# A Novel Wavelet Selection Method for Seismic Signal Intelligent Processing
## 3 Results
### Application in Automated P Arrival Picking
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Wavelet** & **rbio3.1** & **haar** & **db2** & **sym2** & **coif3** & **bior3.1** \\ \hline Test accuracy & 93.55\% & 90.92\% & 91.33\% & 91.83\% & 89.75\% & 91.42\% \\ Test accuracy & 92.75\% & 91.25\% & 90.67\% & 91.83\% & 90.58\% & 91.33\% \\ Test accuracy & 93.08\% & 90.50\% & 87.42\% & 90.92\% & 92.25\% & 91.58\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental results of signal classification under the use of different wavelets. LSTM network for each wavelet was trained 50 times for each comparison experiment. In total, three comparison experiments were conducted. Moreover, to numerically assess the performance, we adopted the arrival picking error metric, which is described as [55]  
\[Error=\left|T_{p}-T_{t}\right|, \tag{11}\]  
where \(T_{p}\) is the arrival picking and \(T_{t}\) is the ground truth. After the model was trained, it was tested using the test set, and the experimental results are shown in Figure 8. Figure 8a shows the results of the first round of comparison experiments. In Figure 8a, the total picking error using selected wavelet rbio3.1 is 612.6 s, and the errors for the other five wavelets are 680.53 s, 621.57 s, 758.52 s, 653.21 s, and 589.80 s, respectively, and the mean of the picking error using rbio3.1 is 0.683 s, and the errors for the other five wavelets are 0.705 s, 0.645 s, 0.788 s, 0.675 s, and 0.615 s, respectively. In Figure 8b, the total picking error using selected wavelet rbio3.1 is 547.63 s, and the errors for the other five wavelets are 633.24 s, 903.34 s, 657.66 s, 684.88 s, and 568.23 s, respectively, and the mean of the picking error using rbio3.1 is 0.570 s, and the means for the other five wavelets are 0.653 s, 0.938 s, 0.683 s, 0.713 s, and 0.593 s, respectively. In Figure 8c, the total picking error using selected wavelet rbio3.1 is 546.85 s, and the errors for the other five wavelets are 685.13 s, 712.30 s, 710.35 s, 654.67 s, and 669.47 s, respectively, and the mean of the picking error using rbio3.1 is 0.570 s, and the errors for the other five wavelets are 0.713 s, 0.743 s, 0.735 s, 0.683 s, and 0.698 s, respectively. Therefore, the wavelet selected using our method make the automatic P arrival picking better than the other randomly selected wavelets. Moreover, in the three-round experiments, the variances of the picking  
Figure 7: Automatic seismic P arrival picking using wavelet packet decomposition and deep learning. After performing a 3-level wavelet packet decomposition, the eight wavelet coefficients can be obtained from the seismic waveform. These wavelet coefficients are adopted as input for the training of the LSTM network. error using rho3.1 are 0.2138, 0.2981, and 0.2475, respectively. As shown in Figure 8, the variance of the picking error using rho3.1 is the smallest, i.e., the results of picking using rho3.1 are the most stable. In summary, the wavelet selected using our method can make the seismic P arrival picking both accurate and stable, proving that our wavelet selection method is indeed effective.