基于扩散模型的全波形反演后验采样
Diffusion Model-Based Posterior Sampling in Full Waveform Inversion
AI总结：
本文提出基于扩散模型的全波形反演后验采样方法，通过结合同时源FWI数据和无条件扩散先验，实现大规模调查中的高效校准后验推断。
摘要：
贝叶斯全波形反演（FWI）提供了具有不确定性的地下模型；然而，直接在观测地震射线记录上进行后验采样在实地规模下很少实用，因为每个样本需要大量的波动方程求解。我们旨在使这种采样在大规模调查中可行，同时保持校准，即在照明较少的区域保持高不确定性。我们的方法将基于扩散的后验采样与同时源FWI数据相结合。在每个扩散噪声水平下，一个网络预测一个干净的速度模型。然后，我们使用兰格-迪纳动力学在模型空间中应用随机细化步骤，基于波动方程似然，并重新引入噪声以解耦后续的层次。同时源批次将正向和共轭求解大约按超集大小的比例减少，而一个无条件扩散先验，通过在速度块和体积上训练，有助于抑制与源相关的数值伪影。我们评估了该方法在三个2D合成数据集（SEG/EAGE Overthrust、SEG/EAGE Salt、SEAM Arid）、一个2D现场线和一个3D上缩放研究上的效果。与基于粒子的变分基线方法相比，即Stein变分梯度下降，没有学习先验和单源（非同时源）FWI，我们的采样器在显著降低的计算成本下实现了更低的模型误差和更好的数据拟合。通过将编码射线似然与基于扩散的采样对齐，并利用样本和源批次上的简单并行化，该方法为在观测射线记录上进行校准的后验推断提供了实用路径，能够扩展到大规模的2D和3D问题。
英文摘要：
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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