The Gutenberg model of the earth mantle and a homogeneous core have been used in a study of statical deformations of the earth by tidal attractions and under surface loads of spherical harmonic n types. Displacement and potential distributions within the earth are shown for eleven n values less than 16, and the values of Love's numbers k, h, and l and the similar k′ and h′ in the load problem are calculated for these n values. Free oscillations of the earth model have also been studied. Displacement and potential distributions for the above n values are drawn. The effect of self‐gravitation on the oscillation periods is about 1 per cent for n = 6, and it would be smaller for larger n. The upper limit of the rigidity of the core which is compatible with the observations of the free oscillations is shown to be 1010 dynes/cm2. The radial displacement distributions within the mantle and the core are shown for various rigidity values of the core.
A method is proposed by which we can calculate group velocity in surface wave problems without using numerical differentiation. This method is applied to the study of shear velocity distribution in the upper mantle by mantle Rayleigh and Love waves. The present study gives preference to the 8099 model proposed by Dorman and to the Lehmann* model proposed here as the models of the upper mantle structure in the oceanic and the continental regions, respectively.
Varying parametrically the rigidity of the earth's core, i.e. µo of the Gutenberg model of the earth, we calculate free periods of spheroidal and toroidal oscillations of the earth for n = 2. For a fixed µo, we get an infinite number of periods for the spheroidal and toroidal modes. Normalizing their surface oscillation amplitudes, we pick up from among them an oscillation of the minimum total kinetic energy. This may be considered to be the most easily excitable oscillation for the µo by surface origins. The periods of both spheroidal and toroidal oscillations thus picked up are plotted against the corresponding µo, and from this we may conclude that the maximum rigidity of the earth's core compatible with the observations of spheroidal or toroidal oscillations is 1010 or 1012 dynes/cm2 for n = 2.
Wave generations from line sources within the ground are studied.Numerical details are worked out for the line source of step function type in time. The results to be noted are as follows;(1) At the "epicenter", the displacement is a simple pulse followed by a gradual decrease to a permanent displacement.(2) RAYLEIGH waves appear at a certain distance from the epicenter. (3) Permanent displacements are rather large even at points far away from the origin. They are comparable with the amplitudes of RAYLEIGH waves at the respective paints.(4) There is no S phase in seismograms to be obtained for the wave origin of dilatational type.
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