Viscoelastic full waveform inversion with Stein Variational Gradient Descent

Jinji Li, Kristopher A. Innanen

Full waveform inversion (FWI) is a powerful method for reconstructing high-resolution subsurface models, yet its intrinsic nonlinearity and the strong coupling among multiple physical parameters make accurate uncertainty quantification particularly challenging in visco-elastic settings. Variational Bayesian formulations provide a computationally feasible pathway to address these issues by minimizing the Kullback–Leibler (KL) divergence between the true and approximate posterior distributions. In this study, we extend variational Bayesian FWI to the visco-elastic multiparameter domain using the Stein Variational Gradient Descent (SVGD) method, where a finite ensemble of particles approximates the posterior distribution of model parameters. Synthetic experiments based on the Marmousi model demonstrate that SVGD-FWI effectively recovers the primary elastic parameters (VP, VS, and density) while providing meaningful uncertainty estimates. The attenuation parameters (QP and QS) exhibit higher uncertainty and cross-talk, reflecting the difficulty of decoupling elastic and anelastic effects. Tests with noisy data further reveal that while inversion stability decreases with degraded data quality, the posterior statistics from SVGD still convey reliable uncertainty information. Overall, the results confirm that SVGD-based visco-elastic FWI offers a practical framework for Bayesian inference and uncertainty quantification in multiparameter inversion, paving the way for future enhancements through improved parameterization and adaptive regularization strategies.