Abstract
Earth sciences phenomena are heterogeneous, anisotropic, non-uniform, and random especially in their spatial behaviors, and their exhaustive sampling is not possible, and the only scientific way for the regional and global assessment of these phenomena is through suitable mathematical modeling techniques. The main purpose is to deduce from limited and small samples the general characteristics and finally the generating mechanism of the phenomenon. Development in computer sciences enhanced time-consuming simulation studies, which developed into a feasible and practical tool to reveal nonlinear and nonequilibrium evolution of an earth sciences phenomenon based on the fundamental laws governing the nature. Nonlinearity and causality of a natural phenomenon are demonstrated to be consistently explained by simulations based on fundamental laws. Simulation methodology is timely born with practically usable starts of digital computers during 1950s. Simulation studies are essential because the existing analytical methods are not sufficiently powerful to prove the validity of the fundamental laws for naturally occurring phenomena, but simulation could do this effectively. Spatial pattern simulations in 1-, 2-, and 3D space are explained through autoregressive models, which are based on the spatial correlation function. Rock masses are fractured into different sizes, and they are intact from each other due to fracturing. Different simulation techniques are presented for dependent (persistent) and independent fracture patterns, which are exemplified in the field by scanline measurements. Along this line, rock quality designation (RQD) quantification is furnished through various simulation models, and final products are presented in terms of various charts that can be used in practical applications. Porous medium is very significant for water, oil, and gas storages, and therefore, its spatial behavior is significant for effective assessments, planning, operation, and management. Autorun spatial modeling technique is developed and applied for the simulation of porous medium. Finally, the application of the cumulative semivariogram technique is presented for intact length simulation in rock masses.