Implicit neural representations for self-supervised seismic deblending

Blended acquisition enables near-simultaneous firing of multiple shots, facilitating faster and denser seismic data collection, which reduces acquisition time, lowers costs, and potentially enhances subsurface illumination. However, these benefits require an additional deblending process to recover the seismic data one would have acquired via a conventional survey. Numerous data-driven deblending algorithms have emerged, predominantly relying on supervised deep learning. Nevertheless, constructing training pairs that are representative and transferable to complex field data remains challenging. Some unsupervised methods have been developed, but they often focus on local similarities within individual seismic data, neglecting the continuity of seismic wavefields and relationships between different data across the entire data set. Implicit neural representation (INR) provides a versatile framework for modeling continuous seismic signals using neural network parameterized functions, capturing the intrinsic relationships throughout the entire data set. Building on this advantage, this study introduces INR for self-supervised seismic deblending. Specifically, to capitalize on the prior knowledge that desired unblended signals in nearby unblended common-receiver gathers (CRGs) vary smoothly due to the continuity of seismic waveforms, a deep neural network is used as an implicit function to parameterize desired unblended CRGs with receiver indices as inputs. By leveraging the blending operator, a physics-informed training strategy is implemented to enforce measurement consistency, enabling the trained network to recover corresponding deblended CRGs accurately. Numerical experiments conducted on synthetic and field data sets demonstrate the efficacy of our approach. Compared with sparsity-promoting inversion with a patched 2D Fourier transform, a widely adopted method in the industry, and the plug-and-play method with blind-spot networks, one of the most widely accepted self-supervised approaches, our method shows superior performance.