## 4 Results  
### Triggered and Background Seismicity Separation  
We fit MAP models with between two and seven states for each earthquake subcatalog, computationally a very demanding process as the number of states increases, especially for large datasets such as D3 with 13043 events. According to the BIC values, six, seven and again six states are sufficient to approximate the temporal distribution of earthquakes for the D1, D2 and D3 datasets, respectively. Next, we evaluate the transitions among the hidden states of the models. Firstly, the state probabilities \(p_{i}(t)=p(I_{t}=i)\) for \(i=1,\ldots,K\) are estimated with the use of the forward and backward vectors given in Equation (A1), and then we assign as state of the hidden process \(I_{t}\), the one with the highest probability, i.e., \(\text{argmax}_{0\leq i\leq K}\,p_{i}(t)\), with \(p_{i}(t)=p_{i}(t_{k})\) for \(t_{k}\leq t<t_{k+1}\). Each state \(i\) corresponds to an occurrence rate, \(\lambda_{i}\), therefore, by evaluating the transitions among the states of the model, we detect change-points in the seismicity rate. Figure 3a-c illustrate the transitions among the states for the datasets D1, D2 and D3, respectively. The colored box at each temporal  
Figure 2: Maps of the study areas depicting seismicity along with major faults (yellow lines). **(a)** The main seismotectonic features of the area of Greece. The black lines illustrate the active boundaries and the arrows the relative plate motions. Rectangles enclose the three study areas. **(b)** The area of Corinth Gulf where the major faults are shown (yellow lines) along with seismicity during 2012–2019. **(c)** The area of Central Ionian Islands where the Kefalonia Transform Fault Zone and the collision front are shown (yellow lines) along with seismicity during 2012–2019. **(d)** The area of North Aegean Sea where the NAT is traced (yellow line) along with seismicity during 2012–2019. The legend is common for the three study areas. interval \(t_{k}\leq t<t_{k+1}\) indicates the state with the maximum probability at the current time and the legend contains its corresponding occurrence rate. The temporal patterns of dataset D1 indicate the dominance of state 2 (yellow color, Figure 3a) with occurrence rate \(\lambda_{2}=3.01\) events/day for almost the entire period. Nevertheless, there is a slight decrease in the occurrence of earthquakes (\(\lambda_{1}=1.23\) events/day) in the second part of the catalog, starting from 02/2016 with transitions to state 1 (red color, Figure 3a) until almost the end of the catalog in 12/2019. This is probably related to the lack of seismic sequences during the last part of the study period compared to the previous intense seismic activity especially during the period 2013-2014 in the western subarea of the CG [57]. The rate threshold is set equal to \(\lambda_{thr}=\lambda_{2}\), which we consider as the background rate during the study period. The seismicity of the CII area is dominated by the two major sequences during the study period, the 2014 Kefalonia doublet (\(M_{w}6.1\) and \(M_{w}6.0\)) [58] and the \(M_{w}6.5\) 2015 Lefkada earthquake sequence [59]. States 7 (brown), 6 (dark cyan), 4 (dark blue), 3 (orange) and 2 (yellow) in Figure 3b are clearly associated with the aftershock evolution of the two sequences--essentially, they approximate the Omori temporal distribution. Background  
Figure 3: Most probable path of the hidden states of the model along with the daily frequency of events (gray vertical lines) with **(a)**\(M\geq 1.5\) for D1, **(b)**\(M\geq 2.2\) for D2 and **(c)**\(M\geq 2.1\) for D3 datasets, respectively. Each color is assigned to a different state \(i\) with seismicity rate \(\lambda_{i}\). Inset magnifies the transitions among the states, which are otherwise difficult to visualize due to the short sojourn times compared to the study period. The rate threshold, \(\lambda_{thr}\), is set equal to \(\lambda_{2}=3.01\), \(\lambda_{1}=0.58\), \(\lambda_{1}=1.53\) for the D1, D2 and D3 datasets, respectively.