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The spectral theory of seismic sources

GEOPHYSICS DIVISION DEPARTMENT OF SCIENTIFIC AND INDUSTRIAL RESEARCH, WELLINGTON, New Zealand

Abstract

The far-field results of Brune's spectral theory are shown to be largely independent of his source model; this implies that the theory has even greater power than it seemed, but that its success in explaining the observed spectra does not in itself justify a dislocation model. Expressions are derived for seismic energy and characteristic stress which are independent of assumptions as to source model. For several models, the characteristic stress is found to be a good approximation to the stress-drop.

A theoretical relationship between earthquake magnitude M_L, stress-drop, and fault size is derived. This provides a means of estimating the stress-drop for earthquakes associated with aftershock sequences, using estimates of M_L and fault size, and is consistent with empirical relationships between magnitude and fault size, and between seismic energy and magnitude.

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