# Seismic Data Denoising Based on Wavelet Transform and the Residual Neural Network
## 3 Synthetic Seismic Data Processing Results
Inspired by the above experiments, the subsequent increase in the number of network layers is either by adding a new layer or by increasing the number of residual blocks in the layer. Following layer4, two further layers, layers 5 and 6, are brought in, where layer5 includes 2 residual blocks, each with 1024 channels, and so on layer6 is a layer composed of 2 residual blocks containing 2048 channels. Then the 20-layer Resnet includes two cases, one is to increase the number of residual blocks of layer4, and the other is to add a layer5 containing 1 residual block, the SNR of the latter is 22.540 dB, which is 1.246 dB higher than the former, making the neural network denoising effect has been  
Figure 3: Denoising results of seismic data with SNR of 4.074 dB for DWT\(-\)Resnet18 networks with different numbers of layers for a fixed wavelet type and wavelet decomposition levels. Figure 2: Trend of the best denoising results of DWT\(-\)Resnet18 with varying SNRs of noisy seismic data under different wavelet basis functions. greatly improved. Inspired by the above experimental results, better results were obtained when the number of layers of the Resnet network was increased to 26, i.e., layer5 containing 4 residual blocks linked after layer4. Although another combination of the 26-layer network is to link layer5 and layer6 in sequence after layer4, when its denoising effect is the best, the training time also increases due to the increase of network layers, and it takes 8251.736 s to train the 26-layer network. However, in terms of SNR, the 26-layer network with layer6 is only 0.280 dB better than the 26-layer network with only layer5, this is obviously a less suitable denoising solution, so the layer5 with 4 residual blocks is used as the optimal denoising network. Next, with the results in Table 1, the denoising performance of DWT-Resnet26 was tested at different SNRs, choosing different wavelet bases, using the number of decomposition levels for the best denoising results in DWT-Resnet18. Following denoising results were obtained through experiments (Table 2, Figure 4). From Table 2 and Figure 4, it is observed that when the number of layers of the residual neural network is increased to 26, the denoising differences are more obvious when different wavelet bases are processed with seismic data at high input SNR; haar performance results have been poor, and rbio does not improve its denoising performance significantly at low SNR, with the increase of noise level, its denoising effect is similar to the performance of several wavelets except haar. Db and coif remain relatively stable. Comparing the best denoising results of Resnet18 and Resnet26, DWT-Resnet18 and DWT-Resnet26 (Figure 5), it is clear that the residual neural network denoising method combined with wavelets performs better. DWT-Resnet26 achieves the best performance at higher SNR, while DWT-Resnet18 and DWT-Resnet26 obtain similar denoising results when the SNR is low. In contrast, the denoising effect of Resnet26 is conversely inferior to that of Resnet18 when processing data without wavelet transform. A possible cause of the conjecture is the deepening of the network model [25], which causes overfitting, but wavelet-transformed data are not affected by overfitting. To visualize the denoising effect of each method, Figure 6 shows the comparison of single-channel clean seismic data and the corresponding single-channel data after denoising with Resnet18, DWT-Resnet18, Resnet26, and DWT-Resnet26 at different SNRs. Results point out that although DWT-Resnet improves the denoising ability of Resnet, even DWT-Resnet is unable to adequately match the original seismic data when the SNRs of the input seismic data decline.