The problem of free oscillations of a heterogeneous sphere is reformulated in terms of dispersion over a plane half-space composed of anisotropic layers having a superposed velocity gradient. This transforms the standing wave discrete spectrum to a traveling-wave continuous spectrum and considerably simplifies the analysis of surface waves on a sphere. Minor modifications make it possible to use any Love wave computer program to compute dispersion on a sphere. Results of the method are compared with those obtained from numerical integration of the exact equations of motion. Agreement is generally better than 0.06 per cent. Dispersion for the fundamental and first seven to eight higher Love modes is presented for a continental and an oceanic path. The oscillatory nature of the group velocity curves becomes more pronounced when, a velocity reversal takes place. Calculations of higher-mode group velocity structure and displacement illustrate the mechanism of propagation of the S_a wave. By successive modifications of a previously developed mantle structure, a new suboceanic model is determined which satisfies Love wave and torsional oscillation data
