Gauge freedoms in the anisotropic elastic Dirichlet-to-Neumann map

We address the inverse problem of recovering the stiffness tensor and density of mass from the Dirichlet-to-Neumann map. We study the invariance of the Euclidean and Riemannian elastic wave equation under coordinate transformations. Furthermore, we present gauge freedoms between the parameters that leave the elastic wave equations invariant. We use these results to present gauge freedoms in the Dirichlet-to-Neumann map associated to the Riemannian elastic wave equation.