| 地球物理中的反问题与不适定问题 |
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| 引用本文： | 栾文贵.地球物理中的反问题与不适定问题[J].地球物理学报,1988,31(1):108-117. |
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| 作者姓名： | 栾文贵 |
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| 作者单位： | 中国科学院计算中心 北京； |
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| 基金项目： | 国家自然科学基金，地震学联合科学基金 |
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| 摘 要： | 本文讨论地球物理中的某些反问题与不适定问题。其内容如下:场的延拓与偏微分方程的不适定Cauchy问题;不适定问题稳定性的性态;线性不适定问题的正则化算法。
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| 关 键 词： | 不适定柯西问题 稳定性性态 正则化算法 适应正则化方法 |
| 收稿时间： | 1985-10-15 |
INVERSE PROBLEMS AND ILL-POSED PROBLEMS IN GEOPHYSICS |
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| LUAN WEN-GUI.INVERSE PROBLEMS AND ILL-POSED PROBLEMS IN GEOPHYSICS[J].Chinese Journal of Geophysics,1988,31(1):108-117. |
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| Authors: | LUAN WEN-GUI |
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| Institution: | Computing Center, Academia Sinica, Beijing |
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| Abstract: | This paper distusses some inverse problems and ill-posed problems in geophysics. The contents are as follows: the continuations of fields and the ill-posed Cauchy problems in partial differential equations (including the new formulations for the inverse problem of fields and the principle of field continuations, the mathematical statements of field continuations, the theoretical expressions of field continuations); the stability behaviours of ill-posed problems (including the ill-posed problem and the new ideal of well posed problem, the stability behaviours of solution of ill-posed problems, the estimates of continuous dependence of solution of field continuation problems); the regularization algorithms of linear ill-posed problems (including the general statements of ill-posed problems, the classical regularization methods, the adaptive regularization methods). |
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| Keywords: | Ill-posed Cauchy problem Stability behaviour Regularization algorithm Adaptive regularization method |
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