Propagating the prior from far to near offset: A self-supervised diffusion framework for progressively recovering near-offsets of towed-streamer data

In marine towed-streamer seismic acquisition, the nearest hydrophone is often two hundred meter away from the source resulting in missing near-offset traces, which degrades critical processing workflows such as surface-related multiple elimination, velocity analysis, and full-waveform inversion. Existing reconstruction methods, like transform-domain interpolation, often produce kinematic inconsistencies and amplitude distortions, while supervised deep learning approaches require complete ground-truth near-offset data that are unavailable in realistic acquisition scenarios. To address these limitations, we propose a self-supervised diffusion-based framework that reconstructs missing near-offset traces without requiring near-offset reference data. Our method leverages overlapping patch extraction with single-trace shifts from the available far-offset section to train a conditional diffusion model, which learns offset-dependent statistical patterns governing event curvature, amplitude variation, and wavelet characteristics. At inference, we perform trace-by-trace recursive extrapolation from the nearest recorded offset toward zero offset, progressively propagating learned prior information from far to near offsets. The generative formulation further provides uncertainty estimates via ensemble sampling, quantifying prediction confidence where validation data are absent. Controlled validation experiments on synthetic and field datasets show substantial performance gains over conventional parabolic Radon transform baselines. Operational deployment on actual near-offset gaps demonstrates practical viability where ground-truth validation is impossible. Notably, the reconstructed waveforms preserve realistic amplitude-versus-offset trends despite training exclusively on far-offset observations, and uncertainty maps accurately identify challenging extrapolation regions.