We discuss unique identification of elastic parameters from
dynamic displacement-traction boundary measurements for anisotropic
elastic media. Surface measurements are encoded in the so-called
Dirichlet-to-Neumann or DN map. It is known that
the elastic moduli are uniquely determined by the DN map for isotropic
media. We consider a certain class of transversely isotropic media,
for which elastic waves propagate along geodesic segments of
three Riemannian metrics. Under mild conditions the
light cone associated to one of the metrics is always disjoint from the
others. By microlocally decoupling the equations of elastodynamics
(following a result of M. Taylor), we show that the DN map
uniquely determines the boundary distance function, or equivalently the
travel times through the object, for the disjoint wave mode.
We have shown that material parameters of general
anisotropic elastic media may be uniquely determined by the
DN map only up to pullback by diffeomorphisms fixing the boundary.
This is joint work with L. Rachele.