Comparison of probabilistic approaches to acoustic full-waveform inversion in compressed model and data spaces

Full-waveform inversion estimates subsurface properties by minimizing the misfit between observed and modelled data. However, conventional deterministic approaches are highly sensitive to noise, dependent on the starting model and prone to converging to local minima of the cost function. Bayesian approaches offer a viable alternative, enhancing solution space exploration and providing uncertainty quantification. This study compares three Bayesian inversion methods: Stochastic-Newton Markov Chain Monte Carlo, Ensemble Smoother with Multiple Data Assimilation and Annealed Stein Variational Gradient Descent. To mitigate ill-conditioning, reduce computational cost, and lower problem dimensionality, we incorporate Discrete Cosine Transform compression of model and data spaces. These methods are evaluated under three scenarios: optimal conditions as a baseline, a less informative prior to assess initialization sensitivity, and a more realistic setting with increased noise, missing traces and wrong assumptions about the source wavelet and noise level. These tests are conducted on a synthetic example based on a portion of the Marmousi model. Results indicate that the ensemble-based approach is the most computationally efficient, is robust to initialization, but strongly underestimates uncertainties. The Markov Chain method, while computationally demanding, is robust to initialization and effectively captures uncertainties. The Variational Inference approach, with intermediate computational cost, achieves good performance in complex scenarios, but it is more sensitive to initialization due to its deterministic nature. This study provides insights into the advantages and limitations of these three Bayesian approaches to acoustic full-waveform inversion and highlights the benefits of the Discrete Cosine Transform compression.