A nearest neighbor multiple-point statistics method for fast geological modeling

Abstract

Multiple-point statistics (MPS) is a powerful method to generate realistic geological models. Given a training image as a prior model, the program iteratively reproduces spatial patterns in the simulation grid. However, running speed becomes a limitation to practical applications. MPS has to handle complicated and high-dimensional structures at the cost of simulation time. With the objective to accelerate geostatistical modeling with categorical variables, we propose a nearest neighbor simulation (NNSIM) method. Several k-nearest neighbor (kNN) classifiers are incorporated into MPS framework. First, we identify representative patterns with a prototype selection method. Different from existing MPS programs, our method selects training patterns according to their influences on simulation quality. A pattern subset of small size has a positive effect on searching time. Second, a teacher-student architecture is suggested to improve the pattern subset. In order to address missing data, our program augments the subset with key patterns during simulation. A cosine distance metric is applied to compare the original dataset and pattern subset. Third, our program organizes patterns with a ball tree. Pattern groups with low similarity are dynamically removed to fulfill fast search. We examine the proposed NNSIM by a benchmark channel simulation, a 2D flume model, and a 3D sandstone modeling. Many quantitative approaches are employed to evaluate geometrical and physical properties. The experimental results indicate that our NNSIM significantly improves the computational efficiency while exhibits comparable simulation quality to traditional MPS programs.