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Characteristic periods of fundamental and overtone oscillations of the earth following a deep-focus earthquake

LAMONT-DOHERTY GEOLOGICAL OBSERVATORY OF COLUMBIA UNIVERSITY, PALISADES, NEW YORK 10964

Abstract

The deep-focus earthquake of July 31, 1970, (1.5°S, 72.6°W, h = 651 km, M_b = 7.1) excited a set of fundamental and overtone free oscillations. From analysis of seismograms recorded at Berkeley, California, at an ocean-bottom station in the Pacific, and at Ogdensburg, New Jersey, the fundamental spheroidal oscillations, l = 10-98, and a number of overtones with n = 1, 2, and 3, fundamental torsional oscillations, l = 3-70, and overtones with n = 1, 2, 3, and 4, are identified. The majority of resolved spectral peaks are above the 95 per cent confidence level. For some modes with periods less than 300 sec, the observed period at each station differs by up to 2 sec. This path-dependency of the period may thus suggest the existence of lateral heterogeneity in the upper mantle. The observed periods are compared to calculated periods for Haddon-Bullen's model HB1 and Derr's model DI-11; for fundamental modes the agreements are good, while differences up to 2 sec exist for some overtone modes. A relationship between order of oscillations, l, the frequency, _nl, and the ray parameter dt/d is derived, which is equivalent to the Jean's equation for phase velocity. The relationship implies that each mode with period _nT_l will travel with phase velocity d/dt along its own ray with parameter dt/d. Other models will travel along the same ray if they have the same ray parameter.