The observed dispersion of Rayleigh waves across the Atlantic and Pacific oceans can be accounted for by considering the propagation of such waves through a system consisting of water and unconsolidated sediments overlying a thick layer of ultrabasic rock. This contrasts with all former treatments, which have considered the effect of the water layer to be negligible. The depth of the water-sediment layer and the speed of shear waves in the underlying ultrabasic layer are obtained for several paths across the Atlantic and Pacific oceans. The results for the Atlantic are in good agreement with the data obtained in a recent seismic refraction measurement made 120 miles northwest of Bermuda, and offer strong evidence that the result of this single refraction measurement will be found to be typical of the entire ocean. No significant difference in the nature of the suboceanic basement of the Atlantic and Pacific has been found, since the velocity of shear waves in the upper-most 50 to 100 km. was calculated to be 4.45 km/sec. for both oceans. Previously reported differences in Atlantic and Pacific velocities for Rayleigh waves of some selected period are now believed to be due primarily to differences in the depth of water plus sediment in the two oceans.