Bayesian full waveform inversion with learned prior using deep convolutional autoencoder

TL;DR

This work tackles Bayesian full waveform inversion (FWI) by addressing its high model dimensionality with a learned prior: a convolutional autoencoder (CAE) compresses velocity models to a low-dimensional latent space $\bar{\mathbf{m}}$, enabling adaptive gradient-based MCMC sampling in latent space with gradients computed through automatic differentiation. The method combines an AD-enabled latent-space MCMC, a forward model implemented as a recurrent neural network, and a CAE-based prior that preserves geologically meaningful features; it also introduces online fine-tuning to adapt the latent prior to out-of-distribution velocity structures. Results on synthetic OpenFWI data show that the approach efficiently recovers posterior means that match true low-wavenumber features and provides uncertainty quantification, with improved sampling efficiency compared to standard MCMC in the high-dimensional space. The authors also demonstrate transfer learning via brief decoder fine-tuning to handle Marmousi-like data, highlighting the potential for generalization through online adaptation and future subsurface foundation models. Overall, the paper provides a data-driven, scalable framework for Bayesian FWI that delivers robust uncertainty estimates while mitigating the curse of dimensionality.

Abstract

Full waveform inversion (FWI) can be expressed in a Bayesian framework, where the associated uncertainties are captured by the posterior probability distribution (PPD). In practice, solving Bayesian FWI with sampling-based methods such as Markov chain Monte Carlo (MCMC) is computationally demanding because of the extremely high dimensionality of the model space. To alleviate this difficulty, we develop a deep convolutional autoencoder (CAE) that serves as a learned prior for the inversion. The CAE compresses detailed subsurface velocity models into a low-dimensional latent representation, achieving more effective and geologically consistent model reduction than conventional dimension reduction approaches. The inversion procedure employs an adaptive gradient-based MCMC algorithm enhanced by automatic differentiation-based FWI to compute gradients efficiently in the latent space. In addition, we implement a transfer learning strategy through online fine-tuning during inversion, enabling the framework to adapt to velocity structures not represented in the original training set. Numerical experiments with synthetic data show that the method can reconstruct velocity models and assess uncertainty with improved efficiency compared to traditional MCMC methods.

Figures (19)

• Figure 1: The proposed Bayesian FWI approach with learned prior from a pre-trained autoencoder.
• Figure 2: Schematic plot showing the online fine-tuning process during inversion.
• Figure 3: Typical velocity models of the dataset used for training the CAE.
• Figure 4: The structure of the convolutional autoencoder used in this paper.
• Figure 5: After training of the CAE, we verify the trained autoencoder by implementing model compression on one sample from the test dataset. Also we compare the performance on dimensionality reduction of CAE with discrete cosine transform (DCT).