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Vol 242
Pages:
133
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Petrographic structures and Hardy – Weinberg equilibrium

Authors:
Yury L. VOYTEKHOVSKY1
Alena A. ZAKHAROVA2
About authors
  • 1 — Ph.D., Dr.Sci. Professor Saint Petersburg Mining University ▪ Scopus
  • 2 — Postgraduate Student Saint Petersburg Mining University
Date submitted:
2019-07-29
Date accepted:
2020-01-10
Date published:
2020-04-26

Abstract

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.

Keywords:
rock petrographic structure quadratic form structural indicatrix classification nomenclature
10.31897/pmi.2020.2.133
Go to volume 242

References

  1. Beskin S.M., Larin V.N., Marin Yu.B. Rare metal granite formations. Leningrad: Nedra, 1979, p. 280 (in Russian).
  2. Beskin S.M., Lishnevskii E.N., Didenko M.I. The structure of the Pitkyaranta granite massif in the North Ladoga area, Karelia. Izvestiya AN SSSR. Seriya geologicheskaya. 1983. N 3, p. 19-26 (in Russian).
  3. Voitekhovskii Yu.L. The problem of rocks organization.. Izvestiya vysshikh uchebnykh zavedenii. Geologiya i razvedka. 1991. N 10, p. 34-39 (in Russian).
  4. Voitekhovskii Yu.L. Methodology for predicting platinum bearing rocks of the Fedorovo-Pansky intrusion by their organization. Zapiski Gornogo instituta. 1993. Vol. 137, p. 49-56 (in Russian).
  5. Voitekhovskii Yu.L. An application of the theory of quadratic forms to the classification of polymineralic rocks structures. Izvestiya vysshikh uchebnykh zavedenii. Geologiya i razvedka. 1995. N 1, p. 32-42 (in Russian).
  6. Voitekhovskii Yu.L. On the structure of the platinum-bearing Fedorovo-Pansky intrusion: to the methodology for predicting mineralization. Zapiski Gornogo instituta. 1997. Vol. 143, p. 93-100 (in Russian).
  7. Voitekhovskii Yu.L. Quantitative analysis of petrographic structures: structural indicatrix method and the method of accessory minerals subtraction. Izvestiya vysshikh uchebnykh zavedenii. Geologiya i razvedka. 2000. N 1, p. 50-54 (in Russian).
  8. Voitekhovskii Yu.L., Pripachkin P.V. The use of statistical methods for the sectional layering of the Fedorovo-Pansky intrusion. Otechestvennaya geologiya. 2001. N 2, p. 48-52 (in Russian).
  9. Gantmakher F.R. Matrix theory. Moscow: Nauka, 1988, p. 552 (in Russian).
  10. Koreneva L.G. Genetics and mathematics. Mathematics and Natural Sciences. Moscow: Prosveshchenie, 1969, p. 326-383 (in Russian).
  11. Laitkhill Dzh., Khiorns R.U., Khollingdeil S.Kh. New areas of math application. Minsk: Vysheishaya shkola, 1981, p. 496 (in Russian).
  12. Levinson-Lessing F.Yu., Struve E.A. Petrographic Dictionary; ed.by. G.D.Afanaseva, V.P.Petrova, E.K.Ustieva. Moscow: Gosgeoltekhizdat, 1963, p. 448 (in Russian).
  13. Manin Yu.I. Cubic forms: algebra, geometry, arithmetic. Moscow: Nauka, 1972, p. 304 (in Russian).
  14. Marin Yu.B. Petrography. St. Petersburg: Natsionalnyi mineralno-syrevoi universitet “Gornyi”, 2015, p. 408 (in Russian).
  15. Petrograficheskii slovar / Pod red. O.A.Bogatikova, V.P.Petrova, R.P.Petrova. M.: Nedra, 1981, p. 496 (in Russian).
  16. Dobretsov G.L., Marin Yu.B., Beskin S.M., Leskov S.A. The principles of differentiation and mapping of granitoid intrusions and revealing of petrological and metallogenic variants of granitoid series. St. Petersburg: Izd-vo VSEGEI, 2007, p. 80 (in Russian).
  17. Savelov A.A. Flat Curves: taxonomy, properties, and applications. Moskva – Izhevsk: NITs “Regulyarnaya i khaoticheskaya dinamika”, 2002, p. 294 (in Russian).
  18. Fedorov E.S. The basics of petrography. St. Petersburg: Tipografiya P.P.Soikina, 1897, p. 236 (in Russian).
  19. Shmidt R.A. Algebra. Part. 2. St. Petersburg: Izd-vo SPbGU, 2011, p. 160 (in Russian).
  20. Harker A. Petrology for students. Cambridge: Cambridge University Press, 1908, p. 336.

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