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Bulletin of the Seismological Society of America; August 1975; v. 65; no. 4; p. 899-913
© 1975 Seismological Society of America
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The use of duration as a measure of seismic moment and magnitude

ROBERT B. HERRMANN

COOPERATIVE INSTITUTE FOR RESEARCH IN THE ENVIRONMENTAL SCIENCES UNIVERSITY OF COLORADO, BOULDER, COLORADO 80302

Abstract

The observed relationship between magnitude and duration is shown to be a result of the particular shape of the signal coda as a function of time. If the envelope of the coda follows a t–q relationship with increasing time, then the magnitude, m{tau}, based on a duration {tau} is consequently of the form


Formula

A study of the duration-magnitude and duration-moment relationships for a set of central United States earthquakes indicates that the linear relationship between m{tau} and log10{tau} is valid only over a limited range. The departure from the simple linear dependence is explained in terms of instrumental response and the shift of the source-spectrum corner frequency with increasing event size.




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