## 2 MAP-DBSCAN Method
### Performance Evaluation
#### 2.4.3 Evaluation
In the second set, RB2, we extend the spatial zone by increasing the factor \(r_{fact}\) from 10 to 20 km, whereas, in the third set, RB3, we also extend the temporal window modifying the parameters \(\tau_{min}\) and \(\tau_{max}\) (see Table A1). The NN method separates seismicity into background and clustered events according to the bimodal distribution of the rescaled time and distance metrics. The algorithm needs as input two parameters, the b-value and the fractal dimension of the earthquake locations, which are considered equal to \(b=1.0\) and \(d_{f}=1.51\), respectively. For the MAP-DBSCAN method, first, the optimal MAP model and the corresponding rate threshold (\(\lambda_{thr}=\lambda_{1}\)) are determined. Then, different temporal constraints are tested for the merging of the potential clusters (consecutive events above the rate threshold) and, subsequently, the DBSCAN is implemented. We set the minimum number of neighbors equal to \(N_{pts}=2\), similar to the minimum size of a cluster that can be given as output from the other algorithms. For the distance threshold, \(\epsilon\), we tested a wide range of possible values (see Table A2). The NN method shows the best performance in the construction of the clusters (\(J_{1}=0.756\)) and in the detection of the mother events (\(J_{2}=0.727\)). This is also evident by its cumulative number of background seismicity (purple line in Figure 1a), which is the closest one to the initial catalog (dotted black line). The temporal evolution of background seismicity is shown in Figure 1b-f across the longitude for ease of reading as west-east normal faults dominate the area. For the NN method, no large gaps are evident in the space-time evolution of the declustered seismicity, although there is a significant concentration of events between the 7 th and 8 th year of the catalog, which is also persistent in both RB2 and GK3 methods (orange ellipses in Figure 1d-f) and less apparent on MAP-DBSCAN method (orange ellipse in Figure 1c). The high efficiency of the NN method is probably related to the metric it uses, which is similar to the ETAS one with \(\lambda_{j}(t_{i},x_{i})=(t_{i}-t_{j})^{-1}r_{ij}^{-d_{f}}10^{bm_{j}}\) and \(c=0,\ p=1,\ d=0,\ q=d_{f}\) and \(a=b\). The windowing technique seems to overestimate the temporal and spatial windows, since it removes large amounts of seismicity (blue ellipse in Figure 1f), in accordance with previous results [11]. The same gap between the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**PS** & **RB1** & **RB2** & **RB3** & **GK1** & **GK2** & **GK3** &
\begin{tabular}{c} **MAP-DBSCAN** \\ **(PS27)** \\ \end{tabular} & **NN** \\ \hline \(J_{1}\) & 0.530 & 0.593 & 0.648 & 0.382 & 0.397 & 0.585 & 0.627 & 0.756 \\ \(J_{2}\) & 0.612 & 0.630 & 0.617 & 0.418 & 0.192 & 0.676 & 0.647 & 0.727 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(J_{i},i=1,2\), values for 3 parameter sets (PS) of RB and GK algorithms, respectively, and the corresponding values of the MAP-DBSCAN and NN methods. 14 th and 15 th year of the catalog is also evident in the background seismicity from the MAP-DBSCAN method, however, it is smaller and some sparse seismicity is left (blue ellipse in Figure 1c). On the other hand, [PERSON]'s declustered catalog has more events than any other method (pink, magenta and green line, Figure 1a) and significant concentrations of events are visible in the space-time evolution of the background seismicity (orange and purple ellipses in Figure 1e). Best overlapping among the true, \(\mathbf{X}\), and the estimated partition, \(\mathbf{Y}\), does not mean necessarily the best detection for the declustered seismicity. For instance, the GK3 partition is characterized by a lower index, \(J_{1}=0.585\), than the MAP-DBSCAN27 partition, \(J_{1}=0.627\), however, its declustering catalog is more accurate (GK3-\(J_{2}=0.676>J_{2}=0.647\)-MAP-DBSCAN27). Nevertheless, both indexes combined, the MAP-DBSCAN partition shows a higher efficiency than the rest of the algorithms, except for the NN.