## 3 Experimental Results
### Quantitative Test  
To further demonstrate the performance of the proposed methodology, a dataset (including 800 micro-fracture waveforms and 800 noisy waveforms) is employed to document the detection performance of the PDNetwork in comparison with existing techniques, such as Correlation [39], VggNet, AlexNet [40], and ResNet [41]. And, the onset time picking of the micro-fracture waveforms is manually picked by experienced engineers, and the obtained result is compared with the picking performance of the proposed PDNetwork. The same training dataset is employed to train the model using five-fold cross-validation, and the optimal model is selected and implemented on the same test dataset. The evaluation indices, namely, accuracy, Precision, Recall, and F1-score, are introduced to monitor the detection performance of the mentioned methods.  
\[Accuracy=\frac{TP+FN}{TP+FP+TN+FN}\times 100\% \tag{2}\]  
\[Precision=\frac{TP}{TP+FP} \tag{3}\]  
\[Recall=\frac{TP}{TP+FN} \tag{4}\]  
\[F1-score=2\times\frac{Precision\times Recall}{Precision+Recall} \tag{5}\]  
In the above equations, _TP_ (true positive) represents the true prediction of the positive sample, whereas _TN_ (true negative) represents the true prediction of the negative sample. _FP_ (false positive) represents the false prediction of the negative sample, whereas _FN_ (false negative) represents the false prediction of the positive sample. Precision is defined as the proportion of the true prediction of positive samples in the positive prediction (_TP_ and _FP_). Recall is defined as the proportion of the true prediction of the positive samples in actual positive samples (_TP_ and _FN_). The \(F1\)-score primarily aims to mitigate the effects of imbalanced sample sizes in the model evaluation based on the Precision and Recall metrics [42]. Hence, a higher F1-score indicates superior model performance.  
Figure 5 shows the comparison results of the onset time picking between the PDNetwork and the manual process. Clearly, the PDNetwork can obtain a high accuracy of onset time picking, even in the case of micro-fracture waveforms with different intensities of noise. Furthermore, the PDNetwork requires approximately 10 s to 15 s to process 800 micro-fracture waveforms in the test dataset, which is a significant reduction in the time required over manual picking. Moreover, approximately 95% of the onset time errors are less than 2.5 ms, which also proves that the PDNetwork has good performance for onset time picking (see Figure 6).  
For another function of the PDNetwork, Table 3 presents the comparison results of the detection performance with those of four existing methods. The results of the evaluation indices of the proposed approach, a validation accuracy of 98.4%, a test accuracy of 97.1, a Precision of 0.968, a Recall of 0.975, and an F1-score of 0.971, indicate that the PDNetwork performs best in the microseismic waveform detection among the above methods. Another  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Section** & \multicolumn{3}{c}{**Validation Accuracy (\%)**} & \multicolumn{3}{c}{**Average (\%)**} \\ \hline Onset time picking & 99.5 & 99.4 & 99.6 & 99.5 & 99.3 & 99.46 \\ \hline detection & 98.3 & 98.3 & 98.4 & 98.2 & 98.1 & 98.26 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results of the five-fold cross-validation for onset time picking and detection, respectively.