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Bulletin of the Seismological Society of America; February 1968; v. 58; no. 1; p. 133-170
© 1968 Seismological Society of America
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Theoretical seismograms of torsional disturbances excited at a focus within a heterogeneous spherical earth—Case of a Gutenberg-Bullen A' earth model

YASUO SATÔ, TATSUO USAMI and MARK LANDISMAN

EARTHQUAKE RESEARCH INSTITUTE UNIVERSITY OF TOKYO
GEOSCIENCES DIVISION SOUTHWEST CENTER FOR ADVANCED STUDIES

Abstract

Torsional disturbances generated by a buried source within a Gutenberg-Bullen A' spherical earth model are calculated and interpreted. Since the earth is a finite bounded body, the entire disturbance can be obtained by a superposition of the contributions from the normal modes of free oscillation. The Stoneley-mode transitions between the higher radial modes, which were previously found for the spheroidal oscillations, do not occur in the present case since the torsional disturbances do not propagate into the fluid core. Phase velocity is a monotonic function of period for all of the radial modes in the period range investigated. Although the group velocity of the fundamental radial mode is also monotonic, the higher radial modes exhibit narrow group velocity maxima. The spectral amplitude common to all epicentral distances, called the Common Spectrum, decays smoothly with increasing source depth for the fundamental radial mode. The excursions of the higher mode eigenfunctions cause complicated relations between the Common Spectrum and the source depth. The fundamental radial mode is mainly related to the surface waves and the higher modes to the body waves. Direct waves as well as reflections from the surface and the mantle-core boundary can be found in the theoretical seismograms. The amplitude of the long period surface waves is appreciable even when the source is 650 km below the surface. The amplitude of the G wave decreases gradually with depth and is smallest for sources beneath the upper mantle low-velocity channel of the Gutenberg-Bullen A' model. The higher mode disturbances which arrive at about the same time as the G wave are smallest when the source depth coincides with the "channel axis" of the upper mantle low-velocity zone in the Gutenberg velocity distribution. This decrease in energy available at the surface indicates that short period waves are efficiently trapped in the channel for sources near the channel axis. At large epicentral distances the theoretical seismograms show a displacement which clearly begins at the travel time of the diffracted S waves.




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S. N. BHATTACHARYA
Exact solutions of the equation for the free torsional oscillations of an inhomogeneous sphere
Bulletin of the Seismological Society of America, February 1, 1972; 62(1): 31 - 38.
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