Hamiltonian Monte Carlo based time-lapse seismic FWI and uncertainty quantification in CO₂ monitoring: a VSP feasibility study

Jinji Li, Kristopher A. Innanen

Time-lapse full waveform inversion (FWI) stands to play an important role in energy-transition applications, particularly in monitoring CO₂ geo-storage. Because of the nonlinearity of the FWI problem, the existence of various sources of uncertainty between the baseline and monitor surveys, and the likely sparseness (or at least variability) of data coverage in these applications, augmenting FWI with robust uncertainty quantification methods is of critical importance. Within the category of Monte Carlo sampling techniques, Hamiltonian (HMC) methods avoid several limitations of classical Markov Chain Monte Carlo (MCMC) approaches, by combining a simulation of Hamiltonian dynamics within the exploration of model space, with a Metropolis acceptance step. The result is a relatively affordable estimation of the uncertainty in models derived from time-lapse FWI. In time-lapse applications, we aim for the use of posterior information deriving from the baseline inversion as prior information within the monitor inversion. With a synthetic feasibility study with a VSP acquisition, we demonstrate that this integration enhances the efficiency and effectiveness of HMC-based FWI, which are critical features of low-cost CO₂ monitoring.