В учебном пособии в интерактивной форме представлены современные представления о теории и методах геостатистики и их применении в почвоведении и экологии для решения актуальных экологических и агроэкологических проблем. Основное внимание уделено вопросам построения семивариограмм и расчета их основных характеристики подбору моделей. Рассматривается понятие кригинга и дается описание некоторых его разновидностей.

Geostatistics aims at providing quantitative descriptions of natural variables distributed in space or in time and space. Examples of such variables are 

Ore grades in a mineral deposit 

Depth and thickness of a geological layer 

Porosity and permeability in a porous medium 

Density of trees of a certain species in a forest 

Soil properties in a region 

Rainfall over a catchment area 

Pressure, temperature, and wind velocity in the atmosphere
Concentrations of pollutants in a contaminated site

Geostatistical simulation makes strong assumptions of stationarity in the mean and the variance over the domain of interest. Unfortunately, geological nature usually does not reflect this assumption and we are forced to subdivide our model area into stationary regions that have some common geological controls and similar statistical properties. This paper addresses the significant complexity introduced by boundaries. Boundaries are often soft, that is, samples near boundaries influence multiple rock types.

The wealth of mineral resources that lies beneath the Earth’s surface drives techno‑logical advancements and underpins our economic prosperity. This comprehensive book presents the methods and processes of mineral resource estimation at each step along the mining value chain and provides a necessary framework for understanding mineral development and exploitation. The complexities associated with mineral resource estimation are addressed by explaining the importance of reliable methodologies and the consideration of uncertainty in decision‑making.

Geological data, notably geochemical data, often take the form of a regionalized composition. The concept of regionalized composition combines the concepts of composition and coregionalization. A composition, also known in the literature as a closed array (Chayes 1962), is a random vector whose components add up to a constant. A coregionalization is a set of two or more regionalized variables defined over the same spatial domain, which is modeled as a realization of a vector random function. Here the term regionalized composition is used both for the vector random function used to model a composition and for the realization that we can observe <...>

Ordinary kriging and non-linear geostatistical estimators are now well accepted methods in mining grade control and mine resource estimation. Kriging is also a necessary step in the most commonly used methods of conditional simulation used in the mining industry. In both kriging and conditional simulation, the search volume or ‘kriging neighbourhood’ is defined by the user. The definition of this search can have a very significant impact on the outcome of the kriging estimate or the quality of the conditioning of a simulation.

So much work has been done in recent years using geostatistics to solve practical problems that we no longer have to apologise for nor justify the method. The method is as good as the practitioner, which goes, after all, for any technical application. There have been enough case studies now to show that almost any orebody, simple or complex in structure, which has a definable spatial continuity, will be amenable to geostatistical evaluation given that it is suitably sampled.

This book is different from most books written about geostatistics. The focus here is not on providing an analytical and deductive understanding. It does not attempt to explain the inner workings of its algorithms or exactly how a variogram is calculated and modeled, nor does it provide an exhaustive list of geostatistical algorithms for seismic-data integration.

The aim of this paper is to demonstrate the importance of using variography for grade interpolation in multielement environments and to illustrate how variography can assist in the understanding of geological controls on mineralisation.
Variography codes mineralisation continuity numerically and it is one of the first links between geology and mine planning, since it guides the choice of the interpolation technique. Owing to advances in computer technology and new visualisation techniques, semi-variogram analysis is becoming more of a routine procedure during both feasibility studies and on operating mines.

The intention of this paper is to provide the user with a few essential and handy hints for variogram analysis. So often one is faced with the task of analysing the spatial continuity of a data set or with the task of generating a resource model using geostatistical techniques. However, practical guidelines for completing these tasks are few and far between and, even though one may attend a geostatistics course, time lapses between exposure to geostatistical techniques and actual application of the techniques to real situations is generally large enough for the handy hints of variography to be lost in the never-never land of memories. <...>