Application to the $M_{w}$ 7.0 Hector Mine sequence

Next, we turn our attention to local and regional recordings of the $M_{w}$ 7.0 1999 Hector Mine mainshock and 6 aftershocks ranging between $M_{w}$ 3.7 and 5.4. In this case we consider 6 broadband stations ranging between  60 and 700 km: GSC, PFO, MNV, CMB, TUC, and ELK. All the events have independent regional seismic moment estimates from full waveform inversion by G. Ichinose (pers. comm., 2006). As observed for San Francisco Bay Area events, the coda spectral ratios for Hector Mine events were very stable, with average standard deviations of less than 0.1 for all frequencies. Figure 2.13 shows all 6 ratios, assuming both simultaneous source model fits and individual ratio fits. In all cases the high frequency asymptote is significantly above the theoretically predicted value. This is consistent with a break in self-similarity and is inconsistent with a standard self-similar Brune (1970) style omega-square model. Our preferred interpretation is that the apparent stresses are systematically lower for the aftershocks than the mainshock. If all events have Brune-style spectra with an f-2 fall-off at high frequencies, this implies the corner frequency scaling is steeper than f-3 for self-similar, constant apparent stress scaling. More in-depth results of this study can be found in (Mayeda et al., 2007).

Figure 2.13: Spectral ratios for the Hector Mine mainshock relative to 6 aftershocks. In each figure, we show the low and high frequency asymptotes assuming constant apparent stress scaling as solid lines. Dashed lines show the case if the spectral fall-off were 1.5 rather than 2.0. However, observations worldwide are inconsistent with a fall-off of 1.5 and we are left to assume that the apparent stresses are systematically lower for the aftershocks than the mainshock, breaking similarity.