  Time-lapse images carry out important information about dynamic changes in
Earth's interior which can be inferred using different Full Waveform Inversion
(FWI) schemes. The estimation process is performed by manipulating more than
one seismic dataset, associated with the baseline and monitors surveys. The
time-lapse variations can be so minute and localised that quantifying the
uncertainties becomes fundamental to assessing the reliability of the results.
The Bayesian formulation of the FWI problem naturally provides confidence
levels in the solution, but evaluating the uncertainty of time-lapse seismic
inversion remains a challenge due to the ill-posedness and high dimensionality
of the problem. The Hamiltonian Monte Carlo (HMC) can be used to effectively
sample over high dimensional distributions with affordable computational
efforts. In this context, we propose a probabilistic Bayesian sequential
approach for time-lapse FWI using the HMC method. Our approach relies on the
integration of the baseline survey information as prior knowledge in the
monitor estimation. We compare the proposed methodology with a parallel scheme
in perfect and perturbed acquisition geometry scenarios. We also investigate
the correlation effect between baseline and monitor samples in the propagated
uncertainties. The results show that our strategy provides accurate times-lapse
estimates with errors of similar magnitude to the parallel methodology.
