Seismic Full Waveform Inversion With Uncertainty Analysis Using Unsupervised Variational Deep Learning

Seismic full waveform inversion (FWI) is a powerful technique for generating high-resolution images of the subsurface, leveraging the rich information content in recorded seismic waveforms. However, due to certain limitations in data acquisition and processing, the optimization of seismic FWI is inherently nonlinear and nonunique, implying the possibility of multiple solutions that can adequately account for the observed data. Unlike deterministic inversion, which seeks a single best-fit solution, probabilistic inversion explores a range of subsurface model parameters adhering to probability distributions that fit the observations in a given confidence level. In this article, we introduce a variational autoencoder (VAE)-based probabilistic FWI method to assess the uncertainty associated with subsurface parameters using unsupervised deep learning. By repeatedly sampling the latent representation distributions of the observed data, a set of predicted results that adhere to the subsurface model's posterior distribution can be reconstructed using the decoder and then calculated for uncertainty quantification. Compared to conventional Markov chain Monte Carlo (MCMC)-based approaches that require substantial computational costs beyond deterministic FWI, the proposed VAE-based FWI offers the opportunity to assess the uncertainty without additional computational demands. Furthermore, the VAE-based method is benchmarked against other deep learning-based approaches, including AE-based deterministic FWI and dropout-based probabilistic FWI, using 2-D Marmousi and Overthrust models. The comparison reveals that the VAE-based approach offers a more nuanced and comprehensive inversion result compared to the single prediction from the AE-based method. Furthermore, it effectively mitigates the dropout-based method's tendency to underestimate uncertainty in deeper layers, offering a more reliable assessment of inversion uncertainty.