Vol 50 Iss. 2

Whenever, in the study of nature, one passes from judgments of a qualitative nature to the elucidation of quantitative regularities, one turns to science, the content of which consists of quantitative relations and geometric forms of the real world. Mathematical methods are adopted by the researcher and become a powerful means of work, allowing us to reveal the general laws, deeply hidden by the diversity of constantly changing phenomena and the abundance of observable facts ...

One of the pressing issues of today is the introduction of mathematics in the field of geological and mineralogical sciences. In this connection it is instructive to trace on the example of crystallography, how the modern science of crystals grew from a purely descriptive natural history discipline, closely related to mineralogy, which is characterized above all by a strictly mathematical character. One of the greatest crystallographers who placed crystallography, in the words of A. K. Boldyrev, "...firmly, invariably and irrevocably on an exact mathematical, geometrical basis", was the world-famous professor and director of the St. Petersburg Mining Institute (now the Leningrad Mining Institute) E. S. Fedorov (1853-1919). His outstanding pupil A. K. Boldyrev (1883-1946) and even later the most talented representative of the Fedorov school V. I. Mikheev (1912-1956) worked successfully in the same direction. They made a significant contribution to the development of the mathematical foundations of modern crystallography, forever linking the history of this science with the history of the Leningrad Mining Institute. ...

The data of quantitative analysis of geochemical materials with the use of statistical indicators indicate the following: 1) the overwhelming masses of metallic elements in the lithosphere are concentrated in a dispersed state in rocks; 2) in total, only tiny fractions of the masses of metals dispersed in rocks (thousandths to hundredths of a percent) have been detached into commercial ore deposits; 3) in recent decades, according to the experience of world practice, the amount of metals extracted from the subsurface is steadily increasing with a simultaneous decrease in the cutoff grades of the extracted ores.

When addressing the issues of structural geology and tectonic zoning, there is a need to evaluate and compare areas of the Earth's surface by the degree of dislocation of rocks. We have carried out such a study in the Taimyr folded region. It consists in transforming data on the geological structure of the Earth's surface (in the form of maps and explanatory notes to them) into a network of quantitative characteristics of the vertical component of tectonic movements and in identifying their variations over the area of the region ...

The study of the deep structure of tectonically complex areas and the search for deeply buried mineral deposits are tasks for which the researcher has to involve a wide range of geological, geophysical, geochemical and other features. As a rule, the more remote from the surface the studied geological objects are, the greater the number of interacting, overlapping geological processes have taken part in the history of the area, the less definite and reliable are the indicators of these objects, and more vague – the boundaries of their manifestation ...

When studying the geology of some area, various methods are often used. Each of them, in terms of a particular task, brings not only information of interest to the researcher at the moment, but also information of much less interest, or information not essential at this stage of research ...

This paper provides the justification of the method of approximation of analytical expressions of geophysical fields by rational fractions and some other expressions. The method is based on the use of mathematical programming, mainly linear programming. The paper summarizes the experience in interpreting magnetic and gravitational anomalies by this method on the “Ural‑2” computer, which can operate in floating point mode ...

A known original method of calculating the intensity of gamma radiation along the axis of the well intersecting the ore bed on the basis of the saturation curve of γ-activity, which characterizes the increase in the intensity of γ-radiation in the center of the formation Imax with increasing formation thickness H ...

In defense planning, production and scientific research in recent years, a new scientific discipline – game theory – has become widely used. Its main feature is that it makes it possible to optimally determine the necessary actions – to choose the most successful line of behavior (strategy). The solution is found provided that the final outcome is not fully determined by any of the parties involved in the conflict situation, and the actions themselves are taken on the basis of incomplete information.

The spatial position of the borehole is usually determined by measuring its inclination θₖ and azimuth φₖ at a number of points Mₖ, the distance Sₖ of which from the wellhead are known (k = 1, 2, ...). Such determination reduces either to the calculation of the coordinates of the well axis, or to its graphical construction according to the measurement data ...

In the course of studies of the behavior of various elements in rocks, ores and minerals, there is a need for mathematical processing of a large number of analyses. The results are used for prospecting for mineral deposits, for elucidating the formation of rocks or ores, for sampling and reserve calculation, and for solving other problems ...

In considering the distribution of global single-cutoff reserves of a metal in postmagmatic deposits, a number of hypothetical relationships have previously been derived for the distribution of the number of deposits (ore bodies) of different sizes and the distribution of total ore volumes contained in ore bodies of the same size ...

To assess the accuracy of spectral analysis, it is necessary to have at one's disposal, as usual, several dozens of twice analyzed samples. Since in semi-quantitative spectral analysis discrepancies between repeated determinations are quite large, and the analysis is usually received, as a rule, samples with sharply different grades, the assessment of the accuracy of the analysis should be carried out in relative units ...

The techniques of correlation analysis as a method of statistical processing of the results of various determinations are now increasingly widely used in geochemical studies.Correlation analysis is used to assess the nature and strength of the relationship between chemical elements in paragenetic associations. For this purpose, regressions between two elements are most often studied by calculating and assessing the significance of pairwise correlation coefficients r. In the geochemical interpretation of regressions, it is necessary to take into account the possibility of influence on the selected relationships of other chemical elements present in characteristic associations ...