Copula-Based Data-Driven Multiple-Point Simulation Method

Multiple-point simulation is a commonly used method in modeling complex curvilinear structures. The method is based on the application of training images that are open to manipulation. The present study introduces a new data-driven multiple-point simulation method that derives multiple point statistics directly from sparse data using copulas and applies them in simulation of complex mineral deposits. This method is based on simplification of N-dimensional copulas by its underlying two-dimensional copulas and taking advantage of conditional independence assumption to integrate information from different sources. The method was compared to Filtersim, a conventional multiple-point geostatistical method, through two synthetic data sets. Reproduction of cumulative distribution function, variogram, N-point connectivity, and visual patterns were considered in comparison. The copula-based multiple-point simulation (CMPS) method was implemented using trivial parts (almost 4%) of the synthetic data to extract required statistics while Filtersim was performed by giving the target image (100% data) as training image. Despite overwhelming data use in Filtersim, the CMPS showed compatible results to it. Application to synthetic data indicated that the method is a promising tool in the simulation of deposits with sparse data. The CMPS were applied in the simulation of two mineral deposits: (1) a porphyry copper deposit and (2) a magmatic iron deposit.