# Random Noise Suppression Method of Micro-Seismic Data Based on CEEMDAN-FE-TFPF
## 3 Experiments and Results
### Actual Data Experiment  
The actual micro-seismic data (as shown in Figure 8) were selected for the application of the CEEMDAN-FE-TFPF method. It was observed that the actual micro-seismic data were significantly polluted by random noise. Figure 9 shows the frequency spectrum of the micro-seismic data, ranging from about 0 Hz to 450 Hz. Through analyzing its frequency characteristics, the frequency of effective signals should mainly be distributed between 0 Hz and 50 Hz. The existence of random noise broadens the frequency distribution.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Noisy Signal** & **ApEn** & **SampEn** & **FE** & **PE** \\ \hline
**MSE** & 0.0043 & \(8.5455\times 10^{-4}\) & \(8.4790\times 10^{-4}\) & \(8.3744\times 10^{-4}\) & \(8.4834\times 10^{-4}\) \\
**SNR** & 4.7011 & 11.7061 & 11.7400 & 11.7939 & 11.7378 \\
**PSNR** & 71.8085 & 78.8134 & 78.8473 & 78.9013 & 78.8451 \\ \hline \hline \end{tabular}
\end{table}
Table 2: MSE, SNR, and PSNR of synthetic data experiment.  
Figure 8: Actual micro-seismic data.  
Figure 7: Denoising results of the synthetic data. (**a**) Original signal and the denoising result with different discriminant factors. (**b**) Local amplification of wave peak.  
The micro-seismic actual data was decomposed by CEEMDAN to obtain 12 IMFs, which are sorted from high frequency to low frequency, as shown in Figure 10. ApEn, SampEn, FE, and PE of each IMF were calculated, respectively, as shown in Figure 11. It can be observed that the trend of ApEn, SampEn, and PE is relatively gentle. However, the trend of FE changes rapidly and has an obvious inflection point. For the actual micro-seismic data processing, FE was chosen as the discriminant factor. Here, the threshold was set to 0.02. The entropy values of IMFs bigger than 0.2 were denoised. Figure 12 shows the denoising result, in which it can be seen that random noise is obviously attenuated. The amplitude and waveform of the effective signals are well preserved.  
By comparing the frequency spectrum of the actual micro-seismic data before and after denoising, as shown in Figure 13, it can be found that the high-frequency part of the denoising result caused by random noise is basically attenuated, and its frequency distribution is still distributed between 0 HZ and 50 HZ. It also shows that the method in this paper can not only suppress random noise effectively, but also preserve the amplitude to the maximum.  
Figure 10: IMFs of actual micro-seismic data.  
Figure 9: Frequency spectrum of the actual micro-seismic data. (**a**) Overall frequency spectrum. (**b**) Part of the frequency spectrum.  
Figure 11: Variation law of different entropies for the actual micro-seismic data. (**a**) ApEn; (**b**) SampEn; (**c**) FE; (**d**) PE.  
Figure 12: Actual micro-seismic data before and after denoising by CEEMDAN-FE-TFFF.  
Figure 13: Frequency spectrum of the actual micro-seismic data before and after denoising. (**a**) Overall frequency spectrum. (**b**) Part of the frequency spectrum.  
Figure 14 shows random noise removed from the actual micro-seismic data. Through its frequency spectrum in Figure 15, it can be observed that the frequency distribution is higher than the effective signals.