Posterior population expansion for solving inverse problems

Solving inverse problems in a complex, geologically realistic, and discrete model space and from a sparse set of observations is a very challenging task. Extensive exploration by Markov chain Monte Carlo (McMC) methods often results in considerable computational efforts. Most optimization methods, on the other hand, are limited to linear (continuous) model spaces and the minimization of an objective function, what often proves to be insufficient. To overcome these problems, we propose a new ensemblebased exploration scheme for geostatistical prior models generated by a multiple-point statistics (MPS) tool. The principle of our method is to expand an existing set of models by using posterior facies information for conditioning new MPS realizations. The algorithm is independent of the physical parametrization. It is tested on a simple synthetic inverse problem. When compared to two existing McMC methods (iterative spatial resampling (ISR) and Interrupted Markov chain Monte Carlo (IMcMC)), the required number of forward model runs was divided by a factor of 8–12.