## 3 Numerical Example  
### Enhanced Reconstruction Results for a Small Number of Seismic Sources  
In this paper, virtual shot records are obtained from twenty velocity models. The velocity model as shown in Figure 2 will be used to obtain passive seismic records, which will be reconstructed into virtual shot records to be used as test data. These velocity models used to generate the training and test sets are randomly generated. To demonstrate the generalizability of the method, the test set is not included in the training set. Here the grid size of the velocity model is 2 m, the geophone spacing is 1 grid spacing, and the sampling interval is set to 1 ms to receive a total of 200 passive seismic records. Random noise sequences were used for the seismic sources. Each velocity model contains 128 seismic traces, and since the intercorrelation method allows the construction of shot points at any geophone point, 128 virtual shot point seismic records can be generated. To address the poor results of reconstructed records due to the small number of sources, we used them as training data and used reconstructed records with a large number of evenly distributed sources as labels. To compress the training cost and reduce unnecessary training, we only show the virtual shot records of the first 800 sampling points after reconstruction. We show the two source distributions as training sets and training labels under the velocity model (see Figure 3). The virtual shot records used as training data are obtained by reconstructing the passive source seismic records under the source distribution shown in Figure 3a. Under the distribution of seismic sources shown in Figure 3b, we reconstructed the virtual shot records as training labels. By inputting training data and training labels into the network, we can obtain a trained network. This network can process the waveforms of the virtual shot records. Figure 3: Completely randomized distribution of passive seismic sources. The red dots represent where the sources are located. (**a**) Distribution of a small number of sources. (**b**) Distribution of a large number of sources. Figure 2: Velocity models used for the test data. (**a**) Test model 1; (**b**) test model 2. To test whether the performance of our designed network is enhanced compared to the original network, we set the UNet neural network with attention mechanisms as the control group to test the improvement effect. By comparison, we can see that the coherent noise is effectively suppressed by the processing of the neural network. To solve the above problem that passive virtual shot records as labels may still be noisy, we found that both the training set and its labels contain a certain amount of coherent noise during the training process. However, due to the differences in objective factors such as their source locations and numbers, the training data and labels corresponding to the same virtual shot recordings under the same velocity model are similar in terms of effective waveforms when reconstructed, whereas the coherent noise in the virtual shot recordings is unmatchable. This also leads to the fact that our neural network does not learn the invalid features of the relevant noise during training. Although the labels also inevitably contain some coherent noise, which is an interesting finding in our suppression of coherent noise. Similarly, it is difficult for the neural network to learn the features of the artifacts because the features recorded by the virtual shot vary in each training data, and the corresponding virtual shot labels contain few or no artifacts in the same position. As a result, the artifacts are eliminated. In contrast, since the effective signals on the training data and corresponding labels are similar, our neural network can learn their features. Therefore, the weaker effective waveforms in the virtual shot records of a small number of sources are better protected and enhanced.