The polar phase shift of surface waves on a sphere

It has been demonstrated by means of a model experiment that elastic surface waves on a sphere advance in phase by π/2 on each crossing of the polar or antipodal region. Comparison of the asymptotic forms of solutions of the wave equation for displacements and dilatation before the polar crossing with those that apply afterward also show the π/2 phase shift. Similarly a π/4 phase advance occurs for waves leaving a point source. Because of the occurrence of the polar phase shift, it is necessary to correct previously published Rayleigh wave and Love wave phase velocities measured by correlation of phases over complete circumferential paths. The corrected Rayleigh wave phase velocity curve is presented here. The polar phase shift is involved in the determination of periods of free oscillation of the earth from surface wave data. Using data from the great Chilean earthquake of May 22, 1960, it is shown that the ratio of the earth's circumference to the wave length at free oscillation periods gives very nearly half integers in accordance with the formula 2 π a λ = n + 1 2 ·