# Self-Supervised Shear Wave Noise Adaptive Subtraction in Ocean Bottom Node Data
## 3 Experiments
### Synthetic Example  
Figure 4a shows the synthetic seismic data obtained from the Pluto velocity model, denoted as **P**. Figure 4b,c show the X- and Y-component from the field data, denoted as **X** and **Y**, respectively. For a clear display, the amplitude of the X- and Y-component are magnified by two times. Due to the complexity of the causes of shear wave leakage, it is difficult to model leaking weighting coefficients that are sufficiently approximate to the actual situation. We add **X** and **Y** to the clean P-wave data (**P**) in a fixed ratio and perform numerical experiments in the simplified case. The synthetic noisy Z-component data (denoted as **Z**) are obtained through Equation (9), where \(\alpha\) represents the proportion of added noise. We set \(\alpha\) to 0.5, 1, and 2, respectively, then generate three clean and noisy data pairs (denoted as Dataset 1-1, 1-2 and 1-3) for experiments. In the network training, the learning rate is set at 0.001, the batch size is fixed to 1, and the number of iterations is 500. The network hyperparameters are selected by trial and error.  
\[\textbf{Z}=\textbf{P}+\alpha(\textbf{X}+\textbf{Y}). \tag{9}\]  
The noisy data (Figure 5a-c) in the synthetic dataset show a large amount of noise with different amplitudes, and in many regions, the noise overlaps the valid signal, such as the blue rectangles area. The second row of Figure 5 displays the denoising results of applying the proposed method, and the predicted noise and the error of the denoising result with respect to the clean data are shown in the third and last rows in Figure 5, respectively. In the denoising results (Figure 5d-f), it can be seen that the large amount of shear noise shown in the noisy data has been eliminated. The similarity of the denoising results to the clean data (Figure 4a) demonstrates the effectiveness of the denoising method. The error graphs (Figure 5j-l) show that there is only a weak residue of noise in the denoising results. Moreover, no significant signal leakage is observed in the predicted noise and error diagrams. To better analyze the results, we give the magnified display results of the two blue rectangles. It can be seen that most of the noise is removed in the noise-signal overlap region, and there is little damage to the signal. The above results indicate that the method in this paper can achieve both signal protection and noise removal, and it is still effective in the signal-noise overlap region.  
Figure 4: Synthetic data and X- and Y-component field data. (**a**) Synthetic P-wave data (synthetic clean Z-component data). (**b**) X-component of field OBN data. (**c**) Y-component of field OBN data.  
Figure 5: Synthetic data example. First row: noisy data of Dataset 1-1 (**a**), Dataset 1-2 (**b**) and Dataset 1-3 (**c**). Second row: noise attenuation results of Dataset 1-1 (**d**), 1-2 (**e**) and 1-3 (**f**). Third row: predicted noise of Dataset 1-1 (**g**), 1-2 (**h**) and 1-3 (**i**). Bottom row: difference between the denoising results and clean data of Dataset 1-1 (**j**), 1-2 (**k**) and 1-3 (**l**) by subtracting Figure 4a from (**d**–**f**), respectively. The two blue rectangles above each image are magnified correspondingly in the lower left and lower right of the figure.  
Additionally, we report the signal-to-noise ratio (SNR) as a quantitative metric to analyze the denoising results. The SNR is calculated as follows:  
\[SNR=10\times\log_{10}\frac{\|S\|^{2}}{\|S^{\prime}-S\|^{2}}, \tag{10}\]  
where \(S\) is the clean signal and \(S^{\prime}\) represents the reconstructed data. As we know, a higher SNR means a better quality of data. After denoising, the SNRs of noisy data from Dataset 1-1, 1-2 and 1-3 are improved from 6.55 dB, 0.53 dB, \(-\)5.49 dB to 16.12 dB, 13.47 dB, 9.47 dB, respectively, indicating the effectiveness of the proposed method. Table 1 shows the SNRs of the data before and after denoising.