Unique Recovery of Piecewise Analytic Density and Stiffness Tensor from the Elastic-Wave Dirichlet-To-Neumann Map
Maarten V. de Hoop, Gen Nakamura, Jian Zhai · SIAM Journal on Applied Mathematics · 2019
We study the recovery of piecewise analytic density and stiffness tensor of a three-dimensional domain from the local dynamical Dirichlet-to-Neumann map. We give global uniqueness results if the medium is (1) transversely isotropic with known axis of symmetry in each subdomain (2) orthorhombic with one of the three known symmetry planes tangential to a flat part of the accessible interface. We also obtain uniqueness of a fully anisotropic stiffness tensor, assuming that it is piecewise constant and that the interfaces which separate the subdomains have curved portions. The domain partition need not to be known. Precisely, we show that a domain partition consisting of subanalytic sets is simultaneously uniquely determined.