Variational full-waveform inversion

Seismic full-waveform inversion (FWI) can produce high-resolution images of the Earth's subsurface. Since full-waveformmodelling is significantly nonlinear with respect to velocities, Monte Carlo methods have been used to assess image uncertainties. However, because of the high computational cost of Monte Carlo sampling methods, uncertainty assessment remains intractable for larger data sets and 3-D applications. In this study, we propose a new method called variational FWI, which uses Stein variational gradient descent to solve FWI problems. We apply the method to a 2-D synthetic example and demonstrate that the method produces accurate approximations to those obtained by Hamiltonian Monte Carlo. Since variational inference solves the problem using optimization, the method can be applied to larger data sets and 3-D applications by using stochastic optimization and distributed optimization.