A Variational Algorithm for Full-Waveform Inversion of Surface Waves: A Real Case Application

Full-waveform inversion (FWI) of surface waves has recently become a popular tool for reconstructing high-resolution subsurface models. However, adopting a deterministic approach to FWI does not account for model uncertainties and its convergence heavily depends on the starting point of the inversion. In this work, we propose a variational Bayesian approach for FWI of surface waves using the Annealed Stein Variational Gradient Descent (A-SVGD) algorithm. This particle-based method combines gradient-informed updates with an annealing schedule to efficiently approximate the posterior distribution of model parameters, offering both high-resolution imaging and uncertainty quantification. We apply our method to a field dataset acquired in Italy and compare its performance against a deterministic L-BFGS inversion. Our results show that our proposed approach delivers consistent velocity models regardless of the initial ensemble and outperforms L-BFGS in terms of data misfit reduction. Notably, it also provides uncertainty maps that highlight areas of reduced resolution, supporting more informed interpretation. The annealing strategy mitigates mode and variance collapse issues, enabling robust exploration of the model space. In contrast, L-BFGS results are highly sensitive to initialization and lack uncertainty estimates. This study demonstrates the potential of A-SVGD as an efficient, uncertainty-aware alternative to conventional deterministic FWI for near-surface applications.