# The Application of Spectral Entropy to P-Wave Detection in Continuous Seismogram Analysis
## 3 Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Stations** & \(\mathbf{H_{1}}\) & \(\mathbf{H_{2}}\) & \(\mathbf{H_{2}-H_{1}}\) & **Polynomial** \\ \hline ARLS & 0.447 (0.048) & 0.518 (0.054) & 0.070 (0.056) & 0.631 \(-\) 0.256 (0.044) \\ BAET & 0.421 (0.002) & 0.485 (0.066) & 0.064 (0.065) & 0.999 \(-\) 0.421 (0.001) \\ BTLS & 0.421 (0.002) & 0.422 (0.002) & 0.001 (0.001) & \(-\)0.053 \(+\) 0.023 (0.001) \\ JNK & 0.422 (0.006) & 0.433 (0.028) & 0.011 (0.026) & 0.910 \(-\) 0.383 (0.005) \\ SHLS & 0.446 (0.063) & 0.550 (0.078) & 0.103 (0.075) & 0.631 \(-\) 0.243 (0.056) \\ TARG & 0.457 (0.069) & 0.692 (0.045) & 0.234 (0.076) & 0.746 \(-\) 0.282 (0.068) \\ TLG & 0.442 (0.038) & 0.565 (0.036) & 0.123 (0.047) & 0.797 \(-\) 0.327 (0.037) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistical results based on the averaged spectral entropy values calculated for each seismic station. Figure 8: The mean spectral entropy values before (blue) and after (red) seismic event detection, along with the increase in entropy (black) and standard deviation, in the data from the seven stations. The increase in entropy as a function of the entropy value at detection is shown for the TARG and ARLS stations in Figure 9. In contrast, the dependency on the initial spectral entropy value is presented in Figure 10.  
Despite the variations in the slope angles and statistical dispersion observed at both stations, an explicit upper limitation can be identified. This limit can be approximated by the linear equation \(dH=x-0.457\), which fits well at all stations analyzed. This value is in good agreement with the result obtained for the individual station BAET, with \(a=0.999\), \(b=-0.421\) (shown in Table 1). In particular, although BAET was brought into operation at a later stage, the data registered at this station appear to be the most homogeneous among the datasets. Figure 10: The dependence of entropy growth on the initial spectral entropy value for various seismic events recorded at the stations TARG (**a**) and ARLS (**b**). The polynomial fits (red lines) and corresponding standard deviations (red dashed) were calculated for events with initial entropy values exceeding the mean (black solid line, as specified in Table 1, and corresponding standard deviations are black dashed). The resulting linear approximations for four stations are as follows: TARG (\(-0.875\times x+0.630\)), SHLS (\(-0.416\times x+0.282\)), TLG (\(-0.561\times x+0.350\)), and ARLS (\(-0.669\times x+0.383\)). Figure 9: The dependence of entropy growth on the maximum entropy value (blue) at the occurrence of events for stations TARG (**a**) and ARLS (**b**). A first-degree polynomial fit (black solid line) and the corresponding standard deviation (black dashed lines) are shown. Notably, a characteristic linear dependence as \(H_{2}-H_{1}=a\times x+b\), where \(a=1\), \(b=-0.457\) (shown in red) can be marked in both plots. This attribute is consistent across all seven stations and represents the upper limit. A crucial question concerns the determination of the spectral entropy levels within the informative region, as well as their relative increase in response to anomalous changes in the signal [25]. The spectral entropy values of white noise, when measured using this method, typically fall within a characteristic normalized range of 0.9 to 1.0 [26]. Specific threshold values for normalized spectral entropy have also been proposed in theoretical studies to support the interpretation of the results [27]. For example, values such as 0.465, 0.567, and 0.618 (the golden ratio) can be considered. However, in this study, we rely on empirical thresholds derived from the available dataset. To assess the robustness and generalizability of the spectral entropy threshold \(\Delta H\), we performed statistical validation across different earthquake magnitudes. Events were grouped into four categories based on their reported magnitudes: M < 4.0, 4.0-4.5, 4.5-5.0, and M > 5.0.