# Combining Higher-Order Statistics and Array Techniques to Pick Low-Energy P-Seismic Arrivals
###### Abstract  
We propose the HOSA algorithm to pick P-wave arrival times on seismic arrays. HOSA comprises two stages: a single-trace stage (STS) and a multi-channel stage (MCS). STS seeks deviations in higher-order statistics from background noise to identify sets of potential onsets on each trace. STS employs various thresholds and identifies an onset only for solutions that are gently variable with the threshold. Uncertainty is assigned to onsets based on their variation with the threshold. MCS verifies that detected onsets are consistent with the array geometry. It groups onsets within an array by hierarchical agglomerative clustering and selects only groups whose maximum differential times are consistent with the P-wave travel time across the array. HOSA needs a set of P-onsets to be calibrated. These sets may be already available (e.g., preliminary catalogs) or retrieved from picking (manually/automatically) a subset of traces in the target area. We tested HOSA on 226 microearthquakes recorded by 20 temporary arrays of 10 stations each, deployed in the Irpinia region (Southern Italy), which, in 1980, experienced a devastating 6.9 Ms earthquake. HOSA parameters were calibrated using a preliminary catalog of onsets obtained using an automatic template-matching approach. HOSA solutions are more reliable, less prone to false detection, and show higher inter-array consistency than template-matching solutions. microearthquakes; automatic P-onset; high-order statistics; seismic array Article  
12242025151172220251511722025151722025151722025151722025151722025151722025151722025151722025151722025151722025151722025151722025151722025151722025151722025151722025151722025151722025151722025151722025151720251517 processing capability of large volumes of seismic data rapidly, possibly facilitating real-time analysis and decision-making, as well as reducing the potential for errors or biases due to human subjectivity, as often introduced by manual picking procedures. Various algorithms and techniques are used to automatically pick seismic phases from the data. After [4]'s pioneering work, which was based on the STA/LTA (short-term average/long-term average) technique, various algorithms for the automatic picking of seismic arrivals have been developed. These include methods based on higher-order statistics (HOS hereinafter) such as kurtosis or skewness [5; 6; 7], on the dominant frequency content of the seismogram [8], on the wavelet transform analysis [9], and on the polarization analysis, particularly for S-wave picking [10; 11]. Nowadays, seismologists are largely adopting machine learning approaches to pick small earthquakes whose recordings are similar to or even lower than the noise. Although many different approaches are being developed, most of them train neural networks from a set of fingerprints from precisely picked earthquakes and try to identify potential hidden events in continuous seismograms. These approaches are allowing us to greatly reduce the earthquake detection threshold, with the effect of enhancing the earthquake catalogs [12; 13; 14; 15]. On the other hand, there are various issues and limitations to the automatic picking of seismic waves that may affect their efficiency and dependability. Noise sensitivity is a critical aspect, as these approaches may fail to distinguish between seismic signal and background noise, especially in situations with high levels of ambient noise. For example, machine learning methods may present the drawbacks that only a part of the detected events are indeed small earthquakes, as a fraction of the automatically identified events must be excluded a posteriori by a user-based revision as they are actually noise [16]. Moreover, the automatic readings of the seismic phases may suffer from large inaccuracies.