Although it is generally understood that the Antarctic Ice Sheet plays a critical role in the changing global system, there is to date still a lack of generally available information on the subject. Climatic change and the role of the polar areas are often discussed in the media.

Spatial statistics has developed rapidly during the last 30 years. We have seen an interesting progress both in theoretical developments and in practical studies. Some early applications were in mining, forestry, and hydrology. It seems to be honest to remark that the increasing availability of computer power and skillful computer software has stimulated the ability to solve increasingly complex problems.

An introduction to the description, analysis, and modeling of geospatial data and of the resulting uncertainty in the models. Theory and its correct application will be integrated with the use of various software tools (including GIS) and appropriate examples to emphasize the crossdisciplinary applicability of geostatistical analysis and modeling.

Since publication of the first volume of Stochastic Modeling and Geostatistics in 1994, there has been an explosion of interest and activity in geostatistical methods and spatial stochastic modeling techniques. Many of the computational algorithms and methodological approaches that were available then have greatly matured, and new, even better ones have come to the forefront. Advances in computing and increased focus on software commercialization have resulted in improved access to, and usability of, the available tools and techniques. Against this backdrop, Stochastic Modeling and Geostatistics Volume II provides a much-needed update on this important technology. As in the case of the first volume, it largely focuses on applications and case studies from the petroleum and related fields, but it also contains an appropriate mix of the theory and methods developed throughout the past decade. Geologists, petroleum engineers, and other individuals working in the earth and environmental sciences will find Stochastic Modeling and Geostatistics Volume II to be an important addition to their technical information resources.

Most of the natural phenomena we study are variable both in space and time. Considering a topographic surface or a groundwater contamination one can observe high variability within small distances. The variability is a result of natural processes, thus deterministic. As most of these processes are sensitive and the conditions under which the they took place are not fully known, it is not possible to describe them based on physical and chemical laws completely. <...>

It is often useful to estimate obscured or missing remotely sensed data. Traditional interpolation methods, such as nearest-neighbor or bilinear resampling, do not take full advantage of the spatial information in the image. An alternative method, a geostatistical technique known as indicator krigingo is described and demonstrated using a Landsat Thematic Mapper image in southern Chiapas, Mexico. The image was first classified into  pasture and nonpasture land cover. For each pixel that was obscured by cloud or cloud shadow, the probability that it was pasture was assigned by the algorithm. An exponential omnidirectional variogram model was used to characterize the spatial continuity of the image for use in the kriging algorithm. Assuming a cutoff probability level of 50%, the error was shown to be 17% with no obvious spatial bias but with some tendency to categorize nonpasture as pasture (overestimation). While this is a promising result, the method's practical application in other missing data problems for remotely sensed images will depend on the amount and spatial pattern of the unobscured pixels and missing pixels and the success of the spatial continuity model used. <...>

Mineral resource evaluation requires defining geological domains that differentiate the types of mineralogy, alteration and lithology. Usual practice is to consider the domain boundaries as hard, i.e. data from across the boundaries are disregarded when estimating the grades within a given domain. This practice may hinder the quality of the estimates when a significant spatial correlation of the grades exists across the domain boundaries.

Geostatistics (also known as kriging) was developed for the mining industry during the 1960s and 1970s to estimate changes in ore grade. The principles of geostatistics are now applied to many applications that require statistically based interpolation techniques. Geostatistics provides a data value estimate for locations that cannot be sampled directly by examining data taken at locations that can be sampled.

Geostatistical techniques are extensively used for mineral resources assessment, including grade estimation and uncertainty analysis. Support is the term used in Geostatistics to describe the size or volume of a sample. For example, suppose a grade sample obtained from diamond drill holes (DDH). In this case, the support is a function of the core’s radius and length.

The objective of this paper is to show how well known the structure is for a particular uranium deposit. After presenting the average vertical variogram for all the holes, some of the individual variograms will be studied and we will show the influence of a few very rich holes on the overall variogram. This turns out to be poorly defined. The first order variogram, which also has been considered, is curiously similar to the usual variogram, whereas the structure of the translated logarithm proves to be better known. <...>