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Ground‐motion prediction equations (GMPEs) are calibrated to predict the intensity of ground shaking at any given location, based on earthquake magnitude, source‐to‐site distance, local soil amplifications, and other parameters. GMPEs are generally assumed to be independent of time; however, evidence is increasing that large earthquakes modify the shallow soil conditions and those of the fault zone for months or years. These changes may affect the intensity of shaking and result in time‐dependent effects that can potentially be resolved by analyzing between‐event residuals (residuals between observed and predicted ground motion for individual earthquakes averaged over all stations). Here, we analyze a data set of about 65,000 recordings for about 1400 earthquakes in the moment magnitude range 2.5–6.5 that occurred in central Italy from 2008 to 2017 to capture the temporal variability of the ground shaking at high frequency. We first compute between‐event residuals for each earthquake in the Fourier domain with respect to a GMPE developed ad hoc for the analyzed data set. The between‐events show large changes after the occurrence of mainshocks such as the 2009 Mw 6.3 L'Aquila, the 2016 Mw 6.2 Amatrice, and Mw 6.5 Norcia earthquakes. Within the time span of a few months after the mainshocks, the between‐event contribution to the ground shaking varies by a factor 7. In particular, we find a large drop in the between‐events in the aftermath of the L'Aquila earthquake, followed by a slow positive trend that leads to a recovery interrupted by a new drop at the beginning of 2014. We also quantify the frequency‐dependent correlation between the Brune stress drop Δσ and the between‐events. We find that the temporal changes of Δσ resemble those of the between‐event residuals; in particular, during the period when the between‐events show the positive trend, the average logarithm of Δσ increases with an annual rate of 0.19 (i.e., the amplification factor for Δσ is 1.56 per year). Breakpoint analysis located a change in the linear trend coefficients of Δσ versus time in February 2014, although no large earthquakes occurred at that time. Finally, the temporal variability of Δσ mirrors the relative seismic‐velocity variations observed in previous studies for the same area and period, suggesting that both crack healing along the main fault system and healing of microcracks distributed at shallow depths throughout the surrounding region might be necessary to explain the wider observations of postearthquake recovery.
We derive a set of regional ground-motion prediction equations (GMPEs) in the Fourier amplitude spectra (FAS-GMPE) and in the spectral acceleration (SA-GMPE) domains for the purpose of interpreting the between-event residuals in terms of source parameter variability. We analyze a dataset of about 65,000 recordings generated by 1400 earthquakes (moment magnitude 2: 5 <= M-w <= 6: 5, hypocentral distance R-hypo <= 150 km) that occurred in central Italy between January 2008 and October 2017. In a companion article (Bindi, Spallarossa, et al., 2018), the nonparametric acceleration source spectra were interpreted in terms of omega-square models modified to account for deviations from a high-frequency flat plateau through a parameter named k(source). Here, the GMPEs are derived considering the moment (M-w), the local (M-L), and the energy (M-e) magnitude scales, and the between-event residuals are computed as random effects. We show that the between-event residuals for the FAS-GMPE implementing M-w are correlated with stress drop, with correlation coefficients increasing with increasing frequency up to about 10 Hz. Contrariwise, the correlation is weak for the FAS-GMPEs implementing M-L and M-e, in particular between 2 and 5 Hz, where most of the corner frequencies lie. At higher frequencies, all models show a strong correlation with k(source). The correlation with the source parameters reflects in a different behavior of the standard deviation tau of the between-event residuals with frequency. Although tau is smaller for the FAS-GMPE using M-w below 1.5 Hz, at higher frequencies, the model implementing either M-L or M-e shows smaller values, with a reduction of about 30% at 3 Hz (i.e., from 0.3 for M-w to 0.1 for M-L). We conclude that considering magnitude scales informative for the stress-drop variability allows to reduce the between-event variability with a significant impact on the hazard assessment, in particular for studies in which the ergodic assumption on site is removed.