Frugal uncertainty analysis for full waveform inversion

Full waveform inversion (FWI) enables us to obtain high-resolution velocity models of the subsurface. However, estimating the associated uncertainties in the process is not trivial. Within the Bayesian framework, sampling algorithms are commonly used to estimate the posterior distribution and identify such uncertainties. However, such algorithms have to deal with complex posterior structures (e.g., multimodality), high-dimensional model parameters, and large-scale datasets, which lead to high computational demands and time-consuming procedures. This work proposes a frugal approach to quantitatively analyze uncertainties in FWI through the Stein Variational Gradient Descent (SVGD) algorithm by utilizing a small number of velocity model ensembles, which could save computational costs and provide swift analysis, especially for applications at the industrial scale. We demonstrate the practicality of our proposed improvements with a numerical example based on the Marmousi model.