An efficient two‐stage Markov chain Monte Carlo method for dynamic data integration

In this paper, we use a two‐stage Markov chain Monte Carlo (MCMC) method for subsurface characterization that employs coarse‐scale models. The purpose of the proposed method is to increase the acceptance rate of MCMC by using inexpensive coarse‐scale runs based on single‐phase upscaling. Numerical results demonstrate that our approach leads to a severalfold increase in the acceptance rate and provides a practical approach to uncertainty quantification during subsurface characterization.