Earthquake source scaling and self-similarity estimation by stacking P and S spectra

We investigate source parameter scaling by stacking P and S spectra from a set of small events (M = 0.5 - 3.0) recorded between 1993 and 2003 by the ANZA Seismic Network (http://eqinfo.ucsd.edu). Around 2700 events were located in a tightly clustered volume (100 km3), which included the October 31 2001, M = 5.1 event and its aftershock sequence. Between 9 and 12 ANZA network stations recorded the ~400 events with M > 0.5, which have high signal to noise ratios. The observed spectra are the product of source spectra, receiver and propagation response functions as well as source and receiver site effects. We apply a signal to noise ratio cutoff and corrections for gain and instrument response. For all events in the tight cluster, assuming they have similar focal mechanisms, we attempt to isolate differences in the source spectra. Since each station records multiple events and each event is recorded at multiple stations, we can solve for source and station terms by an iterative method. For all events in the tight cluster the ray path from source to a single seismic station is similar, making the along-path-attenuation similar as well. We use these results to test whether apparent stress (the ratio between radiated seismic energy and moment) increases with increasing moment or remains constant for a wide range of event sizes. We also examine the self-similarity of earthquakes. If earthquakes are self-similar, the spectra of all events, once corrected for attenuation, should simply be rescaled versions of the spectra of different sized events. This will be true regardless of the specific source model or the assumed spectral falloff at high frequencies.