# The Application of Spectral Entropy to P-Wave Detection in Continuous Seismogram Analysis
## 3 Results  
The application of the proposed spectral entropy method is demonstrated in Figure 6. A fragment of the dataset from 22 January 2024 is presented, predominantly containing aftershocks. The time axis is shown in Coordinated Universal Time (UTC). The seismograms correspond to a selected segment of 240 s within the overall dataset. Spectral entropy is represented by a dashed line, allowing for a visual evaluation of the method's sensitivity to changes in the seismic signal. In this case, the entire time interval was used to construct the spectrogram. Subsequently, to detect the characteristic increase in spectral entropy, 38 s windows centered on the estimated P-wave arrival times are applied. The results are shown in Figure 7 for all of the events recorded at one of the seismic stations. Figure 5: The effect of detrending on the relationship between the signal-to-noise ratio (SNR) and the change in spectral entropy \(\Delta H\). (**a**) Raw data without baseline correction. (**b**) The results after applying a high-pass Butterworth filter (cutoff = 2 Hz) to remove low-frequency drift. Detrending leads to an increased dynamic range and clearer separation between the signal and noise regions. For the BTLS station, the SNR increases from \(4.8512\pm 1.1415\) dB to \(14.6333\pm 1.3843\) dB, and \(\Delta H\) increases to \(0.0925\pm 0.0136\) dB. For the JNKS station, the SNR increases from \(11.4820\pm 1.3353\) dB to \(29.2135\pm 1.8299\) dB, and \(\Delta H\) increases from \(0.0170\pm 0.0062\) dB to \(0.2281\pm 0.0170\) dB. Figure 6: Spectral entropy overlaid onto the time-domain realizations of seismic events recorded at each of the analyzed stations. Amplitude normalization was applied individually to each 240 s segment. A different color represents each segment. The spectral entropy is depicted as a dashed line to visually illustrate the method’s applicability and responsiveness to changes in the seismic signal. Figure 7: Averaged spectral entropy values before (\(H_{1}\), red dots) and after (\(H_{2}\), blue dots) the seismic event, along with their difference (\(H_{2}-H_{1}\), green dots), for each 240 s segment analyzed at the TARG station. Solid lines indicate the mean values, while dashed lines represent the standard deviation. For a statistical evaluation of the results, the mean values and standard deviations computed in this way for all stations are presented in Figure 8 and Table 1.  
As shown in Figure 8, no significant increase in spectral entropy was detected at two stations, BTLS and JNK. In this case, the onset of the seismic event determined by this methodology is not reliable. This lack of entropy changes is the reason for the presence of a low-frequency trend in the data. As a result, the method does not capture significant changes throughout the time window. In its current form, spectral entropy is not applicable to analyzing trended data, and its application to that data requires prior preprocessing. This table presents the results of the averaged spectral entropy values before (column 1) and after (column 3) the registration of seismic events, as well as the corresponding entropy increase (column 5) and the standard deviations in these quantities (columns 2, 4, and 6, respectively). Furthermore, the parameters of a first-degree polynomial, obtained using the least squares method, represent the dependence of the entropy increase \(dH\) on the initial entropy value (before an event) and are provided in columns 7 and 8. Column 9 contains the mean deviation in the polynomial functions. The objective was to identify a relationship between the increase in spectral entropy and both the initial entropy value and the value at the moment of event onset to assess an effective threshold at which this method can be considered a reliable detection measure.