| 2.5维介质Born近似波速反演唯一性 |
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| 引用本文： | 刘继军.2.5维介质Born近似波速反演唯一性[J].应用数学学报,1998,21(1):66-73. |
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| 作者姓名： | 刘继军 |
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| 作者单位： | 东南大学应用数学系!南京.210018 |
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| 摘 要： | 考虑脉冲源引起的２．５维弱不均匀介质波速反演问题，利用线性化方法得到了波速的二维小扰动满足的积分方程，这是一个积分几何的问题，进而由Ｆｏｕｒｉｅｒ变换和脉冲函数的性质将此二维积分方程化为单变量的积分方程，最后用压缩映象理论证明了积分方程解的唯一性。本文给出了二给波速反演的一种新算法。同时，唯一性结果证明了已有的迭代算法的合理性。
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| 关 键 词： | 波动方程 Born近似 地球物理勘探 波速 反演 |
ON UNIQUENESS OF 2.5-D BORN VELOCITY INVERSION |
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| LIU JIJUN.ON UNIQUENESS OF 2.5-D BORN VELOCITY INVERSION[J].Acta Mathematicae Applicatae Sinica,1998,21(1):66-73. |
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| Authors: | LIU JIJUN |
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| Abstract: | Consider a linearized velocity inversion in 2.5-D inhomogeneous medium. FOrpoint-sources and the correspondent responses measured on the earth's surface, we get anintegral equation satisfied by the 2-D wave velocity perturbation, which is a problem ofintegral geometry. Then we convert this 2-D equation into 1-D integral equation by POuriertransform and the properties of Delta function. Finally the uniqueness of solution to this1-D equation is proven by means of contraction mapping. The method proposed in thisarticle give a new algorithm for 2-D wave velocity inversion. |
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| Keywords: | Inverse problem linearization uniqueness integral geometry |
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