# Random Noise Suppression Method of Micro-Seismic Data Based on CEEMDAN-FE-TFPF
## 3 Experiments and Results  
### Synthetic Data Experiment  
Three Ricker wavelets with dominant frequencies of 25 Hz, 30 Hz, and 35 Hz were selected to obtain the synthetic data, as shown in Figure 4a. The sampling rate was 1 ms, and the number of sampling points was 1000. By adding random noise into the synthetic data, the SNR of the noisy data became less than 5 dB. At this time, the noisy data was seriously polluted by random noise, as shown in Figure 4b.  
CEEMDAN was used to decompose the synthetic data and noisy data into several IMFs, which were ordered from high frequency to low frequency, as shown in Figure 4c,d.  
The ApEn, SampEn, FE, and PE of each IMF of the noisy data are calculated respectively, as shown in Figure 5. By using four entropies as the discriminant factors, the IMFs which need to be denoised can be screened out. The window length of TFPF can be selected based on the frequency of these IMFs.  
By observing the variation law in Figure 5, it was found that the trends of different entropies are roughly the same. The entropy value of the high-frequency IMF is higher, which shows that the IMF has complex signal components. The entropy value of the low-frequency IMF is relatively low, indicating that the IMF has simple signal components. However, the variation trend of ApEn, SampEn, and PE is relatively gentle, while FE has an obvious inflection point. In this paper, an appropriate threshold needs to be defined for different entropies to screen the IMFs which need to be denoised.  
For ApEn and SampEn, the threshold is set to 0.2. The entropy values of IMFs bigger than 0.2 need to be denoised. For FE and PE, the thresholds are set to 0.02 and 0.9, respectively. Then, according to the selection rules, different window lengths are selected by TFPF to deal with the screened IMFs.  
Figure 4: Comparison of the synthetic data and noisy data. (**a**) Synthetic data; (**b**) Noisy data; (**c**) IMFs of synthetic data; (**d**) IMFs of noisy data.  
Here, we provide an example of ApEn, as shown in Figure 6. After denoising by TFPF, the noise is obviously suppressed. The effective signals are more prominent. According to the experience of CEEMDAN decomposition and reconstruction, the first two high-frequency IMFs with partial noise are eliminated. Then, the denoised result will be reconstructed as the sum of the denoised IMF groups and the residual IMF group with entropy values smaller than 0.2.  
Figure 5: Variation law of different entropies. (**a**) ApEn; (**b**) SampEn; (**c**) FE; (**d**) PE.  
Figure 6: Comparison of IMFs before and after denoising. (**a**) IMFs before denoising; (**b**) IMFs after denoising by TFPF.  
The denoising signal processed with four entropies as discriminant factors can be seen in Figure 7. In Figure 7a, it can be observed that the four entropies as the discriminant factor used by the CEEMDAN-TFPF method can all suppress random noise and restore the effective signals. However, through comparing the amplitude preservation in Figure 7b, it can be found that the denoising result with FE as the discriminant factor has the best fitting degree at the peak. It shows that CEEMDAN-FE-TFPF can not only attenuate random noise effectively, but also preserve the amplitude to the maximum.