# The Application of Spectral Entropy to P-Wave Detection in Continuous Seismogram Analysis
## 1 Introduction  
The development of early detection and short-term forecasting methods for seismic events remains one of the most pressing challenges in contemporary seismology and geophysical safety [1, 2, 3]. Recent advances [4] have applied full-waveform tomography to revealing the crustal-flow-induced seismicity, with implications for regional geological processes. Detection and characterization of seismic phases such as the P-wave remain critical to real-time monitoring and early warning systems. While waveform-based simulations provide valuable insights into structural responses, entropy-based methods like that proposed in this study can offer lightweight and real-time-compatible tools for seismic phase identification, which can be integrated with large-scale modeling pipelines. A key component of addressing this challenge is the deployment of automated monitoring systems capable of processing large volumes of data in real time and identifying emerging anomalies in seismic signals [5, 6]. The current seismological monitoring techniques are rapidly evolving to improve the accuracy and response time of event detection, particularly in the context of early warning systems [7]. For such systems, accurately extracting informative features that are sensitive to structural changes in the signal duringthe early stages of a seismic event is crucial [8]. Modern seismic signal analysis methods require high sensitivity to the signal dynamics, especially under noisy or non-stationary conditions [9]. Within the broader challenge of the early detection and short-term forecasting of seismic events, spectral entropy emerges as a promising tool for quantitatively assessing the complexity and variability of seismic time series. This metric is sensitive to the relative distribution of the signal energy in the frequency domain [10; 11]. Despite its potential applicability to analyzing seismic wave characteristics, such as distinguishing between background noise and earthquake phases, detecting event onsets, and classifying wave types, spectral entropy has received relatively less attention in seismological studies [12; 13]. However, in the field of seismology, its potential remains relatively unexplored. Seismic signals are typically highly non-stationary and susceptible to external noise, which poses a complex challenge for the detection and classification of early events. Consequently, spectral entropy can function as an indicator of the transition from background noise to an organized seismic process [14], making it a potentially valuable component in monitoring systems and short-term forecasting applications. This study presents an approach to the implementation of spectral entropy in seismic analyses. We have developed criteria that enable the identification of spectral entropy outcomes for detection purposes, with a particular focus on identifying the initial phases of earthquakes, specifically P-waves, which are a critical component in early warning systems. This study was carried out using data collected from a specific area within the city of Almaty. This region is one of the most seismically active regions in Kazakhstan. The proposed solutions could significantly enhance the effectiveness of the seismic monitoring systems that are being developed for this region. The methodology may be extended to other areas, with appropriate calibration, which will also be the subject of subsequent studies. The primary focus of this study is the time intervals surrounding a sequence of seismic events, the largest of which exceeded a magnitude of 5. These earthquakes were strongly felt in Almaty in January 2024, which catalyzed the initiation of this research. The present study builds on previous research [15] in which a convolutional neural network was developed to detect P-waves. In that work, the feature vector was constructed without incorporating the spectral characteristics of the seismic signal.