Bayesian Variational Time-lapse Full-waveform Inversion

Time-lapse seismic full-waveform inversion (FWI) provides estimates of dynamic changes in the subsurface by performing multiple seismic surveys at different times. Since FWI problems are highly non-linear and non-unique, it is important to quantify uncertainties in such estimates to allow robust decision making. Markov chain Monte Carlo (McMC) methods have been used for this purpose, but due to their high computational cost, those studies often require an accurate baseline model and estimates of the locations of potential velocity changes, and neglect uncertainty in the baseline velocity model. Such detailed and accurate prior information is not always available in practice. In this study we use an efficient optimization method called stochastic Stein variational gradient descent (sSVGD) to solve time-lapse FWI problems without assuming such prior knowledge, and to estimate uncertainty both in the baseline velocity model and the velocity change. We test two Bayesian strategies: separate Bayesian inversions for each seismic survey, and a single join inversion for baseline and repeat surveys, and compare the methods with the standard linearised double difference inversion. The results demonstrate that all three methods can produce accurate velocity change estimates in the case of having fixed (exactly repeatable) acquisition geometries, but that the two Bayesian methods generate more accurate results when the acquisition geometry changes between surveys. Furthermore the joint inversion provides the most accurate velocity change and uncertainty estimates in all cases. We therefore conclude that Bayesian time-lapse inversion, especially adopting a joint inversion strategy, may be useful to image and monitor the subsurface changes, in particular where uncertainty in the results might lead to significantly different decisions.