Full-Waveform inversion of surface waves with Annealed Stein Variational Gradient Descent

In recent years, full-waveform inversion of surface waves has become very popular to reconstruct high-resolution subsurface models, even in the presence of strong lateral and vertical velocity variations. However, employing a deterministic approach to solve this inverse problem does not account for the uncertainties affecting the recovered solution, and convergence heavily relies on the starting point of the inversion. Framing this inverse problem in a Bayesian framework can address these challenges but the commonly used sampling algorithms struggle with complex multimodal posterior structures and high-dimensional model spaces, resulting in a formidable computational effort. An alternative approach, Variational Inference, offers a promising solution approaching the inverse problem through optimization, exhibiting superior computational efficiency. In this study, we propose a probabilistic approach to solve full-waveform inversion of surface waves using the Annealed Stein Variational Gradient Descent algorithm, a sample-based inference algorithm that transports the samples to approximate the target posterior distribution with incorporated an annealing strategy. This enhances mode coverage and uncertainty estimation compared to the standard Stein Variational Gradient Descent method. We validate the applicability of our proposed approach by performing a synthetic inversion test and comparing its performance against that of the Stein Variational Gradient Descent method.