论文标题
从高频外部Cauchy数据中恢复分段平滑密度和Lamé参数
Recovery of piecewise smooth density and Lamé parameters from high-frequency exterior Cauchy data
论文作者
论文摘要
我们认为一种占据有界结构域D的各向同性弹性介质，其密度和LAMé参数是平滑的。在弹性波的初始值反问题中，我们为弹性波方程提供了解决方案操作员，但仅在域D之外，仅用于支持d外部的初始数据，我们研究了密度和lamé参数的恢复。对于已知密度，最近使用散射控制方法获得了恢复波速的结果。在这里，我们将此结果扩展到包括在某些几何条件下使用微局部分析的技术以及与局部张量层析成像的连接的技术，还包括在某些几何条件下的LAMé参数之外的恢复。
We consider an isotropic elastic medium occupying a bounded domain D whose density and Lamé parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave equation, but only outside the domain D and only for initial data supported outside D, and we study the recovery of the density and Lamé parameters. For known density, results have recently been obtained using the scattering control method to recover wave speeds. Here, we extend this result to include the recovery of the density in addition to the Lamé parameters under certain geometric conditions using techniques from microlocal analysis and a connection to local tensor tomography.
