Asymptotic Structure in Eigenfrequencies of Spheroidal Normal Modes of the Earth

The modes of the spheroidal oscillations nSl of the Earth can, for small l, be classified according to the body wave modes PKIKP (compressional oscillations in the whole Earth), (ScS)v (shear oscillations in the mantle) and J (shear oscillations in the inner core). Analysis of the asymptotic behaviour of the eigenperiods according to this classification shows that the asymptotic structure for modes PKIKP type is perturbed by the presence of the core-mantle and inner-outer core boundaries, whereas that for modes of (ScS)v of type depends strongly on upper mantle structure. The inner core was virtually homogeneous in the models analysed, and this was reflected in an absence of perturbations in the asymptote of the J mode. Estimates of the radial travel times of each wave type can be derived from the asymptotic eigenperiods. The radial modes nSo are all of PKIKP type, and the asymptotic structure of observed eigenperiods of these modes is clearly perturbed by the presence of the core discontinuities, thus confirming the existence of the solotone effect analysed theoretically by MNabb et al.