TX-DPI: Temporal-Space deep prior interpolation

Seismic datasets are frequently spatially undersampled due to acquisition and economical limitations. Deep learning (DL) algorithms have shown alternative solutions that overcome some of the limitations of traditional interpolation methods while bringing new challenges. One notable example of unsupervised DL methods is the Deep Image Prior (DPI), which leverages convolutional neural networks (CNNs), and has demonstrated successful seismic interpolation. However, strong aliasing and interpolating big gaps of missing traces are still challenging. In this study, we present a novel unsupervised deep learning method for reconstructing missing seismic traces, building on the DPI framework. Our approach leverages the spatio-temporal coordinates of existing traces to accurately reconstruct missing traces. In particular, the proposed approach trains the weights of a CNN to map spatio-temporal coordinates to the available traces. When learning this mapping, a CNN is able to reconstruct missing traces based on its space-time coordinates, enabling accurate reconstructions. We validate our approach on both synthetic and field seismic data, demonstrating accurate reconstructions even in challenging scenarios of big gaps of missing traces. Furthermore, integrating spatio-temporal coordinates into CNN frameworks opens new possibilities for enhancing seismic processing tasks beyond interpolation.