MCMC-based time-lapse full-waveform inversion

Xin Fu, Kristopher A. Innanen

In this study, we have proposed a Bayesian time-lapse full-waveform inversion (FWI) based on the Markov chain Monte Carlo (MCMC) algorithm and a new method to estimate the data error standard deviation for the time-lapse data according to its feature. To achieve the MCMC-based time-lapse FWI, we have employed the inversion strategies including the double-difference time-lapse FWI (DDFWI), the time-domain multisource data, the local-updating target-oriented inversion, calculating model covariance with the adaptive Metropolis algorithm, and the new data error standard deviation estimation method. The MCMC algorithm applied is a random walk Metropolis-Hastings MCMC, a typical stochastic global optimization method. In the conventional deterministic optimization (DO) DDFWI containing a baseline inversion for the baseline model and a monitoring inversion for the monitoring model, both inversions are performed by the DO FWI. In the MCMC DDFWI proposed in this work, we keep the DO FWI for the baseline inversion but employ the MCMC algorithm for the monitoring inversion. And the final time-lapse model is the difference between the inverted monitoring model and the baseline model. Synthetic data tests using a 2D acoustic model have demonstrated the feasibility of MCMC DDFWI on both time-lapse model inversion and uncertainty qualification. We also have compared the MCMC DDFWI with the conventional DO DDFWI, which shows that the inverted average time-lapse model of MCMC DDFWI can provide the results with clearer edges of the nonzero time-lapse model change and fewer coherent errors