An unsupervised posterior sampling framework for multi-purpose seismic data recovery

TL;DR

This work tackles the challenge of seismic data restoration under unknown degradations by introducing an unsupervised Posterior Sampling Framework (PSF) built on pre-trained unconditional Score-based Generative Models (SGMs). PSF derives a generalized conditional score function aligned with arbitrary forward operators, enabling posterior sampling for denoising, interpolation, compressed sensing, and deconvolution without retraining. It couples a memory-efficient SVD formulation with an automatic, pixel-wise noise-level estimation to adaptively regulate noise suppression across varying SNRs, enhancing robustness. Empirical results demonstrate high-quality posterior samples and strong out-of-distribution generalization on both synthetic and real-field data, highlighting SGMs as universal priors for seismic inverse problems. The proposed framework offers a flexible, scalable path toward unsupervised, multi-task seismic data restoration in practical field settings.

Abstract

Seismic data restoration is a fundamental task in seismic exploration, yet remains challenging under complex and unknown degradations. Traditional model-driven or task-specific learning methods often require retraining for each degradation type and fail to generalize effectively to unseen field data.In this work, we introduce an unsupervised Posterior Sampling Framework (PSF) built upon Score-based Generative Models (SGMs) for unified seismic data restoration. PSF leverages a pre-trained unconditional SGMs as a seismic-aware generative prior and derives a generalized conditional score function linked to the forward operator of each inverse problem. This enables posterior sampling across different seismic restoration tasks without retraining or supervision. Additionally, an adaptive noise-level estimation mechanism is incorporated to dynamically regulate the noise suppression strength during sampling, enhancing flexibility under varying signal-to-noise ratios and degradation conditions.Extensive experiments on seismic denoising, interpolation, compressed sensing, and deconvolution demonstrate that PSF delivers high-quality samples and exhibits robust generalization to out-of-distribution data. These results highlight the potential of SGMs as a universal prior for seismic inverse problems and establish PSF as a flexible framework for unsupervised posterior inference across diverse degradation scenarios.

Figures (13)

• Figure 1: Schematic diagram of posterior sampling using Langevin dynamics and conditional score function.
• Figure 2: Schematic diagram of the posterior sampling trajectory of observations for different degradation processes
• Figure 3: Schematic diagram of multiple posterior solutions and their mean and standard deviation, (a) original image (b) locally enlarged wiggle image
• Figure 4: Schematic diagram of unconditional sampling using pretrained score function
• Figure 5: Out-of-distribution generalization results, taking seismic data interpolation as an example. (a,b) post-stack data , (c,d) prestack data.