| Summary: | In addition to the standard description of the structures and textures of crystalline rocks the mathematical approaches have been proposed based on a rigorous determination of the petrographic structure through the probabilities of binary intergrain contacts. In general, the petrographic structure is defined as an invariant aspect of rock organization, algebraically expressed by the canonical diagonal form of the symmetric Pij matrix and geometrically visualized by structural indicatrices – surfaces of the 2nd order. The agreed nomenclature of possible petrographic structures for an n-mineral rock is simple: the symbol Snm means that there are exactly m positive numbers in the canonical diagonal form of the Pij matrix. New types of barycentric diagrams have been proposed. To describe the massive texture, the concept of Hardy – Weinberg equilibrium has been proposed. This boundary classifies barycentric diagrams into areas within which canonical types of Рij matrices and topological types of structural indicatrices are preserved. The change in the organization of the rock within a type is quantitative, the transition from one type to another means structural restructuring. The methods are used to describe ijolites and urtites of the Khibiny massif, the Kola Peninsula. In the modern taxonomy of rocks, the boundaries between them are mostly conditional and are drawn according to the contents of rock-forming minerals, for example, between ijolites and urtites – according to the contents of nepheline and pyroxene. The strict definition of the petrographic structure proposed by the authors makes it possible to introduce into petrography the constitutional principle (structure + composition), which is successfully acting in mineralogy. В дополнение к стандартному описанию структур и текстур кристаллических горных пород предложены математические подходы, основанные на строгом определении петрографической структуры через вероятности бинарных межзерновых контактов. В общем случае петрографическая структура определена ...
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