# A Novel Wavelet Selection Method for Seismic Signal Intelligent Processing
## 3 Results
### Application in Automated P Arrival Picking  
Seismic P arrival picking is essential for calculating seismic source parameters [49; 50; 51]. Effective and fast P arrival picking is an important study in seismology. Therefore, scholars have proposed many P arrival picking methods, such as STA/LTA (short- and long-time average ratio) [52], AIC (Akaike information criterion) [53], and so on. Moreover, deep learning has become a practical approach in many research fields with computer science development. Furthermore, some intelligent automatic P arrival picking methods based on deep learning have been proposed recently [54]. These methods can combine with wavelet transform, so a wavelet selection approach should be used. Therefore, we can test our wavelet selection approach in automatic P arrival picking. A seismic dataset, denoted as M2, containing 9963 seismic records, was collected from the Center for Engineering Strong Motion Data (CESMD). Each seismic record has 1500 sampling points, and the sampling rate is 200 Hz. We used this dataset to train and test an LSTM (long short-term memory) network for P arrival picking, and the wavelet transform was used for input data preparation. Firstly, the decomposition stability \(w\) was calculated for each wavelet listed in Tables 1, 2 and 4 based on our seismic dataset M2. The results of the \(w\) calculation are listed in Table 4, and ribo3.1 is the wavelet that makes the maximum \(w\). Therefore, for M2, \(r\)bio3.1 is the best wavelet for data processing. Secondly, we used the ribo3.1 wavelet and randomly selected five wavelets (including haar, db2, sym2, coif3, and bior3.1) to perform a three-level wavelet packet decomposition, and the wavelet packet coefficients obtained after decomposing each seismic signal were adopted as the input of the LSTM network. Finally, we trained and tested the LSTM network for each selected wavelet and compared their picking accuracy. Thus, the reliability of our method was validated and analyzed. As shown in Figure 7, we built a simple LSTM network containing an LSTM module and two fully connected layers. Similarly, the network was simple enough to ensure that the differences in the experimental results were due to different wavelets and to reduce the interference of the deep learning model. The dataset M2 was divided into the training set (containing 9000 seismic records) and the test set (containing 963 seismic records). The \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Wavelet** & \(\mathbf{w}\) & **Wavelet** & \(\mathbf{w}\) & **Wavelet** & \(\mathbf{w}\) & **Wavelet** & \(\mathbf{w}\) & **Wavelet** & \(\mathbf{w}\) \\ \hline haar & \(-1.207\) & db10 & \(-1.536\) & coif5 & \(-1.533\) & bior3.5 & \(-5.547\) & ribo2.8 & 0.213 \\ db1 & \(-1.207\) & sym2 & \(-1.411\) & bior1.1 & \(-1.207\) & bior3.7 & \(-5.010\) & rbio3.1 & 10.422 \\ db2 & \(-1.411\) & sym3 & \(-1.480\) & bior1.3 & \(-1.139\) & bior3.9 & \(-4.912\) & rbio3.3 & 2.776 \\ db3 & \(-1.480\) & sym4 & \(-1.486\) & bior1.5 & \(-1.144\) & bior4.4 & \(-2.080\) & rbio3.5 & 1.858 \\ db4 & \(-1.496\) & sym5 & \(-1.505\) & bior2.2 & \(-4.874\) & bior5.5 & \(-0.337\) & rbio3.7 & 1.497 \\ db5 & \(-1.497\) & sym6 & \(-1.515\) & bior2.4 & \(-3.961\) & bior6.8 & \(-2.152\) & rbio3.9 & 1.323 \\ db6 & \(-1.519\) & sym7 & \(-1.511\) & bior2.6 & \(-3.752\) & rbio1.5 & \(-1.648\) & rbio4.4 & \(-0.982\) \\ db7 & \(-1.515\) & sym8 & \(-1.543\) & bior2.8 & \(-3.622\) & rbio2.2 & \(0.824\) & rbio5.5 & \(-2.652\) \\ db8 & \(-1.528\) & coif3 & \(-1.517\) & bior3.1 & \(-25.742\) & rbio2.4 & \(0.388\) & rbio6.8 & \(-0.965\) \\ db9 & \(-1.520\) & coif4 & \(-1.541\) & bior3.3 & \(-7.114\) & rbio2.6 & \(0.269\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The decomposition stability \(w\) of each wavelet concerning M2.