Abstract: |
Reproduction of complex 3D patterns is not possible using algorithms that are constrained to two-point (covariance or variogram) statistics. Therefore, new stochastic simulation approaches based on extended multiple-point spatial templates are necessary in order to capture and reproduce complex pattern statistics in spatial stochastic models. A unique pattern-growth algorithm (GrowthSim) is presented in this paper. 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 and cluster analysis. It is demonstrated that these two implementations serve to reduce the computation time significantly. In order to preserve spatial continuity of large-scale features, a multi-level implementation scheme was developed. It is demonstrated that the multi-grid implementation of GrowthSim results in models that exhibit long-range spatial connectivity. 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 meander characteristics characterize the reservoir. The capability of Growthsim to represent such non-stationary features is demonstrated. |
