Unsupervised deep-learning framework for 5D seismic denoising and interpolation

We develop an unsupervised framework to reconstruct missing data from noisy and incomplete five-dimensional (5D) seismic data. Our method comprises two main components: a deep-learning network and the projection onto the convex sets (POCS) method. The model works iteratively, passing the data between the two components and splitting the data into a group of patches. The developed deep-learning model is inspired by the transformer architecture, wherein the extracted patches are flattened, and an embedded layer (fully connected layer) is used to transform the 1D flattened vector into the feature latent space. Afterward, an attention network is used to highlight the important information within these features, which improves the denoising performance of the deep-learning model. Furthermore, we use several skip connections between the fully connected layers to enhance the learning capability of the network. Next, the output of the POCS algorithm is considered the input of the deep-learning model for the following iteration. The developed model iteratively works in an unsupervised scheme wherein labeled data are not required. A performance comparison with benchmark methods using several synthetic and field examples shows that our method outperforms the traditional methods.