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 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 localized that quantifying the uncertainties becomes fundamental to assessing the reliability of the results. The Bayesian formulation of the full waveform inversion 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 can effectively sample over high-dimensional distributions with affordable computational efforts. In this context, we explore the sequential approach in a Bayesian fashion for time-lapse full waveform inversion using the Hamiltonian Monte Carlo method. The idea relies on integrating the baseline survey information as prior knowledge to the monitor estimation. We compare this methodology with a parallel scheme in perfect and a simple perturbed acquisition geometry scenario considering the Marmousi and a typical Brazilian pre-salt velocity model. We also investigate the correlation effect between baseline and monitor samples on the propagated uncertainties. The results show that samples between different surveys are weakly correlated in the sequential case, while the parallel strategy provides time-lapse images with lower dispersion. Our findings demonstrate that both methodologies are robust in providing uncertainties even in non-repeatable scenarios.