In the fall of 1988 the Society of Petroleum Engineers (SPE) held a forum on reservoir characterization in Grindenwald, Switzerland. Many of the authors who have contributed to this volume were at that forum discussing their ideas on stochastic methods for reservoir characterization. All of these ideas were then still quite new and largely untested; indeed, some of them had not been reduced to practice, but were merely the wild imaginings of creative and curious minds. At that time, there was still a fair bit of controversy over whether stochastic methods had any relevance to the practice of modeling petroleum reservoirs.*

Geostatistics is a subset of statistics specialized in analysis and interpretation of geographically referenced data (Goovaerts, 1997; Webster and Oliver, 2001; Nielsen and Wendroth, 2003). In other words, geostatistics comprises statistical techniques that are adjusted to spatial data. Typical questions of interest to a geostatistician are:

how does a variable vary in space?

what controls its variation in space?

where to locate samples to describe its spatial variability?

how many samples are needed to represent its spatial variability?

what is a value of a variable at some new location?

what is the uncertainty of the estimate?

The organization of this book follows the typical mining sequence that starts with the exploration phase aimed at delineating the mineral deposit and detailing its geology.

Geological objects can be singular, like the inverted cone-shaped diatreme of the El Teniente copper mine; more generally, they can be domains with given lithological, mineralogical, structural or alteration properties, which will be designated throughout this book under the name of ‘facies’, commonly used in geosciences. Within each facies, the metal grades have their own distribution and variability. This peculiarity will lead directly to the prediction or simulation of the grades (quantitative variables) taking into account the statistical and spatial characteristics of each facies (categorical variable).

We emphasize these four terms, which will be found throughout this book: prediction, simulation, quantitative variable and categorical variable <...>

В книге, представляющей первый специальный труд по данному вопросу, систематизированы все виды существующих методов измерения кусковатости на открытых и подземных горных разработках. Наряду с анализом сущности и степени точности, различных методов даны практические указания по их рациональному применению. Рассмотрен вопрос о характеристиках и критериях кусковатости. Обобщен большой исследовательский и экспериментальный материал, а также работы научно- методического характера по вопросам измерения и оценки кусковатости, проводившиеся автором почти 15 лет.

Книга предназначена для научно-исследовательских институтов и инженерно-технических работников горнодобывающей промышленности, а также может быть полезна для студентов старших курсов горных вузов, и факультетов.

Mathematical methods have been employed by a few geologists since the earliest days of the profession. For example, mining geologists and engineers have used samples to calculate tonnages and estimate ore tenor for centuries. As Fisher pointed out (1953, p. 3), Lyell’s subdivision of the Tertiary on the basis of the relative abundance of modern marine organisms is a statistical procedure. Sedimentary petrologists have regarded grain-size and shape measurements as important sources of sedimentological information since the beginning of the last century. The hybrid Earth sciences of geochemistry, geophysics, and geohydrology require a firm background in mathematics, although their procedures are primarily derived from the non-geological parent. Similarly, mineralogists and crystallographers utilize mathematical techniques derived from physical and analytical chemistry. <...>

The dissemination of digital spatial databases, coupled with the ever wider use of GISystems, is stimulating increasing interest in spatial analysis from outside the spatial sciences. The recognition of the spatial dimension in social science research sometimes yields different and more meaningful results than analysis which ignores it

Geostatistics, developed originally in the mining industry from the 1950s onwards, is now being applied widely in environmental science for mapping, monitoring and management. It is based on the theory of random spatial processes. There are numerous examples in soil science, meteorology, agronomy, hydrology, ecology and some aspects of marine science. By taking into account and modelling spatial correlation, geostatistics provides unbiased predictions of environmental variables with minimum and known variance in ways that no other method does. The general technique of prediction is known as kriging. It requires a mathematical model to describe the spatial covariance, usually expressed as a variogram, which in its parameterized form has become the central tool of geostatistics. Successful kriging and estimation of the variogram depend on sampling adequately without bias and with suitable spatial configurations and supports. These differ somewhat from design-based estimation with its emphasis on random sampling. <...>

This web page is a set of companion notes to accompany the twelve lectures presented in the summer of 1999 For Landmark Graphics in Austin Texas. The lectures are intended to be an informal training seminar for those employees involved in the development, documentation, and testing of software that implement geostatistics.
 

Сборник содержит оригинальные статьи, посвященные математическим моделям процессов и статистическому анализу некоторых природных геологических закономерностей; аппроксимации наблюдаемых статистических распределений и решению обратных задач в гоохимии, минералогии и петрографии; процессам метаморфизма и определению эпицентров землетрясений на ЭВМ.
Книга рассчитана на геохимиков, минералогов и петрографов.

Geostatistics, which can be de¯ned as the tools for studying and predicting the spatial structure of georeferenced variables, have been mainly used in soil science during the past two decades. Since now, hundreds of geostatistical papers have been published on soil science issues (see bibliography ibid., this volume). The use of geostatistical tools in soil science is diverse and extensive. It can be for studying and predicting soil contamination in industrial areas, for building agrochemical maps at the ¯eld level, or even to map physical and chemical soil properties for a global extent. The users of the output maps are going from soil scientists to environmental modelers. One of the speci¯city of geostatistical outputs is the assessment of the spatial accuracy associated to the spatial prediction of the targeted variable. The results which are quantitative are then associated to a level of con¯dence which is spatially variable. The spatial accuracy can then be integrated into environmental models, allowing for a quantitative assessment of soil scenarios. <...>