Recovery of discontinuous Lam\'e parameters from local dynamic boundary data

Abstract

Consider an isotropic elastic medium $\Omega \subset \mathbb{R}^3$ whose Lam\'e 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 $\Omega$ and only for initial data supported outside $\Omega$. Using the recently introduced scattering control series in the acoustic case, we prove that piecewise smooth Lam\'e parameters are uniquely determined by this map under certain geometric conditions. We also show the extent that multiple scattering in the interior may be suppressed and eliminated with access to only this partial solution map, which is akin to the dynamic Dirichlet-to-Neumann map.