Diffusion Model-Based Posterior Sampling in Full Waveform Inversion

• URL: http://arxiv.org/abs/2512.12797v1
• Date: Sun, 14 Dec 2025 18:34:12 GMT
• Title: Diffusion Model-Based Posterior Sampling in Full Waveform Inversion
• Authors: Mohammad H. Taufik, Tariq Alkhalifah,
• Abstract summary: posterior sampling directly on observed seismic shot records is rarely practical at the field scale.<n>Our approach couples diffusion-based posterior sampling with simultaneous-source waveform inversion data.<n>Our method achieves lower model error and better data fit at a substantially reduced computational cost.
• Score: 3.2800968305157205
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bayesian full waveform inversion (FWI) offers uncertainty-aware subsurface models; however, posterior sampling directly on observed seismic shot records is rarely practical at the field scale because each sample requires numerous wave-equation solves. We aim to make such sampling feasible for large surveys while preserving calibration, that is, high uncertainty in less illuminated areas. Our approach couples diffusion-based posterior sampling with simultaneous-source FWI data. At each diffusion noise level, a network predicts a clean velocity model. We then apply a stochastic refinement step in model space using Langevin dynamics under the wave-equation likelihood and reintroduce noise to decouple successive levels before proceeding. Simultaneous-source batches reduce forward and adjoint solves approximately in proportion to the supergather size, while an unconditional diffusion prior trained on velocity patches and volumes helps suppress source-related numerical artefacts. We evaluate the method on three 2D synthetic datasets (SEG/EAGE Overthrust, SEG/EAGE Salt, SEAM Arid), a 2D field line, and a 3D upscaling study. Relative to a particle-based variational baseline, namely Stein variational gradient descent without a learned prior and with single-source (non-simultaneous-source) FWI, our sampler achieves lower model error and better data fit at a substantially reduced computational cost. By aligning encoded-shot likelihoods with diffusion-based sampling and exploiting straightforward parallelization over samples and source batches, the method provides a practical path to calibrated posterior inference on observed shot records that scales to large 2D and 3D problems.

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