Bulk-wave polarization fields in transversely isotropic elastic media

The bulk-wave polarization field of a transversely isotropic elastic material has three branches, each rotationally symmetric about the axis of transverse isotropy. The branches are not uniquely defined, however, by the propagation condition for plane bulk waves since the polarization of each wave is determined only to within a factor of -1. Two ground rules are adopted: discontinuities in the branches are restricted to the acoustic axes, along which two or all three of the plane bulk waves have equal speeds; and, in a specified ordering, the three polarizations are taken to form a right-handed orthonormal set. The topological character of the branches depends on the combinations C-11 - C-44, C-33 - C-44, C-13 + C-44 of the five distinct elastic moduli of the material. In the regular case in which each combination is non-zero, the ground rules permit an unambiguous specification of the branches, but when C-11 = C-44 nonuniqueness results from the presence of discontinuities in the basal plane. Polarization fields are constructed for all transversely isotropic elastic materials with positive definite strain energy and the results are related to an elastodynamic classification of these materials which is similarly exhaustive.