Unsupervised deep learning for off-the-grid seismic reconstruction and denoising

ABSTRACT Seismic data should ideally be acquired on a regular Cartesian grid for easier subsequent processing, such as denoising, inversion, and imaging. However, due to acquisition limitations and obstacles lying in the direction of seismic survey lines, seismic data are often sampled nonuniformly, thus making off-the-grid (OTG) data regularization necessary. We develop a deep-learning (DL)-based method, guided by the projection onto convex sets (POCS) scheme for simultaneous OTG denoising and reconstruction, namely DLOTG. The network uses fully connected layers to map features into a latent space, while transformers with attention mechanisms and skip connections are used to enhance feature extraction, enabling a better restoration of the useful signals and removal of noise. Following an iterative POCS, the framework will refine the output, gradually regularizing data and improving their quality. More importantly, our DLOTG method can be implemented in an unsupervised manner, making it suitable for unlabeled data and enhancing generalization. It is more robust than conventional OTG reconstruction methods, and it preserves weak signals better. Synthetic and field tests demonstrate its effectiveness in data reconstruction and noise attenuation, particularly with high missing rates (i.e., 50%) and noise levels.