Various aspects of elastic wave propagation in a spherically symmetric, non-gravitating, isotropic, inhomogeneous medium are considered. It is shown through a simple example that the high frequency decoupling conditions of the vector wave equation may be approximately satisfied by real Earth models. An asymptotic theory is developed for the decoupled potential equations. This theory is applied to the case of a shear dislocation and to that of a center of compression in a radially heterogeneous medium. Explicit expressions are obtained for the ray-theoretical displacements.