An MCMC-based approach to time-lapse full-waveform inversion

Abstract

Time-lapse full-waveform inversion (FWI), formulated to determine subsurface variations due to, for instance, CO2 injection or EOR, with a high resolution, is an increasingly important mode of FWI application. Time-lapse FWI normally involves two inversions, for instance a baseline inversion for the baseline model and a monitoring inversion for the monitoring model, after which the time-lapse model is produced by subtracting the baseline model from the monitoring model. However, if a suitably efficient methodology is available, a larger number of inversions can be carried out and uncertainty can be simultaneously determined, which is critical in time-lapse. We set up a Bayesian time-lapse FWI based on the Markov chain Monte Carlo (MCMC) algorithm and a new method to estimate the standard deviation of the data error for the time-lapse data. The approach is an assemblage of: double-difference time-lapse FWI (DDFWI), time-domain multisource data, target-oriented inversion, calculation of model covariance with an adaptive Metropolis algorithm, and our new standard deviation estimation method. The MCMC algorithm is a typical random-walk Metropolis-Hastings MCMC. In the conventional deterministic optimization DDFWI, containing a baseline inversion for the baseline model and a monitoring inversion for the monitoring model, both inversions are deterministic. In the methodology we analyze here, MCMC DDFWI, the baseline inversion is carried out deterministically, but the monitoring inversion occurs within the MCMC/Bayesian inference framework. The final time-lapse model is the difference between the inverted monitoring model and the baseline model. In this paper we set out the ideas, and validate with synthetic tests involving a 2D acoustic model, and illustrate the character of both recovered models and uncertainty quantification.