Evidence for non‐constant energy/moment scaling from coda‐derived source spectra

Abstract

We present two lines of evidence showing the ratio of seismically radiated energy (ER) to seismic moment (Mo) increases with increasing moment for crustal events spanning 5 orders in seismic moment. This ratio, often referred to as the scaled energy (=ER/M0) has been elusive and the subject of recent debate within the seismological community. Because significant frequency‐dependent corrections must be made to account for source and path heterogeneity, it is not uncommon that energy estimates of the same event by different researchers have significantly different values. To minimize some of the potential problems, we used the regional coda methodology outlined by Mayeda et al. (2003) on 4 large earthquake sequences; Mw 7.4 and 7.2 Izmit/Duzce, Mw 7.2 Gulf of Aqaba, Mw 7.3 Landers, and Mw 7.2 Hector Mine. This methodology has been shown to provide the lowest variance estimate of the source spectrum when compared against traditional direct wave estimates. In our first approach we made energy estimates from coda‐derived spectra and observed that increases with increasing moment for 3.7 ≤ Mw ≤ 7.4. In our second approach we used the simple idea outlined by Prieto et al. (2004) to directly test for self similarity. Under self similarity, earthquake source spectra scaled by ω−3 should have the same shape. To test this, one needs very stable spectra either through spectral stacking of direct wave spectra or by the use of stable coda‐derived spectra. For all sequences we found that the mainshocks and larger aftershocks had significantly different spectral shapes than the smaller events. The scaled ω−3 spectra of the larger events represented an upper bound, having larger amplitudes near the corner frequency. In fact, an ω−3.5 scaling moved the larger events closer to the mean of the spectral population, though the spectral shape differences persisted. These results strongly suggest that earthquakes are not scaling self‐similarly and that complexities in the rupture process such as variable slip velocity exist between small and large events.