## Appendix C  
We implemented the clustering procedure MAP-DBSCAN for 16 different combinations of parameters which are shown in Table 11. For the determination of the distance threshold \(\epsilon\), we computed the k-distances between events assigned to the same potential cluster, since the DBSCAN algorithm is implemented in events that have been already grouped into clusters based on their temporal proximity. In particular, for each event included in the potential cluster, its \(k\)-nearest neighbor is computed and plotted in ascending order. If we choose an arbitrary event, \(i\), set the distance threshold \(\epsilon\) to \(k\)-dist\((i)\) and the parameter \(N_{pts}\) to \(k\), all events with an equal or smaller \(k\)-dist value will become core points, in other words, they will be assigned into a cluster. [PERSON] et al. [35] proposed as best \(\epsilon\) value the one that corresponds to a change in the slope of the curve, as corner points indicate a change in the degree of correlation among events. For \(k=4\), which corresponds to the minimum number of neighbors (\(N_{pts}\)), gradient changes in the slope range between 2.5 and 10 km in the datasets of both CG (Figure 11) and NAS (Figure 11) areas, whereas for the CII area (Figure 11), changes in the slope of the curves initiate slightly sooner (below 2.5). The minimum one is chosen as equal to \(\epsilon=2.5\) in order to also ensure that the location errors of the catalog are considerably fewer. For the 16 different realizations of the clustering algorithm, MAP-DBSCAN, we investigated the spatio-temporal properties of the background seismicity. Figure 12 presents the cumulative number of events that have not been assigned to a cluster (declustered seismicity) for each set of parameters along with the initial datasets. Peaks and pronounced concavities in the cumulative curves are indicators of triggered seismicity wrongly assigned as background and vice versa. In datasets D1 and D2 we observe such concaves for thresholds \(\epsilon\geq 5\) km and a rather stable curve for \(\epsilon=2.5\) km (Figure 12), suggesting that events are correctly separated as background and triggered ones. Therefore, the distance threshold is set to \(\epsilon=2.5\) km, for both datasets. In dataset D3, Figure 12 shows that the curves with \(\epsilon\geq 7.5\) km exhibit large concaves, indicating that background seismicity is incorrectly assigned to clusters. For the smallest threshold \(\epsilon=2.5\) km, some small peaks appear and thus the \(\epsilon=5\) km as the optimal value was selected. Dataset D3 containsoffshore seismicity in the NAS area, with probably higher location errors. This supports our choice for a larger distance threshold. To further explore the differences between the spatio-temporal evolution of the declustered catalogs, the space-time pattern of the background events is examined, comparing the full and the declustered catalogs. In dataset D1, a persistent gap of seismicity appears during the second half of 2014, independently of the chosen temporal constraints, associated with the two large earthquake swarms in that period [77]. Due to the intense seismic activity during 2013-2014 in the western Corinth Gulf [57; 65], the classification of seismicity into clusters becomes more complicated, so we have chosen a rather conservative parameter set, \(PS3\), with \(T=0\). In this way, we avoid merging distinct clusters that are spatio-temporally close to each other. Figure A5a shows the space-time evolution of the declustered catalog that corresponds to the final parameter set. The main seismic excitations present in Figure A5b are detected, while preserving the patterns of the background seismicity. In dataset D2, the results are quite similar for all the tested temporal constraints, and for this reason, we adopted parameter set \(PS4\) with \(T=5\) days, which is a more loose constrain. It is more likely for seismic excitations close in time to be part of the same main shock-aftershock sequence, due to the two major sequences that dominate in the study period.