Efficient generation of multi-scale random fields: A hierarchical approach

This paper introduces a new methodology to generate numerically multi-scale random fields. The generation of numerical samples of random fields plays an important role in Monte Carlo simulation methods. We are concerned with porous media flow studies where random field generators are used widely as a tool to model rock heterogeneities for applications in hydrocarbon recovery and groundwater flow. Reservoir rock properties such as permeability and porosity vary in space and may be characterized by their distributions. As the true distribution of these properties is unknown, we assume that they can be approximated by Gaussian (or transforms of Gaussian) random fields. In particular, we focus on correlated random fields with a power-law covariance structure. Our new method for the numerical generation of random fields uses a hierarchy of independent Gaussian variables defined on multiple length scales and is based on a theoretical construction of random fields described in Glimm and Sharp (J. Stat. Phys. 1991; 62(1–2):415–424). Numerical results are presented to show that the proposed method is accurate and numerically efficient. Copyright © 2008 John Wiley & Sons, Ltd.