Consistent Least-Squares Reverse Time Migration Using Convolutional Neural Networks

The data-consistency item is a necessary condition for a reliable solution to the inverse problem. However, the current supervised-based deep-learning reconstruction approaches generally lack the data-consistency item, which directly leads to unreliable subsurface images for field data. To resolve this problem, we have developed a consistent least-squares reverse time migration (CLSRTM) approach using convolutional neural networks (CNNs), which is referred to as CNN-CLSRTM. The key point is that we have enforced that the predicted recording via the inverted image from the CNN model is consistent with the observed recording in the least-squares sense. We utilize the standard reverse time migration (RTM) image of single-shot recording as the input of the constructed CNN model. As a result, the optimal reflection image can be obtained by iteratively updating the parameters of CNN by minimizing the data residuals. Benefiting from the similarity of RTM images of adjacent recordings and the representation ability of the well-trained CNN model, we can directly predict the optimal reflection image for the testing datasets in a very fast way, which can greatly improve computational efficiency. Through synthetic and field data sets, we have determined that the proposed CNN-CLSRTM approach can retrieve high-resolution images with balanced amplitudes and continuous events. At the same time, our approach has better antinoise ability inherited from the benefit of CNN model compared to the standard LSRTM approach. In addition, we analyze the generalization ability of the CNN model for synthetic and field datasets.