The factorization method for inverse acoustic scattering in a layered medium
The factorization method for inverse acoustic scattering in a layered medium
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DOI：
10.1088/0266-5611/29/4/045010
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发表时间：
2013-04
期刊：
影响因子：
2.1
通讯作者：
O. Bondarenko;A. Kirsch;Xiaodong Liu
中科院分区：
文献类型：
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作者：
O. Bondarenko;A. Kirsch;Xiaodong Liu
在本文中，我们考虑了嵌入层状介质中的不可穿透障碍物引起的逆声散射问题。我们将证明分解方法可以用于恢复嵌入的障碍物；也就是说，当且仅当采样点 z 位于未知障碍物内部时，方程才可解。这里， 是与远场算子相关的自伴算子， 是格林函数关于 z 点背景介质散射问题的远场图。借助混合互易原理和散射算子的应用证明了分解方法的有效性。由于建立了混合互易原理，不再需要背景介质的格林函数知识，这使得该方法从计算的角度来看很有吸引力。本文只关注声软障碍，但分析可以很容易地扩展到声硬障碍，或者声软和声硬部分分开的障碍。最后，我们提供了径向对称情况的明确示例，并给出了一些数值示例。
In this paper, we consider a problem of inverse acoustic scattering by an impenetrable obstacle embedded in a layered medium. We will show that the factorization method can be applied to recover the embedded obstacle; that is, the equation is solvable if and only if the sampling point z is in the interior of the unknown obstacle. Here, is a self-adjoint operator related to the far field operator and ϕz is the far field pattern of the Green function with respect to the problem of scattering by the background medium for point z. The validity of the factorization method is proven with the help of a mixed reciprocity principle and an application of the scattering operator. Due to the established mixed reciprocity principle, knowledge of the Green function for the background medium is no longer required, which makes the method attractive from the computational point of view. The paper is only concerned with sound-soft obstacles, but the analysis can be easily extended for sound-hard obstacles, or obstacles with separated sound-soft and sound-hard parts. Finally, we provide an explicit example for a radially symmetric case and present some numerical examples.