This book is aimed at postgraduates, undergraduates and workers in industry who require an introduction to geostatistics. It is based on seven years of courses to undergraduates, M.Sc. students and short courses to industry, and reflects the problems which have been encountered in presenting this material to mining engineers and geologists over a wide age range, and with an equally wide range of numerical ability. The book would provide the foundation of a course of about 20 to 30 hours, or of a five-day short course.

Earth sciences data are typically distributed in space and/or in time. Knowledge of an attribute value, say, a mineral grade or a pollutant concentration, is thus of little interest unless location and/or time of measurement are known and accounted for in the data analysis. Geostatistics provides a set of statistical tools for incorporating the spatial and temporal coordinates of observations in data processing.

This text intends to be a technical one. This means that techniques to solve identified problems will be presented. As the theory which serves as a basis for these techniques is very new, and relatively unfamiliar to the mineral industry, several chapters or sections will be devoted to it. These two ideas of a technique and a theory have been my guideline in preparing this course on the geostatistical estimation of mineral resources. The main target was to stay, as much as possible, close to the practical problems. This is the reason for the many examples which are intermeshed with the text; however, in many cases, staying t o o close t o a problem obscures the broader frame into which a question has to be asked before finding a correct answer. This is the reason for some theoretical digressions, which may seem to some as an attempt to try and make things look complicated. Certainly, in a particular mine, many problems can be solved without a total understanding of the complete theory. On the other hand, when one considers all the problems occurring in different mines, one cannot hope to solve them without having a good grasp, a synthetic view of the theory of regionalized variables as developed by G. Matheron in France, the most advanced developments of which have just been published in the Proceedings of a N.A.T.O. Advanced Study Institute (Guarascio, Huijbregts, David, 1976) <...>

The distribution of ore grades within a deposit is of mixed character, being partly structured and partly random. On one hand, the mineralizing process has an overall structure and follows certain laws, either geological or metallogenic; in particular, zones of rich and poor grades always exist, and this is possible only if the variability of grades possesses a certain degree of continuity. Depending upon the type of ore deposit, this degree of continuity will be more or less marked, but it will always exist; mining engineers can indeed be thankful for this fact because, otherwise, no local estimation and, consequently, no selection would be possible. However, even though mineralization is never so chaotic as to preclude all forms of forecasting, it is never regular enough to allow the use of a deterministic forecasting technique . This is why a scientific (at least, simply realistic) estimation must necessarily take into account both features - structure and randomness inherent in any deposit. Since geologists stress the first of these two aspects, and statisticians stress the second, I proposed, over 15 years ago, the name geostatistics to designate the field which synthetizes these two features and opens the way to the solution of problems of evaluation of mining deposits <...>

Proceedings of the seventh European conference on geostatistics for environmental applications / Материалы Седьмой Европейской конференции по геостатистике для применения в окружающей среде

Characterising spatial and temporal variation in environmental properties, generatingmaps from sparse samples, and quantifying uncertainties in the maps, are key concerns across the environmental sciences. The body of tools known as geostatistics offers a powerful means of addressing these and related questions. This volume presents recent research in methodological developments in geostatistics and in a variety of specific environmental application areas including soil science, climatology, pollution, health, wildlife mapping, fisheries and remote sensing, amongst others.

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. <...>