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.

💡 Research Summary

The paper tackles the pervasive problem of missing near‑offset traces in marine towed‑streamer seismic acquisition, where the physical separation between the air‑gun source and the first hydrophone often leaves a gap of several hundred metres. Traditional gap‑filling approaches—such as transform‑domain interpolation (e.g., F‑X predictive filtering, hyperbolic Radon transforms) or supervised deep‑learning models—either introduce kinematic and amplitude errors or require fully sampled near‑offset data that are unavailable in real surveys. To overcome these limitations, the authors propose a self‑supervised conditional diffusion framework (SSGDM) that learns directly from the recorded far‑offset data and progressively extrapolates toward zero offset without any ground‑truth near‑offset references.

Training exploits the spatial redundancy of the far‑offset aperture by extracting overlapping patches that are laterally shifted by a single trace. The “target” patch (x₀) is one trace closer to zero offset than the “conditioning” patch (y). By feeding the noisy version of x₀ (generated via the forward diffusion process) together with y into a U‑Net‑based denoiser, the model learns the conditional distribution p(x₀|y). This design forces the network to capture offset‑dependent statistical relationships—event curvature, amplitude‑versus‑offset trends, and wavelet evolution—solely from far‑offset observations.

During inference, a deterministic DDIM sampler is used to reconstruct missing traces sequentially. Starting from the nearest recorded trace (r_start), the model predicts the next nearer trace conditioned on the previously reconstructed (or recorded) trace, thereby propagating the learned prior from far to near offsets in a physically consistent, trace‑by‑trace manner. Because the diffusion model is probabilistic, multiple realizations can be generated for each missing trace; the variance across samples yields an uncertainty map that highlights regions where extrapolation is less reliable.

The authors validate the method on synthetic data and two field marine datasets. Quantitatively, SSGDM outperforms a conventional parabolic Radon transform baseline, delivering 3–5 dB higher signal‑to‑noise ratio and 0.12–0.18 improvement in structural similarity index. Importantly, reconstructed amplitude‑versus‑offset (AVO) curves closely match the true trends, indicating that amplitude fidelity is preserved. Qualitatively, after filling the near‑offset gap, surface‑related multiple elimination (SRME) and velocity analysis show clearer events, higher multiple‑suppression efficiency, and smoother V‑A‑O behavior. Full‑waveform inversion performed on the reconstructed sections exhibits a 15 % reduction in data residuals and sharper imaging of subsurface features.

Uncertainty maps correctly flag challenging extrapolation zones—such as areas with complex structural interference or low signal‑to‑noise ratios—providing practitioners with actionable confidence indicators for downstream processing decisions.

In summary, the paper contributes (1) a novel self‑supervised diffusion model that eliminates the need for any complete near‑offset training data, (2) a single‑trace shift patch strategy that directly trains the model for the required extrapolation task, (3) a recursive inference scheme that ensures physical continuity from far to near offsets, (4) a built‑in uncertainty quantification mechanism, and (5) extensive experimental evidence demonstrating superior reconstruction quality and practical utility in real‑world marine seismic workflows. This work opens a new pathway for robust near‑offset recovery in towed‑streamer acquisition, potentially improving multiple attenuation, velocity analysis, and full‑waveform inversion outcomes.