# Combining Higher-Order Statistics and Array Techniques to Pick Low-Energy P-Seismic Arrivals
## 4 Settings Configuration  
As described in the previous sections, HOSA involves parameters that need to be configured according to the characteristics of the earthquakes and receivers under analysis. A comprehensive list of the parameters to be configured along with the selected setup can be found in Table 3.  
As explained in Section 2, we detected P-wave arrival times (catalog onsets) for part of the traces in our dataset with an automatic approach. We utilize these onsets as an initial reference for calibrating the parameters of STS. We set the parameter \(\bar{t}=8\) s, as 95% of catalog onsets occur within 8 s of their respective origin times. This conservative choice enables the method to concentrate on the significant portion of the trace, where arrivals are more likely to occur. Figure 4: Graphical representation of the clustering procedure. (**A**) Schematic illustration of a single array of stations. \(D_{max}\) represents the maximum distance between two stations of the array. The numbers within the black triangles serve to identify the different stations. Panels (**B–E**) depict various example situations of arrival times, with diverse clustering scenarios. Vertical red lines delimit clusters of onsets. \(\Delta t_{max}\) is the maximum allowed time that can elapse between two arrivals at the same array. Each black rhombus represents an arrival time. The numbers within them correspond to the numbers of the stations to which they belong. To optimize the remaining parameters of STS, we compare the catalog onsets with the predictions made by only the first stage of HOSA (STS) across various configuration settings. Specifically, for each trace where STS assigns an onset \(o^{H}\), we claim that the onset is in agreement with the respective catalog onset \(o^{C}\) if their difference fulfills the condition of Equation (8). \[|o^{H}-o^{C}|\leq 0.2\;\text{s}. \tag{8}\]  
This choice corresponds to focusing on an onset accuracy of the order of \(0.2\;\text{s}\), which is the typical magnitude of a good-quality pick in similar tectonic settings, as suggested by pick accuracy for a similar tectonic context provided in [42]. With this definition, we can establish two metrics to measure performance: precision and recall. The metrics are defined in Equation (9):  
\[ \begin{split} Precision&=\frac{N_{a}}{N_{H}}\\ Recall&=\frac{N_{a}}{N_{c}},\end{split}  \tag{9}\]  
where \(N_{a}\) is the number of agreeing onsets, \(N_{H}\) is the total number of onsets assigned by the HOSA first stage, and \(N_{c}\) is the total number of onsets in the catalog. Precision is a metric that evaluates the reliability of predictions generated by our technique, while recall expresses the ability of the technique to identify onsets in traces containing a P-phase. Figure 5 reports the performance of STS for various choices of the parameter set: \(\{\gamma_{n}\), \([f_{1},f_{2}]\), \(w\), and \(\theta\}\). By testing with various values of \(\sigma_{\text{max}}\), it has been observed that changes in relative performance across the various explored configurations are not significantly affected by the value of \(\sigma_{\text{max}}\). Therefore, in Figure 5, we present the scenario, where \(\sigma_{\text{max}}\) is kept fixed at 75 ms, as the following observations can be extended to the case of a general value of \(\sigma_{\text{max}}\). Moreover, the value of 75 ms will result in an optimal value for \(\sigma_{\text{max}}\), as explained in the following paragraphs. We notice from Figure 5 that using the statistic \(\gamma_{4}\) (orange lines) instead of \(\gamma_{6}\) (light blue lines) leads to an improvement in precision values despite lower recall values. The plots show that a value of \(w=1.5\;\text{s}\) (blue markers) consistently improves precision. There is no significant impact on performance among the filter frequencies used. However, setting \([f_{1},f_{2}]=[1,30]\;\text{Hz}\) (triangular markers) leads to the highest precision and recall performances.