# Self-Supervised Shear Wave Noise Adaptive Subtraction in Ocean Bottom Node Data
## 4 Discussions  
### Order of Denoising  
Since the shear noise in the Z-component is related to both of the two horizontal components, we need to consider a different denoising order. First, we do not consider the case of removing the noise related to both components simultaneously, as this would make it difficult for the network to distinguish the features of the noise and the signal. After removing one first, the SNR of the data is improved and the features of the other are more easily recognized by the network. Different from the previous operation of removing X- and Y-component leakage successively, we consider the case where the noise related to the Y-component is removed first in step one and then the noise of the X-component in the second step.  
Table 2 shows the denoising results and SNRs before and after denoising on the synthetic Dataset 1-1, 1-2 and 1-3 by first removing the noise related to the Y-component and then removing the noise related to the X-component. The network training parameters are the same as those in Section 3.1 for comparison. Combined with Table 1, it can be seen that both denoising orders improve the SNRs of the original data, with little difference in the magnitude of the improvement.  
Considering that the X- and Y-components of the field data may leak noise in different proportions, we generated a second set of clean-noisy data pairs in the manner of Equation (11).  
\[\mathbf{Z}=\mathbf{P}+\alpha\mathbf{X}+\beta\mathbf{Y}. \tag{11}\]  
We generate a total of six clean-noisy data pairs by setting different combinations of values for \(\alpha\) and \(\beta\) and then perform numerical experiments under two denoising orders. The network parameters are all set with reference to Section 3.1. The SNRs before and after denoising are shown in Table 3. Denoising order I means that the noise associated with the X-component is removed first, followed by the noise associated with the Y-component, and order II is reversed. These results show that both denoising orders improve the SNRs of the data in various scenarios. Additionally, the proportion of noise leakage associated with each component is stronger, achieving better denoising results by removing the noise first. At the same time, this is also related to the energy strength of the two horizontal components themselves. Overall, removing the component that leaks stronger noise first can achieve better denoising results. For the field data, we cannot know the proportion of noise leakage. By comparing the data, we can roughly see that the energy of the noise related to X-component is slightly stronger than that of the Y-component (seen in Figure 11). Therefore, for field OBN data, we choose to remove the noise related to the X-component first and then remove the noise related to the Y-component.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Dataset 1-1** & **Dataset 1-2** & **Dataset 1-3** \\ \hline Noisy data & 6.55 dB & 0.53 dB & \(-\)5.49 dB \\ Denoising result & 16.36 dB & 14.69 dB & 11.14 dB \\ \hline \hline \end{tabular}
\end{table}
Table 2: SNRs of synthetic data examples before and after denoising for removing Y-component first.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Dataset 2-1** & **Dataset 2-2** & **Dataset 2-3** & **Dataset 2-4** & **Dataset 2-5** & **Dataset 2-6** \\  & (\(\alpha=1,\beta=0.5\)) & (\(\alpha=0.5,\beta=1\)) & (\(\alpha=2,\beta=1\)) & (\(\alpha=1,\beta=2\)) & (\(\alpha=2,\beta=0.5\)) & (\(\alpha=0.5,\beta=2\)) \\ \hline Noisy data & 3.62 dB & 1.81 dB & \(-\)2.40 dB & \(-\)4.21 dB & \(-\)1.01 dB & \(-\)3.77 dB \\ Order I & 15.61 dB & 13.43 dB & 13.13 dB & 8.18 dB & 15.57 dB & 8.17 dB \\ Order II & 14.74 dB & 16.27 dB & 10.76 dB & 13.59 dB & 10.84 dB & 14.83 dB \\ \hline \hline \end{tabular}
\end{table}
Table 3: SNRs of the second set of synthetic data examples before and after denoising.