The interactions of elastic SH waves with a given set of m concentric elastic spherical layers immersed in an infinite, homogeneous, isotropic, elastic space are studied. The expansion of the generalized Debye potential which corresponds to the exact solution of this scattering problem is obtained directly from the solution of two simpler problems. From this expansion is extracted the series of elements which corresponds to waves which have interacted with the interface below any layer. A detailed asymptotical study of this series is given. The results of this study are interpreted in terms of geometrical optics.