Multiple Point Geostatistics (MPS) is a timely approach for the three-dimensional modeling of the geological substrate. As compared with 3D design approaches, model update is straightforward and reproducible. In contrast to traditional, variogram-based geostatistical modeling and simulation, MPS incorporates geological expert knowledge via a Training Image (TI). The TI permits geologists the intuitive formulation of geometrically complex geological structures plus their genetic relationships like cross-cutting joint generations or mutually eroding sediment types. MPS extracts patterns and associated statistical parameters from the TI. During simulation, patterns are conditioned to hard or soft primary data like outcrops, drillings or geophysics. MPS simulation yields equally probable realizations, enabling scenario modeling at the voxel-level. In a processing pipeline, MPS results convey to FE or particle modeling (hydrological, rock mechanical) as 2D or 3D grids. MPS versatility is demonstrated with examples from tunneling in hard rock and from aquifer modeling.
With roots in the concept of random variables (Journel 1989, Cressie 1993), geostatistics deals with "the study of phenomena that fluctuate in space and/or in time" (Olea 1991). More on an applied geology level, geostatistics can be seen as a toolbox for the analysis, optimized modeling and simulation of 3D spatial variability. Geostatistics handles metric data - e.g., geochemical concentration or porosity - as well as categorical data like rock class or joint type. Compared with 3D design approaches (CAD-based 3D modeling sensu lato), which yields surfaces or internally homogeneous 3D-solid bodies, geostatistics provides results in grid format. Geostatistical 3D-models are voxel models i.e., the modeling volume is made up of adjacent, non-overlapping prismatic unit cells that store the result (Marschallinger et al. 2014). As opposed to deterministic grid modeling approaches like inverse distance, minimum curvature, radial basis functions etc., geostatistics explicitly incorporates uncertainty. This is the basis for dedicated scenario modeling (Caers 2011).
