A Bayesian approach to Full-Waveform inversion

The thesis introduces innovative Bayesian techniques to FWI, focusing on two main approaches: the gradient-based Markov Chain Monte Carlo (GBMCMC) and the Annealed Stein Variational Gradient Descent (A-SVGD). The GB-MCMC method, combined with Discrete Cosine Transform (DCT) compression, enhances sampling efficiency and computational feasibility in high-dimensional problems. This method is applied to both acoustic and elastic FWI, using synthetic and real datasets, demonstrating its ability to handle complex subsurface structures, mitigate cycle-skipping and improve convergence rates. Additionally, this thesis explores SVGD and its annealed variant as alternative probabilistic methods. These are again applied to acoustic and elastic FWI, providing robust uncertainty quantification and accurate model predictions, with a limited computational cost. A detailed comparison between GB-MCMC and A-SVGD is presented, assessing their performance in terms of prediction accuracy, uncertainty estimation and parameter correlation. By integrating FWI into a Bayesian framework, this work advances subsurface imaging techniques, offering more reliable and informative solutions.