Since M w is based on an estimate of the seismic moment M 0 4, 5, it provides fault-averaged, low-frequency information on source processes but relatively less information about the small-wavelength high-frequency rupture details 6. The moment magnitude M w 2, 3 is used by the seismological community as the primary measure of the earthquake size. To improve the spatial resolution of such maps for rapid response actions, the rapid determination of an earthquake size and location supports the information provided by the actual ground motion measurements (if available) and predicted ones. In this context, shaking maps 1 become a de-facto standard for a timely dissemination of the ground shaking experienced in the area struck by an earthquake. In the aftermath of an earthquake, the rapid assessment of both location and extension of potentially damaging ground shaking is a primary task for seismological agencies supporting emergency managers. The procedure we propose is therefore a significant step towards a quick assessment of earthquakes damage potential and timely implementation of emergency plans. The new M r scale allows us to improve the prediction of the earthquake shaking potential, as shown by the reduction of the between-event residuals computed for the peak ground velocity. Since the observed seismicity does not agree with the assumptions on stress drop in the definition of M w, we exploit the availability of both E r and M 0 to modify the definition of M w and introduce a rapid response magnitude (M r), which accounts for the dynamic properties of rupture. Our results show the limitation of using M 0, and in turn M w, to capture the variability of the high frequency ground motion. The analysis of the M 0-to-E r scaling highlights a breaking of the source self-similarity, with higher stress drops for larger events. In this work the scaling of seismic moment (M 0) and radiated energy (E r) is investigated for almost 800 earthquakes of the 2016–17 Amatrice-Norcia sequences in Italy, ranging in moment magnitude (M w) from 2.5 to 6.5.
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