# Combining Higher-Order Statistics and Array Techniques to Pick Low-Energy P-Seismic Arrivals
## 5 Results
### SNR Examination and Solution Inspection  
The initial evaluation of the proposed technique involves computing the signal-to-noise ratio (SNR) across the three distinct subsets \(N_{catalog}\), \(N_{common}\), and \(N_{HOSA}\) (see Figure 6). For each trace, SNR is calculated by dividing the standard deviation of the signal (i.e., the 4 s of waveform starting from the onset) by the standard deviation of the noise (i.e., the 4 s of waveform before the origin time).  
Figure 6 shows that the SNR distribution of traces with onsets solely in HOSA is more similar to the distribution of the common set, whereas the subset with onsets exclusively in the catalog is more concentrated towards lower SNR values, indicating that HOSA can pick traces with higher SNR. Approximately 50% of the traces belonging exclusively to HOSA have an SNR greater than 4, compared to 25% of the only catalog subset. Furthermore, the median values of the SNR distributions are 4.0 and 2.1 for HOSA and the catalog, respectively.  
This implies that there are traces exclusively identified by HOSA that exhibit a high value of SNR. A visual examination has confirmed them to represent clear onsets of local events, correctly detected by our approach. They constitute additional high-quality onsets that were overlooked by the automated machine learning approach employed but retrieved by HOSA.  
On the other hand, the catalog can pick more traces with low SNR that HOSA disregards. However, upon visually inspecting traces within the catalog's densely populated bin where SNR \(<\) 1.5, it becomes evident that many of them consist predominantly of pure noise. In other cases, the catalog onset often shows a significant error as it is placed far from the event within the noisy segment. Only a small fraction of these traces represent reliable onsets (some examples are displayed in Figure 7).  
Figure 6: Log-scaled SNR distribution of traces with onsets detected by both techniques (black line, 4797 traces), exclusively by the HOSA method (blue rectangles, 3316 traces), and only by catalog (red rectangles, 3888 traces). Red and blue arrows refer to the median of the catalog and HOSA SNR distributions, with values of 2.1 and 4.0, respectively. The median SNR value for the common traces is 8.4. For common traces, considering the catalog onsets or the HOSA onsets does not affect the SNR distribution.  
Figure 7: Examples of traces belonging to the catalog’s high-populated bin with SNR < 1.5. Traces have been aligned by their respective event origin times, corresponding to the 0 point on the \(x\)-axis, indicated by green lines. Red lines denote the catalog arrival times. (**A**) Catalog onset showing a significant error. (**B**) Catalog onset assigned to noise. (**C**) Reliable catalog onset. Most of the traces in the considered bin belong to cases (**A,B**). HOSA doesn’t assign any onset to these traces. For cases (**A,B**), this is due to the barrage of the multi-threshold criterion in the STS, i.e., for the high standard deviation among the diverse potential onsets for the same trace. For case (**C**), the onset is rejected in the MCS barrage due to the non-satisfaction of the first criterion of Equation (7).