| Stochastic simulation of spatial patterns of complex subsurface geological structures is critical for decision making under uncertainty. The challenge is to represent this complexity using training images that incorporate typical local structures and textures, and to derive distributional properties from such training images for purposes of stochastic simulation. The large number of local pattern possibilities requires dimension reduction, then methods for pattern sampling and data conditioning towards simulation require careful attention.; This thesis proposes a method for grouping local training image patterns into classes based on a numerical scoring of these patterns that uses local filters. The pattern scoring and classification methods are developed for categorical attributes such as lithology, as well as continuous geologic attributes such as petrophysical properties, and are illustrated both for two-dimensional as well as three-dimensional structures. Stochastic pattern simulation then proceeds sequentially by retrieving conditioning data in the neighborhood of the current simulation node, identifying the pattern class most consistent with these conditioning data, and then sampling a local pattern from the identified pattern class. The sampled pattern is centered at the simulation node. This process proceeds until all nodes are simulated. The code for this pattern classification and stochastic simulation algorithm is termed filtersim .; filtersim is used to create sample simulations using a variety of training images, including an actual 3D case study. The simulation results show that filtersim appears to be practical, computationally efficient, and faithful to the structure information contained in the training image. |
