  This paper is devoted to studying impedance eigenvalues (that is, eigenvalues
of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic
wave problem, and their potential use as target-signatures for fluid-solid
interaction problems. We first consider several possible families of
eigenvalues of the elasticity problem, focusing on certain impedance
eigenvalues that are an analogue of Steklov eigenvalues. We show that one of
these families arises naturally in inverse scattering. We also analyse their
approximation from far field measurements of the scattered pressure field in
the fluid, and illustrate several alternative methods of approximation in the
case of an isotropic elastic disk.
