Multiscale data integration using coarse-scale models

In this paper we combine a multiscale data integration technique introduced in [Lee SH, Malallah A, Datta-Gupta A, Hidgon D. Multiscale data integration using Markov Random Fields. SPE Reservoir Evaluat Eng 2002;5(1):68–78] with upscaling techniques for spatial modeling of permeability. The main goal of this paper is to find fine-scale permeability fields based on coarse-scale permeability measurements. The approach introduced in the paper is hierarchical and the conditional information from different length scales is incorporated into the posterior distribution using a Bayesian framework. Because of a complicated structure of the posterior distribution Markov chain Monte Carlo (MCMC) based approaches are used to draw samples of the fine-scale permeability field.