Variability of seismic source spectra derived from cohesive-zone models of circular rupture

Static stress drop of earthquakes is often estimated from far-field body-wave spectra using measurements of corner frequencies, together with seismic moment, which can be computed from the low-frequency part of the spectrum. Corner frequencies are used to infer the source dimension based on a specific theoretical model. The most widely used model is from Madariaga (1976), who considered a bilateral rupture expanding at a constant speed on a circular fault. This model assumes that the rupture front is characterized by an abrupt change of fault strength from a uniform initial prestress to a kinetic frictional stress, and hence the stress is singular at the rupture front. In this study, we investigate variability of source spectra derived from dynamic models of expanding bilateral ruptures on a circular fault with a cohesive zone that prevents a stress singularity at the rupture front. We study the dependence of far-field body-wave spectra on the rate of frictional weakening, rupture speed, and dynamic stress drop. Our results show that P- and S-wave corner frequencies of displacement spectra are systematically larger than those predicted by Madariaga (1976). Well-resolved stopping phases generated at the edge of the slipping zone result in a shorter source duration and hence higher corner frequencies. For ruptures propagating at 90 percent of the S-wave speed, models with the cohesive-zone size much smaller than the source dimension show that the azimuthal average of P-wave corner frequencies is about 20 percent larger than that of Madariaga (1976). Thus for these ruptures, application of the Madariaga model overestimates stress drops by factors of 1.7.