. 中国科学院科学与工程计算国家重点实验室, 北京 100080 |
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| 摘 要： | 讨论了一维声波方程的声阻抗反演问题。对于脉冲激发的情况,得到反问题适定的充分、必要条件,适定条件的形式非常简单,在实际计算中易于判定。对于子波激发的情况,由子波响应反演声阻抗通常是不适定的,不适定程度与子波的奇性有关,子波越光滑,相应的反问题的不适定程度越高。同时给出了定量的说明,为一维声波方程声阻抗反演问题的数值计算提供了理论。
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| 关 键 词： | 波动方程 反问题 稳定性 |
| 收稿时间： | 1996-11-25 |
| 修稿时间： | 1998-03-19 |
THE STABILITY ANALYSIS FOR THE INVERSE PROBLEM OF ONE DIMENSIONAL ACOUSTICS WAVE EQUATIONS |
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| Hao Xianjun,Zhu Benren,Zhang Guanquan. THE STABILITY ANALYSIS FOR THE INVERSE PROBLEM OF ONE DIMENSIONAL ACOUSTICS WAVE EQUATIONS[J]. Chinese Journal of Computational Physics, 1998, 15(5): 559-567 |
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| Authors: | Hao Xianjun Zhu Benren Zhang Guanquan |
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| Affiliation: | 1. Institute of Computational Mathematics and Scientific & Engineering Computing Chinese Academy of Sciences, Beijing 100080;2. Department of Mathematics Shandong University, Jinan 250100;3. State Key Laboratory of Scientific & Engineering Computing Institute of Computational Mathematics and Scientific & Engineering Computing Chinese Academy of Sciences, Beijing 100080 |
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| Abstract: | The inverse problem for the one-dimensional acoustic wave equations is discussed.For the inverse problem to determine acoustic impedance from impulse response,sufficient condition and necessary condition are obtained for the wellposedness.These conditions are very simple and can be verified easily in numerical computation.For the inverse problem to determine acoustic impedance from wavelet response,it's usually illposed.The detailed analysis indicates that the more smooth the wavelet is,the more illposed the inverse problem is. |
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| Keywords: | wave equation inverse problem stability |
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