# Combining Higher-Order Statistics and Array Techniques to Pick Low-Energy P-Seismic Arrivals
## 5 Results
### Consistency Examination: Semblance
Remarkably, in cases where the number of detected arrivals exceeds eight, HOSA shows approximately half or more of the onsets with strong alignment, indicating a high capability to produce very accurate predictions. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Onsets per Array** & **HOSA** & **Catalog** \\ \hline All (3–10) & 35\% & 23\% \\
3 & 31\% & 26\% \\
4 & 25\% & 16\% \\
5 & 31\% & 19\% \\
6 & 31\% & 17\% \\
7 & 34\% & 15\% \\
8 & 40\% & 20\% \\
9 & 45\% & 25\% \\
10 & 68\% & 0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Percentages of residual semblance values (a measure of onset alignment) greater than 0.1 for HOSA and catalog onsets, corresponding to each case represented in Figure 9. In all cases, HOSA demonstrates higher percentages of residual semblance values above 0.1, indicating better onset alignment. Figure 8: Example cases of Semblance (S) computation for traces at a fixed array, along with respective temporal semblance (\(S^{t}\) last row). The waveforms belong to the events represented by yellow stars in Figure 1: the waveforms in the left panel are associated with the event located at (40°44’ N, 15°25’ E), while those in the right panel correspond to the event at (40°31’ N, 15°40’ E). Waveforms are aligned according to their respective onsets, indicated by dashed red lines. Different colors are used for the waveform lines solely to distinguish between them. In the first row, traces are aligned by catalog onsets \(o^{C}\), while, in the second row, they are aligned by HOSA onsets \(o^{H}\). Traces are considered in counts and normalized, dividing by the maximum values present in each displayed window. Dashed gray lines highlight the time interval of 0.2 s width considered to compute the residual semblance: \(S^{\prime}=\int_{T_{1}}^{T_{2}}S^{t}\,dt\), where \(T_{1}\) corresponds to onset time minus 0.1 s and \(T_{2}\) to onset time plus 0.1 s. These cases demonstrate HOSA’s ability to provide very precise predictions, as it leverages array concordance checks performed during the MCS. Impact of Noise Levels on Semblance  
To compare the qualities of HOSA and catalog onsets based on noise levels, we examine how residual semblance varies with SNR. While SNR is computed for individual traces, semblance values are calculated using all traces of an event at a fixed array. To categorize semblance by SNR, we assign an average SNR to each array, computed as the mean SNR of its traces. The histograms in Figure 10 illustrate this categorization: the left panel includes semblance values for arrays with a mean SNR below 4, the right panel includes arrays with a mean SNR above 10, and the central panel represents all others. In each case of Figure 10, we observe that bins corresponding to higher residual semblance values are more populated for HOSA onsets than catalog onsets. The improvement is further evident in the case of SNR > 10, where, for all bins above 0.1 (the condition for strong alignment defined in Section 5.2), the histogram for HOSA onsets shows values significantly higher than the catalog onsets histogram. As further demonstrated by Table 6, we notice that HOSA consistently improves prediction accuracy across all SNR ranges, with a greater improvement at higher SNR values. Figure 9: Histograms of residual semblance values considering catalog and HOSA onsets. Bins have a width of 0.5. Each semblance value is computed by fixing an event and an array and utilizing all the waveforms with an onset assigned. We recall that residual semblance computed on uncorrelated noise assumes values equal to 0. Higher values correspond to better alignments of onsets. The top-left panel illustrates the case of considering all onsets, while the other panels show cases for arrays with a number of onsets specified in the respective panel’s title, varying from 3 to 10. HOSA shows higher residual semblance values, especially in the cases where the number of detected onsets per array is higher (>5), resulting in better overall alignment.