# Seismic Blind Deconvolution Based on Self-Supervised Machine Learning
## 3 Experiments
### Field Experiment I  
To demonstrate the practicality of the SSL-BD method, we present two field examples. The first field dataset comes from CNPC, as shown in Figure 11. It comprises 976 seismic traces, and each trace has 688 sampling points with an interval of 1 ms. Figure 12a shows the wavelet extracted from the CNPC seismic data. Figure 12b shows the wavelet estimated by the proposed SSL-BD method. Figure 13 shows the comparisons of wavelet amplitude spectra and phase spectra between the wavelet extracted from the CNPC data and the wavelet estimated by the proposed SSL-BD method. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **MAE (10\({}^{-5}\)) \(\downarrow\)** & **MSE (10\({}^{-5}\)) \(\downarrow\)** & **MAE\(\downarrow\)** & **MSRE \(\downarrow\)** & **SSIM \(\uparrow\)** & **PSNR \(\uparrow\)** \\ \hline SSL-D & 1.078175 & 1.335004 & 0.641659 & 0.434459 & 0.741858 & 26.806973 \\ SSL-BD & **0.599912** & **0.449987** & **0.258171** & **0.172519** & **0.995130** & **31.529794** \\ \hline \hline \end{tabular} \(\downarrow\) means the lower the better and \(\uparrow\) means the higher the better. The best values are in bold.  
\end{table} 
Table 3: Metric values of the predicted reflectivity profiles of 2D synthetic test. Figure 10: Reflectivity inversion results with regard to the different noise levels. (**a–d**) Reflectivity inversion results of SSL-D [23] when SNR equals 5, 10, 15, and 20 dB. (**e–h**) Reflectivity inversion results by SSL-BD when SNR equals 5, 10, 15, and 20 dB. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **MAE (10\({}^{-5}\)) \(\downarrow\)** & **MSE (10\({}^{-5}\)) \(\downarrow\)** & **MAE\(\downarrow\)** & **MSRE \(\downarrow\)** & **SSIM \(\uparrow\)** & **PSNR \(\uparrow\)** \\ \hline SSL-D & 1.078175 & 1.335004 & 0.641659 & 0.434459 & 0.741858 & 26.806973 \\ SSL-BD & **0.599912** & **0.449987** & **0.258171** & **0.172519** & **0.995130** & **31.529794** \\ \hline \hline \end{tabular} \(\downarrow\) means the lower the better and \(\uparrow\) means the higher the better. The best values are in bold.  
\end{table} 
Table 4: Comparison of reflectivity inversion results with regard to different noise levels. Figure 14 shows a detailed comparison among the impedance curve from the well, a reflectivity calculated using the impedance curve, and the reflectivity calculated by the SSL-D method [23] and the proposed SSL-BD method, respectively. In Figure 14, the reflectivity predicted by our proposed SSL-BD method has a similar trend to the well reflectivity. However, the resolution of the predicted reflectivity is much lower than the well reflectivity, which needs to be further improved in the future. The predicted reflectivity profiles of the SSL-D method [23] and the SSL-BD method are presented in Figure 15a  
Figure 11: Two-dimensional field test of CNPC data. Figure 12: Two-dimensional field test of CNPC data. (**a**) Wavelet extracted from the CNPC seismic data. (**b**) Wavelet estimated by the proposed SSL-BD method. Figure 13: Two-dimensional field test of CNPC data. (**a**) Amplitude spectra of wavelet extracted from the CNPC data. (**b**) Amplitude spectra of wavelet estimated by the proposed SSL-BD method. (**c**) Phase spectra of wavelet extracted from the CNPC data. (**d**) Phase spectra of wavelet estimated by the proposed SSL-BD method. and Figure 15b, respectively. The results demonstrate that both methods can enhance the resolution of seismic profiles, but the proposed SSL-BD method reveals detailed information between layers more clearly, as indicated by the arrows and ellipses. Figure 15c shows the reconstructed seismic profile of the SSL-D method [23]. It is the convolution result of the reflectivity profile (as shown in Figure 15a) and the wavelet extracted from seismic data (as shown in Figure 12a). Figure 15d shows the reconstructed seismic profile of the proposed SSL-BD method. It comes from the convolution of the predicted reflectivity profile (as shown in Figure 15b) and the estimated wavelet (as shown in Figure 12b).