Abstract
Seismic full-waveform inversion (FWI) can produce high resolution images
of the Earth’s subsurface. Since full waveform modelling 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 3D applications.
In this study we propose a new method called variational full-waveform
inversion (VFWI), which uses Stein variational gradient descent (SVGD)
to solve FWI problems. We apply the method to a 2D synthetic example and
demonstrate that the method produces accurate approximations to those
obtained by Hamiltonian Monte Carlo (HMC). Since variational inference
solves the problem using optimization, the method can be applied to
larger datasets and 3D applications by using stochastic optimization and
distributed optimization.