  Seismic full-waveform inversion (FWI) uses full seismic records to estimate
subsurface velocity structure. This requires a highly nonlinear and nonunique
inverse problem to be solved, and Bayesian methods have been used to quantify
uncertainties in the solution. Variational Bayesian inference uses optimization
to provide solutions efficiently. The method has been applied to solve a
transmission FWI problem using data generated by known earthquake-like sources,
with strong prior information imposed on the velocity. Unfortunately such prior
information about velocity structure and earthquake sources is never available
in practice. We present the first application of the method in a seismic
reflection setting, and with realistically weak prior information. We thus
demonstrate that the method can produce high resolution images and reliable
uncertainties given practically reasonable prior information.
