## 4 Experimental Results and Analysis
### Comparison with State-of-the-Art (SOTA) Methods  
In this subsection, the performance of the proposed algorithm on synthetic seismic data and forward models is evaluated, respectively. To improve comparability, all algorithms were trained using the same training set. The denoised data were justified quantitatively  
Figure 6: (**a**) Original synthesized signals, (**b**) forward model, and (**c**) background noise. by using the evaluation metric of the peak signal-to-noise ratio (PSNR) [50]. Tables 2 and 3 present the PSNR values (dB) for comparison with other state-of-the-art methods; values in bold font indicate optimal values. As shown in the tables, the PSNR values resulting from the deep learning-based methods were higher by a large margin quantitatively compared with the traditional methods, such as the wavelet, curvelet, and shearlet transform-based seismic denoising algorithms, especially with higher noise levels. Particularly, our method performed better in denoising with a higher PSNR value. Figures 7 and 8 present the qualitative comparison results on the synthetic data and forward model data. Figure 7a shows the original synthetic data, and Figure 7b shows the data after adding white Gaussian random noise and linear noise. Figures 7c, 7e and 7g are the results processed by the shearlet algorithm, USRNET, and our method, respectively; Figure 7d,f,h are the corresponding eliminated noises. It is obvious that the resulting data of our method were closer to the original data, obtaining excellent qualitative results. Furthermore, Figure 8a shows a forward model of well data. We added real background noise to the forward model, as shown in Figure 8b. Figures 8c, 8d and 8e show the results processed by the IDN, the USRNET, and our method, respectively. We can see that our method achieved better results that were closer to the original forward model, and the weak signals were effectively restored compared with the other two methods. Next, we focus on evaluating the performance of our method on real seismic data. The FID-N worked well in low-SNR conditions, improving the signal quality by reducing noise and preserving important features. Figure 9 presents the processed comparison results of the original real seismic data with a low SNR. It can be seen that the effective signals processed by the commercial software were very limited due to noise. After denoising by our method, the effective signals became clearer. Figure 9b,c show the results processed by the commercial software and our method at high frequencies. For 40-80 Hz and 60-120 Hz, the results processed by the commercial software were not ideal, and our method could highlight the effective signals. On the contrary, the effective signals obtained by our method were obviously outstanding, improving the high-frequency SNR of the real seismic data. The FID-N preserved high-frequency details effectively, which are essential for detecting fine geological features. Furthermore, we processed the migrated profile data obtained by the seismic data processing flow, as shown in Figure 10. The red dashed line denotes the focusing target layer, under which the reservoir weak signal exists. However, the processing result of the commercial software was not obvious in terms of performance. We can clearly see that the result processed by our method presented more weak seismic signals and was better than that of the IDN, which provides significant contributions to the prediction of oil and gas reservoirs. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Noise** \\ **Level** \\ **(dB)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Noisy** \\ **Data** \\ **(dB)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Wavelet** \\ **[47]** \\ **(dB)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Wavelet** \\ **[47]** \\ **(dB)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Wavelet** \\ **[49]** \\ **(dB)** \\ \end{tabular}  } & \multirow{2}{*}{