Correlation-driven direct sampling method for geostatistical simulation and training image evaluation

Multiple-point geostatistics (MPS) is a competitive algorithm that produces a set of geologically realistic models. Viewing a training image (TI) as a prior model, MPS extracts patterns from the TI and reproduces patterns which are compatible with the hard data (HD). However, two challenges within the MPS framework are the geologically complex simulation and the TI evaluation. With the objective to achieve a high-quality simulation, we explore a way to address these two issues. First, correlation-driven direct sampling (CDS) is proposed to realize geostatistical simulation. We introduce the correlation-driven distance as a measure of similarity between two patterns. The weights in our distance measurement are derived by the concepts of the ellipse, correlation coefficient, Gaussian function, and affine transformation. Second, we fulfill TI evaluation on the basis of the consistency between TI and HD. Inspired by CDS, the minimum correlation-driven distance (MCD) is proposed to improve the evaluation accuracy. We suggest a conditioning pattern extraction history strategy to speed up the evaluation program. Third, the local consistency is presented to address nonstationarity. The program automatically divides the simulation domain into several subareas. A two-dimensional (2D) channelized reservoir image and a three-dimensional (3D) rock image are used to validate our proposed method. In comparison with previous methods, CDS yields better simulation quality. The further applications include a set of 2D TI evaluations and a 3D simulation domain segmentation. MCD exhibits sensible evaluation accuracy, excellent computational efficiency, and the ability to deal with nonstationarity.