By their very nature, earth science data have an inherent spatial structure. That is, variables we measure, like elevation, lithology, or porosity, are tied to geographic positions on the earth. Observations taken in close proximity will be more strongly correlated than observations separated by more distance. Although this relationship is an accepted norm to geologists, it is not the case in most other sciences. Classical statistical analysis does not necessarily account for spatial relationships, and its use in the earth sciences can often produce misleading results. A prerequisite of any geostatistical study is the development of the spatial model. R. A. Olea provides an excellent overview of semivariograms, the tool used in geostatistics to estimate and model spatial variability, in the chapter entitled Fundamentals of Semivariogram Estimation, Modeling, and Usage.

The sample support is the area or volume over which a measurement is made. Understanding how one measurement relates to another in close proximity is critical because geostatistical methods are highly sensitive to the spatial controls on variability. This is particularly true with tensor variables like permeability, for which mathematical averaging over volumes of various dimensions tends to be a problem. Y. Anguy et al. discuss how image analytical data can be blended with physical measurements to provide information for modeling permeability at scales greater than the permeability plug in The Sample Support Problem for Permeability Assessment in Sandstone Reservoirs.

In the nineteenth century, Johannas Walther, a noted geologist, recognized the Law of Correlation of facies. The law, as paraphrased by Krumbine and Sloss (1963, Stratigraphy and Sedimentation, W. H. Freeman and Company), states that "in a given sedimentary cycle, the same succession of facies that occurs laterally is also present in vertical succession." Taken commutatively, geologists have often attempted to predict the lateral variability of facies from a vertical sequence of stratigraphy. In the chapter Theory and Applications of Vertical Variability Measures from Markov Chain Analysis, J. H. Doveton presents an interesting alternative to the geostatistical simulation approach of reservoir facies. He points out that Markovian statistics of vertical variability are applicable to selected problems of lateral facies prediction and simulation.

The final chapter in this section is A Review of Basic Upscaling Procedures: Advantages and Disadvantages. Upscaling is the term applied to the process of changing from a fine scale of resolution to a coarser scale of resolution. The process is often necessary when translating a digital geostatistical model consisting of perhaps millions of grid nodes to a model consisting of tens of thousands of grid nodes, which is a more economically viable size for reservoir simulation. All of the techniques presently available cause a severe reduction in vertical and horizontal resolution, and thus can present a problem for estimating reservoir performance and maintenance. Rather than trying to provide an exhaustive review of all practical details, J. Mansoori highlights permeability upscaling methods and provides an annotated bibliography of pertinent reference literature.