Miguel Corrales, Sean Berti, B. Denel, Paul Williamson, M. Aleardi, and Matteo Ravasi

GitHub: https://github.com/DeepWave-KAUST/AnnealedSVGD_FWI

Full-Waveform Inversion (FWI) is a widely used method for generating high-resolution subsurface models from seismic data, but it faces challenges due to its nonlinear and ill-posed nature. Traditional optimization methods often fail to quantify uncertainty, which is essential for informed decision-making. While Bayesian approaches like Markov Chain Monte Carlo (MCMC) can assess uncertainty, they are computationally prohibitive for high-dimensional problems like FWI. Variational Inference (VI), particularly Stein Variational Gradient Descent (SVGD), provides a more efficient alternative but can suffer from mode and variance collapse in complex scenarios. This study introduces an annealed SVGD algorithm combined with a multi-scale strategy to enhance performance and address high-dimensional challenges. Post hoc techniques, including Principal Component Analysis (PCA) and clustering, are employed after optimization to assess performance and gain insights into the statistical properties of the posterior distribution. Numerical tests on the Marmousi model show that annealed SVGD improves uncertainty estimation with a limited number of particles.