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Recovery of piecewise smooth Lamà © parameters for local exterior data de Hoop, Maarten


We consider a bounded domain $\Omega \subset \mathbb{R}^3$ on which Lam\'{e} parameters are piecewise smooth. We consider the elastic wave initial value inverse problem, where we are given the solution operator for the elastic wave equation, but only outside $\Omega$ and only for initial data supported outside $\Omega$. Using our recently introduced scattering control series in the acoustic case, and a layer stripping argument, we prove that piecewise smooth Lam\'{e} parameters are uniquely determined by this map. We make use of microlocal analysis to avoid using unique continuation results but require a convex foliation condition, introduced by Uhlmann and Vasy, for both the \textit{P}- and \textit{S}-wave speeds. Joint research with P. Caday, G. Uhlmann and V. Katsnelson.

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