# Seismic Data Denoising Based on Wavelet Transform and the Residual Neural Network
## 5 Conclusions and Discussion  
In this paper, combining traditional methods and deep learning methods, we propose an improved deep learning denoising method for random noise denoising of seismic data, that is DWT-Resnet. It is reflected in (1) the preliminary processing of noisy seismic data by utilizing the ability of wavelet transform separating the effective signals from noise in traditional denoising methods, and then feeding the processed signal into the residual neural network. With this step, the capability of network denoising is improved. (2) By varying the number of layers of the neural network, a deep network applied to the wavelet domain noisy data is proposed, further improving the denoising effect of the network.  
The comparison of the denoising results of the same denoising method for seismic data with different SNRs shows that excellent denoising results can be obtained for high SNR seismic data. As for DWT-Resnet, it can separate the effective signal from the noise by wavelet decomposition, which initially improves the quality of the data entering the network, and therefore improves the denoising ability of the neural network. Yet, as the noise contaminates the data, this ability of wavelets to separate the effective signal from the noise gradually diminishes, making DWT-Resnet subject to this limitation of wavelets. Furthermore, with deeper neural networks, the training time of DWT-Resnet keeps growing, therefore, it is a direction requiring further research to train the network quickly and well. In this paper, an attempt is made to find a wavelet basis and wavelet decomposition levels that can achieve better results for different data at different SNR levels through experiments. However, synthetic seismic data and real seismic data show that there is no generalized rule that can be obtained on which wavelet to choose for different data, at different neural network depths, to obtain the best denoising effect for noisy seismic data. Iterative wavelet base selection trials may remain necessary for applications of denoising other seismic  
Figure 11: (**a–e**) Illustrates the single–channel real data compared with the original single–channel real data after denoising with four denoising methods at SNRs ranked from high to low.  
data, which somewhat dissipates the advantage of just using a neural network approach to denoising, i.e., not requiring a more manual selection of parameters. Moreover, with high noise levels, although the DWT-Resnet26 denoising effect is improved compared to Resnet18, the improvement is limited. Therefore, how to develop a new neural network structure to more effectively combine the advantages of wavelet transform and the neural network with a fixed number of wavelet-based transforms and decomposition levels to obtain a more general DWT-Resnet method with better denoising effects will be the focus of the next research work.  
T.L.: conceptualization, methodology, software; Z.Z.: review and guidance, supervision; L.H.: review and guidance, funding acquisition, supervision; J.Z.: data curation, validation. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (grant no. 42074154).  
Not applicable.  
The authors are very grateful for all constructive comments that helped us improve the original version of the manuscript.  
The authors declare no conflict of interest.