Accurate recoverable resource estimation and grade control procedures are the foundation of successful mining ventures. Long, medium and short term planning in a mining operation are all dependent upon precise estimations. For example, poor estimation may result in the long term in a pit being incorrectly optimised, in the medium term cashflow forecasts may be disastrously inaccurate, and in the short term the allocation of ore and waste material by grade control may be erroneous.

In this introductory chapter we describe general problems of spatial environmental data analysis, modeling, validation and visualization. Many of these problems are considered in detail in the following chapters using geostatistical models, machine learning algorithms (MLA) of neural networks and Support Vector Machines, and the Bayesian Maximum Entropy (BME) approach. The term “mapping” in the book is considered not only as an interpolation in two- or threedimensional geographical space, but in a more general sense of estimating the desired dependencies from empirical data.

Effectiveness of ore grade control at operating mines depends on both the quality and quantity of the samples used. Therefore, optimisation of grade control procedures requires analysis of sample quality and their spatial distribution. This approach, implying quantitative estimation of both these factors and quantification of their contribution to the grade control errors, was used for comparing two different grade control procedures at the Yandicoogina (Yandi) iron-ore open pit mine, located in the eastern part of the Pilbara region of Western Australia. At Yandi, pisolitic iron oxide mineralisation is distributed within a meandering palaeoriver channel, characterised by abundant clay pods that contain the deleterious components; in particular Al2O3 and SiO2.

В учебнике описаны математические методы решения промыслово-геологических задач при разработке нефти и газа, прежде всего оценки неоднородности продуктивного пласта и моделирования пространственного распространения неоднородностей 

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 <...>