Stable and transportable regional magnitudes based on coda-derived moment-rate spectra

We describe an empirical calibration method for obtaining stable seismic source moment-rate spectra derived from regional coda envelopes using broadband stations. The results of applying this method yield source spectra that are more stable than any other direct-phase measure to date. The procedure accounts for all propagation, site, and S-to-coda transfer function effects. The resultant coda-derived moment-rate spectra are then used to provide traditional band-limited magnitudes (e.g., M-L, M-b), as well as an unbiased, unsaturated magnitude (moment magnitude, MW) that is tied to a physical rneasure of earthquake size (i.e., seismic moment). We validate our results by comparing our coda-derived moment estimates with those obtained from long-period waveform modeling. Most importantly, we demonstrate that the interstation magnitude scatter is significantly reduced when using long-window-length coda (i.e., M-w(coda) and m(b)(coda)). However, when we use short-window coda measurements of 5 sec in length taken after twice the direct-wave travel time, the scatter remains large, comparable to direct waves. Once calibrated, the coda-derived source spectra provide stable, unbiased magnitude estimates for events that are too small either to be reliably waveform modeled or to be seen at far-regional and teleseismic distances. This property is ideal for sparse local or regional networks. We found that our source amplitude estimates were nearly insensitive to the expected source radiation pattern and exhibited roughly a factor of 3-5 less interstation scatter when compared against coda duration and conventional direct-phase measurements (e.g., P-g, L-g). We also found that the coda stability, as measured by the interstation scatter for common events, reached a minimum value beyond a certain critical measurement window length. For example, at 6-8 Hz, the interstation standard deviation was less than 0.08 provided the coda measurement was at least similar to80 sec in duration, whereas at 1.5-2.0 Hz, the critical window length was similar to100 sec. For all frequency bands, as the coda window becomes shorter, the standard deviation increases, asymptotically approaching the direct-wave scatter. In this article we describe in detail the calibration methodology and address concerns related to choosing optimal measurement window lengths, estimating error, testing empirical path corrections, and tying coda amplitudes to an absolute scale. In order to demonstrate the usefulness and transportability of our method, we chose the Dead Sea Rift as our study area.