## 4 Verification of Algorithm Feasibility  
To verify the algorithm's feasibility, we used microseismic signals with a high signal-to-noise ratio and artificially added noise to obtain a microseismic dataset with a low signal-to-noise ratio and input the dataset into an algorithm model. The noise added in this study included random noise and power frequency interference, which have a frequency of about 50 Hz. Before processing microseismic signals, we first trained the SVM by genetic algorithm for optimization to obtain the best SVM parameters c and g. Then, the microseismic signals in the dataset were processed by VMD to extract the characteristics of each IMF. Effective microseismic signals were labeled as effective components, while ineffective components and those components after noise interference and decomposition were labeled as ineffective ones. Finally, a training set was formed. The training process is shown in Figure 1. The accuracy rate of the algorithm was improved after 100 iterations and finally reached 97%. By cross-validation, we continuously updated and optimized the SVM parameters and finally acquired the optimal penalty factor c and kernel function parameter g. The number of IMFs from decomposition was determined according to the actual signals and noise. In general, a higher number of IMFs means a better decomposition effect of a signal, but an excessively high number of IMFs will lead to a significant reduction in the computing speed. After testing, five mode components were chosen, which showed better performance in practice. The algorithm here was used for the processed dataset. Typical signals and processing results are shown in Figures 2 and 3. The dataset here contained 300 pieces of data, of which 100 pieces of data were effective signals and 200 pieces of data referred to noise. The data here were randomly selected from a large data set of 300 data. Each piece of data was decomposed by VMD into five IMFs and one residual, and there were 1800 sets of data in total. In this study, the number of signal sampling points was 4096, and the signal waveform was a velocity waveform. The analysis in Figures 2 and 3 reveals that VMD can effectively separate effective signals from the microseismic signals with a low signal-to-noise ratio. In Figure 2, the first three IMFs are ineffective, while the fourth and fifth IMFs are effective. The GA-SVM successfully identifies and reconstructs effective components and obtains the denoised microseismic signals. However, all components after decomposition in Figure 3 are ineffective. SVM failed to find effective IMFs after identification, leading to the absence of signals in the reconstruction results. Figure 1: The change in the accuracy rate of the SVM model after iterative training. In order to evaluate the effect of recognition and processing by the algorithm here on effective microseismic signals, we calculated the signal-to-noise ratio (SNR) and root mean square error (RMSE) of the processed effective microseismic signals. The signal-to-noise ratios and root mean square errors of some typical signals are presented in Figures 4 and 5. Figure 3: VMD results of noise signals: (**a**) original waveforms, (**b–f**) IMF1–5, (**g**) residuals, (**h**) reconstructed signals. Figure 2: VMD results of effective signals: (**a**) original waveforms, (**b–f**) IMF1–5, (**g**) residuals, (**h**) reconstructed signals. SNR was increased by 19.11\(\sim\)36.62, and SNR was between 37.78 and 52.51 after the algorithm's processing. RMSE was reduced by 1.65 \(\times\) 10\({}^{-2}\)-7.96 \(\times\) 10\({}^{-2}\), and RMSE after algorithm processing was between 0.06 \(\times\) 10\({}^{-2}\) and 0.64 \(\times\) 10\({}^{-2}\). Therefore, after the algorithm processing, the signal-to-noise ratio of the signal was greatly improved, and the root-mean-square error was effectively reduced.