## 4 Numerical Experiments
Additionally, due to the low signal-to-noise ratio of the original passive data and the difficulty in accurately identifying effective body wave noise and surface wave noise Figure 3b ([PERSON] et al., 2014) [43], purely time-domain or frequency-domain analysis is insufficient for a comprehensive understanding of the effective signals in passive data. Time-frequency-domain analysis methods are more conducive to analyzing passive seismic data. Compared to general time-frequency transforms, SWT provides higher resolution in the time-frequency spectrum. Therefore, we chose SWT to identify surface wave noise and body wave noise in the passive seismic data. The behavior of surface waves and body waves in the time-frequency domain in an ideal case is shown in Figure 6 (the intensity of the energy in the figure represents the strength of the signal). In Figure 6a, the scale parameter is inversely proportional to frequency. Therefore, we can obtain the time-frequency spectrum (Figure 6b). Since surface wave frequencies are  
Figure 5: Comparison of passive seismic data cross-correlation results with active source results: (**a**) virtual shot gather reconstructed from passive seismic data in an acoustic medium; (**b**) shot gather recorded from direct forward modeling of a cross-correlation in an acoustic medium. relatively low and body wave frequencies are relatively high, we can easily distinguish surface waves and body waves in the time-frequency spectrum. It can be seen that there are obvious energy bands at low frequencies and high frequencies, which are the energies of surface wave noise and body wave noise, respectively. Among them, the relatively weaker energy comes from some signals or noises with smaller contributions. After extracting the wavelet coefficients from the regions corresponding to surface waves and body waves, we can proceed with their respective processing. We begin by reconstructing the body wave signal. The passive seismic record simulated in Figure 4a is subjected to SWT, and after identifying the surface wave and body wave components, Gaussian filtering and wavelet thresholding are applied. To effectively reconstruct the reflected waves, the high-frequency band with relatively strong body wave noise is selected (we selected a frequency band range of 10-30 Hz). However, there is an inevitable overlap between the frequency bands of body wave noise and surface wave noise. To further suppress surface wave energy and some signals with weak contributions to the reconstruction of the reflected waves, SWT is used for filtering and thresholding denoising. The results before and after processing are shown in Figure 7. Figure 7a is the time-frequency spectrum of the raw data, while Figure 7b is the processed time-frequency spectrum. It can be observed that, within the frequency band range of 10-30 Hz, the stronger energy, which we consider as body wave noise, is retained, whereas some of the weaker energy, which we identify as surface wave noise, is eliminated. Due to the uniform spatial distribution of the sources, the seismic records received by each geophone exhibit similar time-frequency-domain distributions. Therefore, the same steps are repeated for other geophones until all seismic traces are processed. Figure 6: The ideal representation of passive source seismic data in the time–frequency domain: (**a**) time–scale; (**b**) time–frequency. After thresholding the body wave noise, wavelet cross-correlation is applied, followed by inverse transformation to the time domain, yielding the reconstructed virtual body wave seismic record, shown in Figure 8a. We also compare this result with the commonly used bandpass filtering method in passive data processing. Figure 8b shows the virtual shot gather obtained through cross-correlation after bandpass filtering the raw data. The bandpass filter is applied to the same frequency band as selected in SWT.