Propagation of Rayleigh Waves in the Earth

Abstract

As when the massy substance of the Earth quivers."-C. Marlowe, Tamburlaine the Great. Pt. 2 , I. I . SummaryThe 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 jlat Earth method, with neglect of gravity, gives values for the phase velocity C correct to within I per cent up to T = 50s only, and for the group velocity U up to T = 250s. The method of the jlattening of the Earth, with neglect of gravity, has the I 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( 7') and U( T) for (I) Bullen's Model B, (2) the Jeffreys-Bullen Model, as modified by Dorman, Ewiag and Oliver, and (3) the Gutenberg Model. The observed Rayleigh group velocity data of Ewing and Press for T < 380s and the phase velocity data of Nafe and Brune for T < 300s 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 lowvelocity layer. The few observed Rayleigh group velocities between T = 400 and 600 are substantially lower than the theoretical values for ail the three models.

Deep Earth Seismology: An Introduction and Overview

“…This instrument was deployed at 10 globally distributed International Geophysical Year network stations operated by Lamont. The modern approach was developed by Alterman et al (1959), who recast the system of three second-order partial differential equations into a system of six first-order differential equations, thus removing the need for differentiation of the elastic constants, and allowed the use of standard numerical methods to obtain the solution. Benioff (1958) reported an oscillation with a period of 57 min seen in the record of the 1952 Kamchatka earthquake.…”

Lateral Variations of Density in the Mantle

“…In the numerical calculations, Gutenberg's earth model is used and it is assumed that Ap does not change with depth. If we use Jeffreys's model instead, there will be no significant difference in the results Both of these models are listed by Alterman, Jarosh & Pekeris (1961). Table 4 gives the spherical harmonic coefficients of Ap as computed through equation (3.5).…”

Regionalization of the Arctic Region, Siberia and Eurasian Continental Area

“…Several attempts have been made to develope the same type of transformation for Rayleigh-wave computations (Alterman, Jarosch and Pekeris, 1961;Bolt and Dorman, 1961;Biswas, 1972;Schwab and and Knopoff, 1972), but these have all yielded only empirical results which lack general applicability. Thus, at the present time at least, it appears that one cannot apply transformation theory to Rayleigh-wave dispersion computations on any arbitrary, spherical, gravitating earth.…”