# Seismic Data Denoising Based on Wavelet Transform and the Residual Neural Network
## 4 Real Seismic Data Processing Results  
Real data consists of 14,735 seismic traces, with 256 sample points per seismic trace and a 0.002 s sampling period. The process of making the training set, test set, and validation set is the same as making the synthetic seismic dataset. For verifying the feasibility of the method, the results of denoising with different wavelet bases at different numbers of decomposition layers with different input SNRs were measured. The experiments demonstrate that in most cases, after the wavelet decomposition at level 2 or 3, optimum denoising results can be obtained by residual neural network processing. When the input SNR is \(-\)5.203 dB and \(-\)2.273 dB, the optimal denoising result mostly appears in the wavelet decomposition of level 1 and 2. However, in case the optimal denoising result appears in the wavelet decomposition of level 1, it is not much different from the result of the level 2 or 3 wavelet decomposition, which is within 0.5 dB. Notice that unlike the simulated data, where the optimal wavelet for each wavelet basis is essentially fixed even at different noise levels, this property of the real data is related to the data itself, where the simulated data have zero data except where seismic waves are not present, while the real data still have non-zero irrelevant data where there are no seismic waveforms, even though they are not visible to the naked eye. Figure 7 plots the trend of the denoising capability of Table 3. Except for the substantial discrepancies at high SNRs for haar, db, sym, coif, and bior wavelets, it is evident that the difference between the Resnet18 denoising outcomes under various wavelets reduces as the noise level increases. The overall denoising effect under rbio is stable, and as the input SNR decreases, its denoising effect gradually outperforms the denoising effect of Resnet18 under other wavelet bases. Figure 6: (**a**–**e**) illustrates the single\(-\)channel data compared with the clean single\(-\)channel data after denoising with four denoising methods at SNR ranked from high to low. To verify the impact of network depth on the denoising effect in the DWT-Resnet denoising method with real seismic data. To verify the effect of the network depth of DWT-Resnet on the real seismic data denoising results. Taking the real seismic data with a SNR of \(-7.1157\) dB as an example, the effect of the number of Resnet layers on the denoising results in the case of a 2-level decomposition using haar is as follows (Figure 8). The image shows that the DWT-Resnet26 still has a remarkable denoising capability. When increasing the number of layers of the residual neural network to 26, the denoising difference is obvious when different types of wavelets process the real seismic data with high input SNR (Figure 9). Except for the db and haar wavelets, the denoising ability of other wavelets fluctuates somewhat when processing real seismic data, db, and haar behave more consistently when processing seismic data with different SNR compared to other wavelets. Figure 8: Denoising results of real seismic data with SNR of \(-7.116\) dB for DWT-Resnet networks with a different number of layers for a fixed number of wavelet bases and wavelet decomposition levels. Figure 7: Trend of the best denoising results of DWT\(-\)Resnet18 with varying SNRs of real noisy seismic data under different wavelet basis. Figure 10 shows the comparison of the denoising results under the optimal performance of Resnet18, DWT-Resnet18, and DWT-Resnet26. From the comparison, it is clear that the DWT-Resnet method performs well, and DWT-Resnet18 performs best at higher SNRs, while the DWT-Resnet26 performs optimally when the SNR is low. Figure 11 shows the comparison of single-channel seismic data with clean seismic data after denoising by four denoising methods at different noise levels. As the noise level rises, even the denoised data using DWT-Resnet26 is gradually failing to fit the original seismic data well.