Bayesian full waveform inversion with learned prior using deep convolutional autoencoder

TL;DR

This paper introduces a Bayesian full waveform inversion method that uses a deep convolutional autoencoder as a learned prior, enabling efficient and geologically consistent velocity model reconstruction with uncertainty quantification.

Contribution

The paper develops a novel deep autoencoder-based prior for Bayesian FWI, combined with an adaptive MCMC algorithm and transfer learning for improved efficiency and adaptability.

Findings

Reconstructs velocity models accurately from synthetic data.

Provides uncertainty quantification in model estimates.

Achieves computational efficiency over traditional MCMC methods.

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.