# Combining Higher-Order Statistics and Array Techniques to Pick Low-Energy P-Seismic Arrivals
## 6 Discussions and Conclusions  
Higher-order statistics for array algorithms (HOSAs) combine single-trace statistical analysis with multi-channel coherence analysis to infer P-wave onsets for a list of earthquakes. HOSA can work to refine, filter, and integrate a set of available arrival times or to define a new set of arrival times. HOSA first includes a single-trace stage that uses a multi-threshold criterion to estimate the P arrival times, while the position of the sensors in arrays is exploited in the second part of the algorithm to refine and consolidate the arrival times estimated from the first module. The presence of two separate modules in HOSA allows its usage in cases not limited to array-like seismic sensor spatial configurations, which are only seldom available. In this sense, HOSA differs from classical array-based approaches such as the beamforming method, in which the single-station recordings of a seismic array are time-shifted to maximize the constructive interference between the traces and are eventually stacked. This results in the generation of one signal with a possible higher SNR than the individual recordings of the array. HOSA does not perform any similar data reduction, while the spatial redundancy of recordings due to the array-based geometry is exploited in the second module. It is worth noting that HOSA, in its current form, is not optimized for detection purposes. Instead, it requires an earthquake catalog as input and aims to integrate/refine P arrival times using an approach that complements both classical STA/LTA methods and machine learning-based techniques. Here, we tested HOSA on a catalog of 226 microearthquakes recorded in Irpinia (Italy) by twenty 10-receiver seismic arrays deployed between 2021-2022. We compared the results of HOSA with a set of P-arrivals automatically computed using a template-matching approach (whose detections are here referred to as \"catalog onsets\"). In less than 5 min of computation, HOSA detected 8113 onsets out of the 30,700 analyzed traces, a number slightly lower than the 8685 catalog onsets. Among these, 3316 onsets were uniquely detected by HOSA and exhibited higher SNR values (median SNR = 4.0) than catalog-exclusive ones (median SNR = 2.1). Traces exclusively identified by HOSA exhibited high SNR values and were confirmed to represent clear onsets of local events. These high-quality onsets, overlooked by the automated machine learning approach, were successfully detected by HOSA. Residual semblance analysis revealed better onset consistency and alignment for HOSA, with up to 68% of arrays achieving strong alignment (residual semblance > 0.1), compared to 0% for the catalog in the 10-arrival case. Table 6 demonstrates the better consistency of HOSA's prediction across all the investigated SNR ranges, achieving up to 50% strong alignment in the cases of SNR > 10. Additionally, the single-trace Stage of HOSA is compared with the widely used STA/LTA method. The comparison demonstrated the reduced false detection rate for our technique in noise-only traces by a factor of six compared to STA/LTA. The application of HOSA to the Irpinia microseismicity shows that this algorithm relevantly improves performance in accurately picking the P onset when the first module returns five arrivals or more within a 2-3 km spacing array (see Table 5); this implicitly implies that HOSA, similarly to other array techniques, works better for dense seismic arrays. The same test case also shows that HOSA improves its resolution in P picking mostly for SNRs larger than four (although actually, HOSA shows more accurate P pickingthan the template matching approach for all levels of SNR, Figure 10). These results should be taken into account when HOSA is applied to different seismic areas possibly dominated by microseismicity (for which the accurate phase picking is especially challenging though crucial), such as a tool to complement other picking systems.