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We consider the inverse boundary value problem of recovering piecewisehomogeneous elastic tensor and piecewise homogeneous mass density from alocalized lateral Dirichlet-to-Neumann or Neumann-to-Dirichlet map for theelasticity equation in the space-time domain. We derive uniqueness foridentifying these tensor and density on all domains of homogeneity that may bereached from the part of the boundary where the measurements are taken by achain of subdomains whose successive interfaces contain a curved portion.

Uniqueness for the inverse boundary value problem of piecewise homogeneous anisotropic elasticity in the time domain