Bayesian Time-Lapse Full Waveform Inversion using Hamiltonian Monte Carlo

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 levels of confidence 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.