A Gradient-Based Blocking Markov Chain Monte Carlo Method for Stochastic Inverse Modeling

Abstract

Inverse modeling for subsurface flow and transport in porous media is expected to improve the reliability of predictions in that the realizations generated are consistent with the observations of states. A gradient-based blocking Markov chain Monte Carlo (McMC) method is presented for stochastic inverse modeling. The method proposed effectively takes advantage of gradient information for tuning each realization to create a new ``candidate'' proposal, and hence it is capable of improving the performance of McMC. The gradients are efficiently computed by an adjoint method. The proposal mechanism is based on the optimization of a random seed field (or probability field), and thus it is able to preserve the prior model statistics. The method proposed has better performances than the single-component McMC and also avoids directly solving a difficult large-scale ill-conditioned optimization problem simply by turning it into a sampling procedure plus a sequence of well-conditioned optimization subproblems. A synthetic example demonstrates the method proposed.