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Recovery of piecewise smooth Lamà © parameters for local exterior data

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Global analysis, analysis on manifolds; Dynamical systems and ergodic theory

video/mp4

Author affiliation: Rice University

2019-10-15

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/71907

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/