# MA_W-Net-Based Dual-Output Method for Microseismic Localization in Strong Noise Environments
## 3 Numerical Example
### Results  
Microseismic records from geophones contain not only microseismic waveforms but also varying degrees of noise. Random noise with an SNR of \(-5\), \(-10\), and \(-15\) were added to the training data to simulate the field data. An example of the input data is shown in Figure 10, where it can be seen that as the noise increases, the in-phase axis of the seismic record becomes less and less distinct and the continuity deteriorates. Seismic signals are barely visible at SNR \(=-15\). We trained the network for 600 epochs. Figure 11 shows the loss curve of the network, which achieved convergence in the later stages of training. \[\text{SNR}=10\lg\frac{P_{s}}{P_{n}} \tag{7}\]  
where \(P_{s}\) is the power of the signal, \(P_{n}\) is the power of the noise, and \(\lg\) denotes a logarithm with a base of 10. Figure 10: Microseismic recordings under different noises: (**a**) Original Record; (**b**) SNR \(=-5\); (**c**) SNR \(=-10\); (**d**) SNR \(=-15\). After the network is trained, we verify its performance using a test set. To evaluate the proposed algorithm in different SNR scenarios, we add random noise with SNR of \(-5\), \(-10\), and \(-15\) to the microseismic records in the test set, respectively. Figure 10 shows the seismic recordings at different noise levels. We input the test set into the model, with the primary task outputting microseismic locations and the secondary task outputting microseismic records after noise suppression. Figure 12 shows the localization results under different noises, from which it can be seen that the resolution of the source location imaging is high and the model-predicted source location almost exactly matches the real source location. Figure 13 shows the microseismic recordings after suppression noise. Each record is essentially free of noise residue, and the in-phase axis becomes clear and continuous. Since the denoising task is only an auxiliary task and the network focuses on extracting robust features of the microseismic recordings, it is less capable of recovering the local details of the microseismic waveforms, and some erroneous waveforms can be clearly seen below the in-phase axis. In Table 1, the localization effects are summarized for different SNRs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**SNR**} & \multicolumn{2}{c}{**Average**} & \multirow{2}{*}{**Accuracy**} & \multirow{2}{*}{**Accuracy (\(<\)10 m)**} & \multirow{2}{*}{**Accuracy (\(<\)20 m)**} & \multirow{2}{*}{**Accuracy (\(<\)50 m)**} \\  & \multicolumn{2}{c}{**Error Distance**} & & & & \\ \hline Original & & & & & \\ Record & 0.03 m & 99.75\% & 100.00\% & 100.00\% & 100.00\% \\ SNR = \(-5\) & 0.11 m & 99.00\% & 99.75\% & 100.00\% & 100.00\% \\ SNR = \(-10\) & 0.29 m & 97.50\% & 99.50\% & 99.75\% & 100.00\% \\ SNR = \(-15\) & 0.76 m & 93.50\% & 98.50\% & 99.75\% & 100.00\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Localization effects for different SNRs. Figure 11: Training loss curve. To show the superiority of the proposed method, we trained a localization model using an ordinary U-Net network. Both the training and test sets use seismic recording data with SNR = \(-15\). Figure 14 shows a sample of events in the test set and their localization results. The localization results of the model did not accurately locate the source position of the single event and disturbances were observed in the surroundings. We randomly selected 400 events in the test set, and the average error distance of their localization results was 2.60 m, with an accuracy of 78% for an error of zero. Compared with the proposed model, the model still has a large gap between the average error distance and accuracy and is less noise-resistant. This suggests that auxiliary tasks are critical for improving the noise immunity of localization models. Figure 12: Localization effects of microseismic recordings under different noises (black crosses indicate the true source locations): (**a**) Original Record; (**b**) SNR = \(-5\); (**c**) SNR = \(-10\); (**d**) SNR = \(-15\).