Impact of Magnitude Selection on Aleatory Variability Associated with Ground-Motion Prediction Equations

In this study, we analyzed 10 yrs of seismicity in central Italy from 2008 to 2017, a period witnessing more than 1400 earthquakes in the magnitude range 2.5≤Mw≤6.5⁠. The data set includes the main sequences that have occurred in the area, including those associated with the 2009 Mw 6.3 L'Aquila earthquake and the 2016–2017 sequence (⁠Mw 6.2 Amatrice, Mw 6.1 Visso, and Mw 6.5 Norcia earthquakes). We calibrated a local magnitude scale, investigating the impact of changing the reference distance at which the nonparametric attenuation is tied to the zero‐magnitude attenuation function for southern California. We also developed an attenuation model to compute the radiated seismic energy (⁠Es⁠) from the time integral of the squared ground‐motion velocity. Seismic moment (⁠M0⁠) and stress drop (⁠Δσ⁠) were estimated for each earthquake by fitting a ω‐square model to the source spectra obtained by applying a nonparametric spectral inversion. The Δσ‐values vary over three orders of magnitude from about 0.1 to 10 MPa, the larger values associated with the mainshocks. The Δσ‐values describe a lognormal distribution with mean and standard deviation equal to log(Δσ)=(−0.25±0.45) (i.e., the mean Δσ is 0.57 MPa, with a 95% confidence interval from 0.08 to 4.79 MPa). The Δσ variability introduces a spread in the distribution of seismic energy versus moment, with differences in energy up two orders of magnitudes for earthquakes with the same moment. The variability in the high‐frequency spectral levels is captured by the local magnitude (⁠ML⁠), which scales with radiated energy as ML=(−1.59+0.52logEs) for logEs≤10.26 and ML=(−1.38+0.50logEs) otherwise. As the peak ground velocity increases with increasing Δσ⁠, local and energy magnitudes perform better than moment magnitude as predictors for the shaking potential. The availability of different magnitude scales and source parameters for a large earthquake population will help characterize the between‐event ground‐motion variability in central Italy.