Recent results concerning the relationship of S-wave far-field frequencies to stress drop are discussed. It is suggested that the corner frequency as picked by Madariaga <1977> from his theoretical spectra is not consistent with the way in which corner frequencies were picked by Tucker and Brune <1973, 1977>. When the difference is taken into account, the stress drops inferred from the Madariaga relationship and his method of picking corner frequencies are roughly the same as inferred using the Brune <1970, 1971> relationship and the Tucker and Brune method of picking corner frequencies (for those relatively few experimental spectra which are similar in shape to the Madariaga theoretical spectra). Far-field spectra for a number of new finite element models of fault ruptures in a half-space are presented, and for these data, new values for the relationship between source dimension and corner frequency are obtained. Fault models used include semicircular faults with rupture initiation at the surface and at depth and rectangular faults with unilateral and bilateral rupture propagation. The results indicate that there is a considerable variation in corner frequency with respect to type of rupture and position around the rupture. Because of the variation it is not possible to conclude, without more calculations, what the best average relationship between corner frequency and source dimension is; however, a value of K about 1/2 is reasonable where K = fcr/β (fc = corner frequency, r = radius, and β = shear wave velocity). Dahlen <1974> speculated that the corner frequencies picked experimentally could be significantly altered by scattering. For the San Fernando aftershocks, it is possible to make a case tht this is not so. Many of the San Fernando aftershocks show very simple pulse shapes, with a pulse duration consistent with the spectral corner frequency and little latter arriving energy - a direct indication that scattering is not radically affecting the results. |