Abstract

Consider an isotropic elastic medium $\Omega \subset {\mathbb{R}}^3$ whose 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 Ω and only for initial data supported outside Ω. Using the recently introduced scattering control series in the acoustic case, we prove that piecewise smooth Lamé parameters are uniquely determined by this map under certain geometric conditions.

中文翻译：

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从外部柯西数据中恢复不连续的Lamé参数

摘要

考虑各向同性弹性介质 $\Omega \subset {\mathbb{[R}}^3$其Lamé参数分段平滑。在弹性波初始值反问题中，我们为弹性波方程提供了求解算子，但仅在Ω以外，并且仅在Ω之外支持初始数据。使用在声学情况下最近引入的散射控制序列，我们证明了在某些几何条件下，该图唯一确定分段平滑Lamé参数。