## Moment-Rate Scaling for Earthquakes 3.3 <= M <= 5.3: Spectra Are Not Classic Aki-Brune

### Ralph Archuleta

UC Santa Barbara

- Date & Time
- Location
- Building 3, Rambo Auditorium
- Host
- Annemarie Baltay
- Summary
Since the classic papers by Aki (1967, JGR) and Brune (1970, JGR), a basic axiom in seismology is that for all earthquakes the Fourier amplitude spectra of the source moment rate have a similar shape characterized by 1) a low-frequency asymptote f0 proportional to seismic moment, 2) spectral decay of the high-frequencies as f-2 and 3) a single corner fc (intersection of the low- and high-frequency asymptotes) such that the seismic moment is proportional to fc3. We (Archuleta and Chen, 2016, GRL) have recently found an apparent moment rate function that accurately predicts the scaling with magnitude of peak ground acceleration (PGA), peak ground velocity (PGV), peak Wood-Anderson displacement and the ratio of PGA/2?PGV (a dominant).

The moment rate function is characterized by two time constants that scale with seismic moment: 1) a time to reach the peak moment rate and 2) a time for the total duration. The source spectrum is not the classic Aki-Brune spectrum. While the new source is also flat at low-frequencies and has a f-2 decay at high frequencies, there is an intermediate trend where the spectral amplitudes decay like f-1. Thus, the spectrum has two corners?a lower frequency one associated with the total duration and a higher frequency one associated with the time to reach the peak moment rate. We show that if an earthquake occurs where the medium has typical attenuation observed in tectonically active areas (e.g., western US, Japan, Taiwan), the higher corner will be masked and in all likelihood never recovered. However, in regions with low attenuation, e.g., parts of eastern US or stable craton areas, the second corner should be observed. The presence of the second corner has direct implications about stress drop. It is a possible explanation for the difference between seismologically determined stress drops and stress parameters used to predict peak ground motions. The scalable moment rate function might be explained by different physical models of t he earthquake source, but our preference is an asperity model first described by McGarr (BSSA, 1981) and later by Boatwright (BSSA, 1988).