Efficient Conditional Simulation of Spatial Patterns Using a Pattern-Growth Algorithm

Abstract

Reproduction of complex 3D patterns is not possible using algorithms that are constrained to two-point (covariance or variogram) statistics. A unique pattern-growth algorithm (GrowthSim) is presented in this paper that performs multiple point spatial simulation of patterns conditioned to multiple point data. Starting from conditioning data locations, patterns are grown constrained to the pattern statistics inferred from a training image. This is in contrast to traditional multiple-point statistics based-algorithms where the simulation progresses one node at a time. In order to render this pattern growth algorithm computationally efficient, two strategies are employed—(i) computation of an optimal spatial template for pattern retrieval, and (ii) pattern classification using filters. To accurately represent the spatial continuity of large-scale features, a multi-level simulation scheme is implemented. In addition, a scheme for applying affine transformation to spatial patterns is presented to account for local variation in spatial patterns in a target reservoir. The GrowthSim algorithm is demonstrated for developing the reservoir model for a deepwater turbidite system. Lobes and channels that exhibit spatial variations in orientation, density and meandering characteristics characterize the reservoir. The capability of GrowthSim to represent such non-stationary features is demonstrated.