Показаны статистические методы, развиваемые авторами для описания петрографических структур и текстур. Для отображения статистик бинарных и тернарных межзерновых контактов, определяемых в шлифах, предложены диаграммы нового типа -барицентрические треугольник (p ii , p ij , p jj ) и тетраэдр (p iii , p iij , p ijj , p jjj ). В обоих показано положение линии равновесия Харди -Вайнберга, характеризующей массивные текстуры горных пород. Вычислительные процедуры и результаты показаны на примере амфиболитов островов Виченная Луда и Сидоров (Керетский архипелаг, Белое море). К л ю ч е в ы е с л о в а: кристаллическая горная порода; структура; текстура; бинарные и тернарные межзерновые контакты; барицентрическая диаграмма; равновесие Харди -Вайнберга. Yu. L. Voytekhovsky, A. A. Zakharova. A STATISTICAL DESCRIPTION OF THE STRUCTURES AND TEXTURES OF KERETSKY ARCHIPELAGO (WHITE SEA) AMPHIBOLITESThe article presents the statistical methods developed by the authors for the description of petrographic structures and textures. To display the statistics of binary and ternary intergrain contacts detected in thin sections, diagrams of a new type are proposedbarycentric triangle (p ii , p ij , p jj ) and tetrahedron (p iii , p iij , p ijj , p jjj ). Both show the location of the Hardy-Weinberg equilibrium line, which characterizes massive rock textures. Computational procedures and results are demonstrated using the example of amphibolites of Vichennaya Luda and Sidorov islands (Keretsky Archipelago, White Sea). K e y w o r d s: crystalline rock; structure; texture; binary and ternary intergrain contacts; barycentric diagram; Hardy-Weinberg equilibrium.
The article describes a technique for 2D modeling of structures and textures of bimineral rocks in terms of the probabilities of binary intergranular contacts. It is shown that typical petrographic structures (disseminated, chained, poikilitic, porphyric) and textures (massive, banded, schlieren) regularly fill the barycentric diagram (pii, pjj, pij) of contact probabilities. These structures and textures are correlated with the Hardy-Weinberg equilibrium. The problems of modeling polymineral petrographic structures and textures are discussed. A new type of structural diagrams is suggested. The article is dedicated to the memory of Dr. Sci. Yu. A. Tkachev — a well-known Russian specialist in the field of modeling the structures of sedimentary rocks.
For the purposes of modeling and classification of structures and textures of bimineral rocks, a diagram of a new type is proposed — a barycentric tetrahedron (piii, piij, pijj, pjjj) of probabilities of ternary intergrain contacts. The position of the Hardy-Weinberg equilibrium line is calculated. Correspondences between the classification fields and boundaries in the barycentric tetrahedron and the previously proposed barycentric triangle (pii, pij, pjj) of the probabilities of binary intergrain contacts are established. The prospects for the classification of petrographic structures and textures in a barycentric tetrahedron based on Newton's classification of curves of the 3rd order are discussed.
The article is devoted to the most narrative side of modern petrography – the definition, classification and nomenclature of petrographic structures. We suggest a mathematical formalism using the theory of quadratic forms (with a promising extension to algebraic forms of the third and fourth orders) and statistics of binary (ternary and quaternary, respectively) intergranular contacts in a polymineralic rock. It allows constructing a complete classification of petrographic structures with boundaries corresponding to Hardy – Weinberg equilibria. The algebraic expression of the petrographic structure is the canonical diagonal form of the symmetric probability matrix of binary intergranular contacts in the rock. Each petrographic structure is uniquely associated with a structural indicatrix – the central quadratic surface in n-dimensional space, where n is the number of minerals composing the rock. Structural indicatrix is an analogue of the conoscopic figure used for optical recognition of minerals. We show that the continuity of changes in the organization of rocks (i.e., the probabilities of various intergranular contacts) does not contradict a dramatic change in the structure of the rocks, neighboring within the classification. This solved the problem, which seemed insoluble to A.Harker and E.S.Fedorov. The technique was used to describe the granite structures of the Salminsky pluton (Karelia) and the Akzhailau massif (Kazakhstan) and is potentially applicable for the monotonous strata differentiation, section correlation, or wherever an unambiguous, reproducible determination of petrographic structures is needed. An important promising task of the method is to extract rocks' genetic information from the obtained data.
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