## 2 Materials and Methods
### Identification Methods
#### 2.3.1 Statistical Analysis and Spectral Analysis  
Statistical analysis and spectral analysis are traditional methods for microseismic event identification [52]. These methods aim to extract meaningful information by quantitatively analyzing specific attributes in microseismic event waveform data. In statistical methods, researchers typically focus on the statistical distribution, mean, variance, and other statistical characteristics of the signals to differentiate between different types of microseismic events. However, spectral analysis methods emphasize the frequency characteristics of the signals, such as spectral density and power spectral density, to distinguish the frequency domain features of microseismic events [53]. Although these techniques are simple and intuitive, they frequently require careful selection and feature extraction, which can be cumbersome when dealing with complicated and diverse waveforms. Statistical analysis plays an important role in the recognition and classification of microseismic waveforms. Common statistical analysis methods include (1) mean and standard deviation: calculating the average and standard deviation of microseismic signals provides information about the overall level and variability of the signals; (2) correlation analysis: by calculating the correlation coefficient or correlation matrix between microseismic signals, the mutual relationship between the signals can be revealed, helping to determine their similarity or correlation; (3) probability distribution analysis: analyzing the probability distribution of microseismic signals, such as normal distribution, exponential distribution, etc., can provide insights into the distribution characteristics within different ranges, facilitating classification and discrimination; (4) statistical feature extraction: extracting statistical features of microseismic signals, such as kurtosis, skewness, energy, etc., can capture specific statistical patterns of the signals, assisting in identification and classification; (5) hypothesis testing: utilizing statistical hypothesis testing methods like \(t\)-test, analysis of variance, etc., to compare microseismic signals of different categories and examine if significant differences exist between them; and (6) cluster analysis: applying cluster analysis methods to group microseismic signals based on their features, thereby achieving waveform classification and recognition. Statistical analysis methods provide an overall description and summary of microseismic signal data, aiding in understanding the distribution patterns and features of the signals and providing a basis for subsequent recognition and classification. Furthermore, combining statistical methods with other techniques like machine learning and deep learning can further enhance the accuracy and reliability of waveform recognition and classification. On the other hand, spectrum analysis reveals the frequency characteristics of signals by transforming them into the frequency domain. It involves key concepts and methodssuch as (1) Fourier transform: Fourier transform is the foundation of spectrum analysis, converting signals from the time domain to the frequency domain, representing them as functions of frequency and amplitude. (2) Power spectral density: power spectral density describes the energy distribution of a signal across different frequencies, which can be obtained through the Fourier transform. It displays the intensity or energy distribution of the signal in different frequency bands, helping to identify the frequency components of the signal. (3) Fast Fourier transform (FFT): FFT is commonly used for efficient computation of signal spectra. It allows for the fast calculation of the frequency spectrum of discrete signals, improving computational efficiency. (4) Spectrogram: a spectrogram is a visual representation of the signal's frequency spectrum, with frequency on the horizontal axis and amplitude or energy on the vertical axis.