Propagation of Rayleigh Waves in the Earth

The propagation of Rayleigh waves in the Earth is investigated in the whole range of periods T from about 10s up to one hour. Three methods are necessary in order to cover this range of periods effectively. The standard flat Earth method, with neglect of gravity, gives values for the phase velocity C correct to within 1 per cent up to T = 50s only, and for the group velocity U up to T = 250s. The method of the flattening of the Earth, with neglect of gravity, has the 1 per cent accuracy limits for C and U at 300 and 400, respectively. Inclusion of gravity effects in the flattening of the Earth approximation does not alter the above limits. For T > 300 (n < 25) one must determine the period T(n) of free oscillation of the Earth as a function of the order of the spherical harmonic n. This involves the solution of a system of differential equations of the sixth order, in which the gravitational effects are included. The wave penetrates appreciably into the core already at T = 600. Using the above three methods in their respective ranges of validity, we have evaluated C(T) and U(T) for (1) Bullen's Model B, (2) the Jeffreys-Bullen Model, as modified by Dorman, Ewing and Oliver, and (3) the Gutenberg Model. The observed Rayleigh group velocity data of Ewing and Press for T < 380 s and the phase velocity data of Nafe and Brune for T < 300 s agree with the values computed for the Gutenberg model, but not for the other models. This substantiates a previous conclusion reached by Takeuchi, Press and Kobayashi and by Dorman, Ewing and Oliver that the observed Rayleigh wave data provide evidence in support of Gutenberg's low-velocity layer. The few observed Rayleigh group velocities between T = 400 and 600 are substantially lower than the theoretical values for all the three models.