## 5 Conclusions  
We propose a novel CNN-based algorithm, FID-N, specifically designed to suppress seismic noise. Our method introduces several key innovations: (1) the use of a feedback structure combined with a two-path ID block, which significantly enhances the seismic denoising performance by effectively exploiting the inherent features of seismic signals; (2) the integration of an NSCT, which allows the network to retain fine-grained information from noisy seismic data, further improving denoising outcomes. The experimental results demonstrate that the FID-N consistently outperformed the SOTA methods, achieving higher PSNR values, particularly in scenarios with low SNR values. This highlights the superiority of our method, especially in preserving weak signals that are critical in seismic data analysis. Future work will focus on extending the FID-N to handle other types of noise and improving real-time processing capabilities.  
K.C., G.Z. and Q.R.: conceptualization, analysis, and framework construction. C.T. and L.W.: writing--review and editing, and investigation. S.H., H.L. and H.Y.: methodology,  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**High-Frequency Levels of** & **Synthetic Data** & **Forward Model** \\
**NSST Decomposition** & **(Noise Levels: 0.06)** & **(Noise Levels: \(1\times 10^{-5}\))** \\ \hline
2 levels (numbers of & & \\ decomposition directions & 89.6527 dB & 71.6639 dB \\ are 2 and 4, respectively) & & \\ \hline
2 levels (numbers of & & \\ decomposition directions & 89.9253 dB & 72.0663 dB \\ are 4 and 8, respectively) & & \\ \hline
3 levels (numbers of & & \\ decomposition directions & 90.5265 dB & 72.7694 dB \\ are 2, 4, and 8, respectively) & & \\ \hline \hline \end{tabular}
\end{table}
Table 6: Average PSNR values for different high-frequency levels of decomposition based on our FID-N.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Iteration \(T\)** & **3** & **5** & **7** & **9** & **11** & **13** \\ \hline Synthetic data (noise & & & & & & \\ levels: 0.06) & 89.3611 dB & 89.5482 dB & 90.0663 dB & 90.5265 dB & 90.5915 dB & 90.6638 dB \\ \hline Forward models (noise & & & & & \\ levels: \(1\times 10^{-5}\)) & 71.3616 dB & 71.6228 dB & 72.1654 dB & 72.7694 dB & 72.8859 dB & 72.9863 dB \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average PSNR values on synthetic data and forward models under different iterations \(T\).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Noise Level** & **Single Scale** & **Two-Path** & **Noise Level** & **Single Scale** & **Two-Path** \\
**(dB)** & **(Baseline)** & **(dB)** & **(dB)** & **(Baseline)** & **(dB)** & **(dB)** \\ \hline
0.02 & 93.1491 & 93.7661 & \(1\times 10^{-6}\) & 83.4659 & 84.0452 \\
0.04 & 91.2566 & 91.8348 & \(5\times 10^{-6}\) & 79.6658 & 80.1026 \\
0.06 & 89.9013 & 90.5265 & \(1\times 10^{-5}\) & 72.1438 & 72.7694 \\
0.1 & 87.5524 & 88.1273 & \(5\times 10^{-5}\) & 61.5471 & 62.4617 \\
0.15 & 82.0659 & 82.5441 & \(1\times 10^{-4}\) & 49.4936 & 50.3967 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of average PSNR values on synthetic data and forward models for single-scale feature extraction and our two-path information distillation block (IDB).  
validation, and visualization. All authors have written, revised, and improved this paper. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Major Science and Technology Project of PetroChina Company Limited (grant no. 2023 ZZ16 YJ04).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
We acknowledge all supporting organizations.  
Authors [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] were employed by PetroChina Southwest Oil & Gasfield Company. The remaining author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.