A simple algorithm to generate small geostatistical ensembles for subsurface flow simulation

This note describes the theory behind a simple Matlab program to generate ensembles of geological realizations of relatively small-scale reservoir models (permeability fields) for subsurface flow simulation. The algorithm makes use of Principal Component Analysis (PCA) to parameterize the spatial covariance of a reference image, and a Bayesian optimization approach to condition the realizations to well data. The method is limited to relatively small images, mainly because of memory requirements, and only uses two-point statistics. However, it does not require iteration or rejection of ensembles and is computationally efficient because of the use of vectorized Matlab operations.