固体中弹性波的被动层析成像
Passive tomography for elastic waves in solids
摘要：
本文导出了在两个不同点记录的环境噪声的互相关与粘性阻尼介质中弹性波的格林函数之间的关系。格林函数允许估计物理参数，例如速度或距离。此外，通过引入J-L提出的格林关联函数，扩展了这一工作。[Lacoume 07]中的Lacoume。最近的一些工作证明了从环境噪声的互关联函数中重构标量波格林函数的可能性。在这项工作中，我们考虑矢量波在三维固体介质中传播。开发了两种方法。首先，我们推广了Y. Colin de Verdi`ere在[ColinDeVerdiere 09]中，使用线性算子理论将标量波的互相关与1D格林函数联系起来。第二种方法在傅立叶理论的框架内重铸了三维问题。这可以提高对[Lacoume 07]中概述的潜在物理过程的物理理解。
英文摘要：
In this paper we derive relations between the cross-correlation of ambient noises recorded at two different points and the Green's function of the elastic waves in a medium with viscous damping. The Green's function allows to estimate physical parameters such as speeds or distances. Furthermore, this work is extended by introducing the Green's correlation function proposed by J-L. Lacoume in [Lacoume07]. Some recent works proved the possible reconstruction of the Green's function for scalar waves from the cross-correlation function of ambient noise. In this work, we consider vector waves propagating in a three dimensional solid medium. Two approaches are developed. Firstly, we extend theoretical derivations proposed by Y. Colin de Verdi`ere in [ColinDeVerdiere09], relating cross-correlation of scalar waves to 1D Green's function using linear operator theory. The second approach recasts the three dimensional problem in the framework of Fourier theory. This allows to improve physical understanding of the underlying physical processes as outlined in [Lacoume07].
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