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 ML, 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 ML and fault size, and is consistent with empirical relationships between magnitude and fault size, and between seismic energy and magnitude.