Petrographic structures: Khibiny ijolites and urtites
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 i...
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ftoceandocs:oai:aquadocs.org:1834/41693 2023-05-15T17:04:58+02:00 Petrographic structures: Khibiny ijolites and urtites Петрографические структуры: ийолиты и уртиты Хибин Voytekhovsky, Yu. L. Zakharova, A. A. Russia Khibiny Rock Massif Kola Peninsula Россия Хибинский горный массив Кольский полуостров 2021 pp.160-167 http://hdl.handle.net/1834/41693 ru rus http://vestnik.mstu.edu.ru/show-eng.shtml?art=2097 http://vestnik.mstu.edu.ru/show.shtml?art=2097 http://hdl.handle.net/1834/41693 Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ Ijolite Urtite Hardy–Weinberg equilibrium Ийолит Уртит Равновесие Харди–Вайнберга Mathematical models Petrographic structure Математические модели Петрографическая структура ASFA_2015::E::Earth sciences ASFA_2015::G::Geology ASFA_2015::R::Rock properties ASFA_2015::R::Rocks ASFA_2015::P::Probability theory Journal Contribution 2021 ftoceandocs 2023-04-06T17:07:02Z 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 ... Other Non-Article Part of Journal/Newspaper kola peninsula IODE-UNESCO: OceanDocs - E-Repository of Ocean Publications Khibiny ENVELOPE(33.210,33.210,67.679,67.679) Kola Peninsula |
institution |
Open Polar |
collection |
IODE-UNESCO: OceanDocs - E-Repository of Ocean Publications |
op_collection_id |
ftoceandocs |
language |
Russian |
topic |
Ijolite Urtite Hardy–Weinberg equilibrium Ийолит Уртит Равновесие Харди–Вайнберга Mathematical models Petrographic structure Математические модели Петрографическая структура ASFA_2015::E::Earth sciences ASFA_2015::G::Geology ASFA_2015::R::Rock properties ASFA_2015::R::Rocks ASFA_2015::P::Probability theory |
spellingShingle |
Ijolite Urtite Hardy–Weinberg equilibrium Ийолит Уртит Равновесие Харди–Вайнберга Mathematical models Petrographic structure Математические модели Петрографическая структура ASFA_2015::E::Earth sciences ASFA_2015::G::Geology ASFA_2015::R::Rock properties ASFA_2015::R::Rocks ASFA_2015::P::Probability theory Voytekhovsky, Yu. L. Zakharova, A. A. Petrographic structures: Khibiny ijolites and urtites |
topic_facet |
Ijolite Urtite Hardy–Weinberg equilibrium Ийолит Уртит Равновесие Харди–Вайнберга Mathematical models Petrographic structure Математические модели Петрографическая структура ASFA_2015::E::Earth sciences ASFA_2015::G::Geology ASFA_2015::R::Rock properties ASFA_2015::R::Rocks ASFA_2015::P::Probability theory |
description |
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 ... |
format |
Other Non-Article Part of Journal/Newspaper |
author |
Voytekhovsky, Yu. L. Zakharova, A. A. |
author_facet |
Voytekhovsky, Yu. L. Zakharova, A. A. |
author_sort |
Voytekhovsky, Yu. L. |
title |
Petrographic structures: Khibiny ijolites and urtites |
title_short |
Petrographic structures: Khibiny ijolites and urtites |
title_full |
Petrographic structures: Khibiny ijolites and urtites |
title_fullStr |
Petrographic structures: Khibiny ijolites and urtites |
title_full_unstemmed |
Petrographic structures: Khibiny ijolites and urtites |
title_sort |
petrographic structures: khibiny ijolites and urtites |
publishDate |
2021 |
url |
http://hdl.handle.net/1834/41693 |
op_coverage |
Russia Khibiny Rock Massif Kola Peninsula Россия Хибинский горный массив Кольский полуостров |
long_lat |
ENVELOPE(33.210,33.210,67.679,67.679) |
geographic |
Khibiny Kola Peninsula |
geographic_facet |
Khibiny Kola Peninsula |
genre |
kola peninsula |
genre_facet |
kola peninsula |
op_relation |
http://vestnik.mstu.edu.ru/show-eng.shtml?art=2097 http://vestnik.mstu.edu.ru/show.shtml?art=2097 http://hdl.handle.net/1834/41693 |
op_rights |
Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |
_version_ |
1766059326520164352 |