## 3 Seismotectonic Model  
The seismogenic model of the study area straddles northern and central Italy from the large flat area of the Po Plain (to the north) toward the northern flank of the Gran Sasso mountain range, the highest sector of the Apennines (to the south, Figure 1). The study area is wider than that previously studied ([PERSON] et al. [8]) through an old version of the simulator and the seismogenic sources now come from the latest 3.3.0 version of the DISS (DISS Working Group [9]). Historical and instrumental seismicity in the study area is mainly distributed along the axis of the northern and central Apennines chain and, secondarily, in correspondence with its foothills, plains, and coastal areas ([PERSON] et al. [10]). The causative sources of the earthquakes of these two regions have different parameters and kinematics, as shown by focal mechanisms ([PERSON] et al. [11]), active stress indicators ([PERSON] and [PERSON] [12]), geological data (see DISS Working Group [9] and references therein), and active strain data ([PERSON] et al. [13]). As matter of fact, the GPS data show the crustal extension at a rate of about 3 mm/yr across the Apennines belt and the compression towards the Adriatic foreland ([PERSON] et al. [13]). The active extension along the backbone of the Apennines is accommodated by normal faulting, which dominates along the hinge of the chain at shallow crustal seismogenic depth (blue polygons in Figure 1; e.g., [PERSON] et al. [14]). The strongest extensional recent earthquakes in the study area occurred during the 2016-2017 central Italy seismic sequence \begin{table}
\begin{tabular}{p{12.8 pt} p{128.0 pt} p{128.0 pt} p{128.0 pt}} \hline \hline \multicolumn{2}{c}{**Criterion**} & **Derived by** & **Formula** & **Our Choice** \\ \hline \multirow{3}{*}{1} & Threshold magnitude for the first event (named pivot) (\(M_{thr}\)) & Expert & \multirow{3}{*}{\(M_{pivot}\geq M_{thr}\)} & \multirow{3}{*}{\(M_{thr}=5.5\)} \\ \cline{1-1} \cline{3-4}  & Magnitude difference with the pivot (\(M_{pivot}-M_{E2}\)) & & & \\ \cline{1-1} \cline{3-4}  & Time difference between the occurrence of main shocks (\(t_{E2}-t_{E1}\)) & Empirical Relationship ([PERSON] and [PERSON] [5]) & \multirow{3}{*}{\((t_{E2}-t_{E1})\leq t_{GK}(M_{E1})\)} & \\ \cline{1-1} \cline{3-4}  & Spatial distance between hypocenters (\(|\vec{x}_{E2}-\vec{x}_{E1}|\)) & Empirical Relationship ([PERSON] and [PERSON] [5]) + Expert Judgment & & \(|\vec{x}_{E2}-\vec{x}_{E1}|\leq\text{chosen from:}\) \\ \cline{1-1} \cline{3-4}  & Spatial distance between hypocenters (\(|\vec{x}_{E2}-\vec{x}_{E1}|\)) & Empirical Relationship ([PERSON] and [PERSON] [5]) + Expert Judgment & & \(r_{GK}(M_{E1})\) \\ \cline{1-1} \cline{3-4}  & & & & \\ \cline{1-1} \cline{3-4}  & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Constitutive criteria for our clustering analysis algorithm. For each criterion, the second column shows rationale on which it is based, the third column contains formulas, and the last column contains choices used in this paper. that struck central Apennines with multiple mainshocks (Table 2). The sequence initiated on 24 August 2016 with the \(M_{w}\) 6.2 Amatrice earthquake and was followed on 26 October 2016 by the \(M_{w}\) 6.1 Visso earthquake, about 25 km to the north. The largest event, the \(M_{w}\) 6.6 Norcia earthquake, occurred on 30 October 2016 and nucleated between the source regions of the two previous mainshocks (e.g., [PERSON] et al. [15]; [PERSON] et al. [10]). Low-magnitude earthquakes of this sequence still occur today ([[http://terremoti.ingv.it/](http://terremoti.ingv.it/)]([http://terremoti.ingv.it/](http://terremoti.ingv.it/)) accessed on 22 November 2021). This seismic sequence activated a circa 80 km long, NNW-SSE trending, low-angle multiple fault systems (IDs 127 and 128 in Figure 1). These fault systems exhibit complex ruptures and are the easternmost normal faults of the central Apennines, just west of where compressional activity prevails (e.g., [PERSON] et al. [16]; [PERSON] et al.