# Combining Higher-Order Statistics and Array Techniques to Pick Low-Energy P-Seismic Arrivals
## 4 Settings Configuration
In Figure 5, each set of five consecutive points identified with equal markers and connected by identical line color denotes the different thresholds \(\{\theta_{k}\}=\{0.1,0.2,0.3,0.4,1.0\}\) of the multi-threshold criteria. Points are sorted in a way that the values of the respective \(\theta_{k}\) increase from left to right: the first point belongs to the case \(\theta_{1}=0.1\), the second point to the case \(\theta_{2}=0.2\), and so on. We notice that in each case, the minimum threshold value of \(\theta_{1}=0.1\) exhibits the best performance in terms of both \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Stage** & **Setting** & **Symbol** & **Optimal Setup** \\ \hline STS & Length of cut trace & \(\bar{t}\) & \(8\;\text{s}\) \\ STS & Maximum allowed std & \(\sigma_{\text{max}}\) & \(75\;\text{ms}\) \\ STS & Statistic used & \(\gamma_{n}\) & \(74\) \\ STS & Filtering frequencies & \([f_{1},f_{2}]\) & \([1,30]\;\text{Hz}\) \\ STS & Time window length & \(w\) & \(1.5\;\text{s}\) \\ STS & Threshold corresponding to final onset & \(\theta\) & \(0.1\) \\ MCS & Tolerance & \(\delta\) & \(0.2\;\text{s}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Settings to be configured, along with respective optimal setup for our case study. Refer to Algorithm 1 and Section 3 for an explanation of their meaning. precision and recall. Therefore, in our case, it is evident that the optimal value for the final P-onset corresponds to the first potential onset \(o_{1}\), related to the first threshold \(\theta_{1}=0.1\). To select the optimal setup, we choose to adopt a conservative approach, prioritizing the reliability of predictions over their retrieval capacity (i.e., optimizing primarily for precision rather than recall). Therefore, we focus our attention on the behavior of the configuration exhibiting the best precision performance when varying the \(\sigma_{\max}\) value. Performance indicators for this configuration and different \(\sigma_{\max}\) are reported in Table 4. Precision values decrease as \(\sigma_{\max}\) increases, while the opposite behavior is exhibited by recall values. We fixed \(\sigma_{\max}=75\) ms as a good trade-off that maximizes the recall value and allows, at the same time, a high precision performance (which is not significantly lower than the optimal value). As expressed in Table 3, the chosen setup of the parameters of STS is \(\{\gamma_{n}=\gamma_{4};\)\([f_{1},f_{2}]=[1,30]\) Hz; \(w=1.5\) s; \(\theta=0.1;\)\(\sigma_{\max}=75\) ms\(\}\), which leads to the best precision performance. The only parameter to be set for the MCS is the \(\delta\) of Equation (6). We opt to set a value of \(\delta=0.2\) s for all the arrays. This choice allows us to set a tolerance that is in accordance with the precision sought in Equation (8). Based on the values of \(D_{i}^{\max}\) for our arrays, presented in Table 1, we assume a propagation velocity of \(v_{p}=5.5\) km/s for the area under study [43], which approximately corresponds to 20% of the maximum of \(D_{i}^{\max}/v_{p}\). \begin{table}
\begin{tabular}{l c c} \hline \(\sigma_{\max}\) & **Precision** & **Recall** \\ \hline
25 ms & 82.0\% & 38.3\% \\
50 ms & 81.9\% & 46.3\% \\
75 ms & 81.8\% & 50.5\% \\ \hline
100 ms & 81.0\% & 52.0\% \\
150 ms & 80.2\% & 55.7\% \\
200 ms & 78.8\% & 57.2\% \\
250 ms & 77.1\% & 58.2\% \\ \hline \end{tabular}
\end{table} 
Table 4: Performance relative to the maximum-precision setting (i.e., the set \(\{\gamma_{n}=\gamma_{4};\)\([f_{1},f_{2}]=[1,30]\) Hz; \(w=1.5\) s; \(\theta=0.1\)) across different values of \(\sigma_{\max}\). The green-highlighted row refers to the chosen \(\sigma_{\max}\) value. Figure 5: Performances of STS across various settings, fixing the value \(\sigma_{\max}=75\) ms. The trends of performances as parameters change are independent of values of sigma. Precision is displayed on the left panel, while, on the right panel, recall is displayed. Each point denotes a distinct configuration.