*2.2. Temporal Constraints*

The earthquakes above the defined rate threshold comprise the potential clusters. However, results on methods that are based solely on changes in the seismicity rate can sometimes be misleading. One such case is when the rate at the tail of aftershock sequences has reached the level of the background seismicity, so it becomes difficult to discriminate these events from background ones. One similar case is related to the sparse foreshock activity, which, as it is shown in Lippiello et al. [42], exhibits significantly smaller frequency than the aftershock activity. Therefore, a day rule, *dt*, is assigned in the sense that events in ±*dt* from the potential cluster are included within. Another case that we observed is related to the existence of fluctuations during a seismic excitation, when the seismic activity that is triggered by the same underlying mechanism is divided into smaller clusters. For this reason, we assign a time window, *T*, so that clusters in temporal distance smaller than or equal to *T* are merged into one.

## *2.3. DBSCAN Algorithm*

The merged clusters comprise seismicity concentrated in time. However, events with temporal proximity can be spatially sparse and are falsely assigned into the same cluster. To overcome this ambiguity, a density-based clustering algorithm, DBSCAN, is applied to separate events in space based on a distance metric on the earthquakes' epicentral

distribution. Depending on the adopted distance metric, the algorithm can be used for grouping events with waveform similarities [4] as well as earthquakes with related rupture styles and orientations (focal mechanism clustering) [43]. Density-based algorithms search for areas where the event density exceeds a threshold, . The boundaries of these areas are set where the spatial density falls below that threshold. The DBSCAN algorithm in particular requires as input two parameters, the upper threshold, , and the minimum number of neighboring events, *Npts*. A cluster is defined if an earthquake *i* exists along with at least *Npts* events within distance *d* ≤ , including itself. Earthquake *i* is then considered a core point of the cluster and the algorithm moves to the investigation of the other events. If *Npts* neighbors are identified, they are also considered core events; otherwise, they consist of the boundary points of the cluster and the algorithm stops. Events that have not been assigned to any cluster at the end of the procedure are included to the background seismicity and are merged with events that occurred during periods with estimated rate under the rate threshold, *λthr*. In this way, the algorithm can remove events that are sparsely distributed in space. It has been efficiently applied for detecting similarities among earthquake locations, origin times and focal mechanisms [34,44]. An advantage of the algorithm is that it does not require as input a predefined number of earthquake clusters, such as the k-means algorithm, where further optimization techniques for the determination of the clusters number are necessary [45].
