# Accelerating High-Resolution Seismic Imaging by Using Deep Learning
## 3 Results  
The end-to-end high-resolution imaging method was applied for a real field data set. Additionally, the synthetic Ricker wavelet plane was input into the learned model to illustrate the model learning. In addition, the spectrum of the original and learned high-resolution imaging was compared. Figure 8 shows the input patches and corresponding learning targets (high-resolution imaging using QPSTM) obtained from these samples. It can be noted that in the conventional PSTM imaging patches, the seismic event is absorbed, with insufficient resolution. However, the corresponding high-resolution imaging patches have more detailed information. These patches are fed into the  
Figure 7: Network workflow for training and prediction. In the training phase, the patches of the PSTM images are fed into the network and the predicted output is determined. Thereafter, the difference between the prediction patches and the actual migration patches obtained using the QPSTM is calculated, and the loss error is back-propagated to update the network parameters to make it more suitable for the training samples. After training for many epochs, the network converges to a fine state, which can be used to predict unseen patches. In the prediction phase, using the well-trained network and the PSTM patch as the input, we can predict the output patch with a high-resolution feature. network, and the network is trained using the TensorFlow program [39] by employing a GPU. The loss curve for the training data and validation data is obtained, as shown in Figure 9. The horizontal axis denotes the training epochs, which represents the number of times that the samples are fed to the network. The vertical axis represents the loss, in particular, the MAE, which indicates the discrepancy between the predicted output and the actual QPSTM imaging result. As the epoch increases from 1 to 25, both the training loss and validation loss decrease dramatically, which means that the network converges to a more fitting state for the provided data. As the epoch moves beyond 25, the loss decreases; however, the speed reduces, indicating that the network is in a fine tuning state. Finally, the validation loss is more than the training loss, accompanied by vibration. This phenomenon indicates that the network model has achieved its state-of-the-art state, and more training may lead to over-fitting or instability. Therefore, we terminate training just before this point, and it takes approximately 4 h to train the whole network by using a TiTan XP GPU. Figure 8: PSTM patches and the corresponding QPSTM patches used for network training. Panel (**a**) shows the four input patches, whereas panel (**b**) shows the corresponding learning targets (high-resolution imaging using QPSTM) from the 14,256 samples. It can be observed that the seismic events are absorbed with insufficient resolution in the conventional PSTM imaging patches, whereas the corresponding high-resolution imaging patches have more detailed information. Figure 9: Training loss and validation loss in the training process. After approximately 100 epochs, the model loss remains largely constant, and the training process can be stopped at this point. To validate the proposed approach and illustrate the network learning, a Ricker wavelet compounded plane with a dominated frequency at 30 Hz is used. This Ricker wavelet patch is fed into the network model, and the predicted output of the network is obtained. As shown in Figure 10, the trained model can improve the dominated frequency from 30 Hz to approximately 40 Hz, and the phase is corrected as expected. The synthetics indicate that the model learned the ability to improve the resolution and correct the phase, as described previously using Formula (1). For further evaluation, a prediction is performed using the patches that the network does not encounter in the training stage.