Self-supervised diffusion model for 3D seismic data reconstruction

ABSTRACT Seismic data reconstruction is an effective tool for compensating for nonuniform and incomplete seismic data. Compared with the methods for 2D seismic data, 3D reconstruction methods can consider more spatial correlation in seismic data. However, most existing 3D reconstruction methods are mainly theory driven and have some limitations due to their prior assumptions about seismic data. To overcome these limitations, deep-learning-based reconstruction methods emerged and have shown some potential in practical applications. However, there are mainly two shortcomings of the existing deep-learning methods. On the one hand, most of the existing deep-learning-based methods adopt convolutional neural networks, which have some difficulties in dealing with data that have complex or time-varying distributions. Recently, the diffusion model has been reported to have the capability to handle data with complex distributions. On the other hand, existing methods need sufficient paired data to train the network, which are difficult to obtain, especially in three dimensions. Deep prior-based unsupervised and sampling-based self-supervised networks offer a solution to this problem. Motivated by these, we develop a self-supervised diffusion model for 3D seismic data reconstruction (3D-SSDM). Our model mainly contains a diffusion restoration model and a variational time-spatial module. Synthetic and field data experiments demonstrate the superiority of our 3D-SSDM algorithm.