RHA-CODING OF MINERAL COMPOSITION OF CRYSTAL ROCKS AND THEIR SYSTEMATIZATION METHOD

Transcription

1 RHA-CODING OF MINERAL COMPOSITION OF CRYSTAL ROCKS AND THEIR SYSTEMATIZATION METHOD T. Petrov, N. Krasnova Department of Mineralogy, University of St. Petersburg Introduction. Mineral composition of rocks, in general, is characterized by: multicomponent nature, variety and inconstancy of composition with a continuous transition between "different" rocks. Transitions between igneous, altered, sedimentary, metamorphic, ore and impact rocks are also continuous. This creates difficulties in an effort to order the knowledge of one of the main types of objects of geological science. After 200 years of efforts of individual geologists on imposing order in the study of rocks (if we start from the establishment by the St. Petersburg Academy of Sciences of the award for the best attempt (only!) to classify them), in 1967, A.L. Streckeisen sent out proposals for the classification and nomenclature of igneous rocks, which were the basis for the next, collective, attempt to solve the problem. From 1969 to 1989, "419 people from 49 countries took part in the discussions and decisions" of meetings held in different countries. The result was creation of the classification [1]; its methodology and construction method are described in [2]. Ten principles that formed the basis of this classification and nomenclature can be analyzed for the degree of certainty, but it is enough that they did not enable either to cover all igneous rocks, not to mention all the crystalline ones, or to satisfy domestic scientists. This resulted in three editions of the Petrographic Code drawn up based on the assigned genesis as the ground for classification of endogenous formations and further use of the structural, mineral, and chemical approaches [3]. The absence of lamproite, kimberlite, lamprophyre classifications was stated. Rocks enriched in ore minerals, sedimentary ores remained behind. The authors believe that the failure stems from the fact that from the very beginning it was proposed to order not the facts, but the results of their multifaceted interpretations in establishing the "genesis", product of reconstruction of overlapped indefinite number of multi-million year processes, ideas of which are constantly evolving. This inevitably involves uncertainty and volatility of nomenclature, loss of knowledge about the rocks that changed their names, as well as difficulties with the names of new rocks. As a separate, historical circumstance, we note that all dictionaries and reference books known to the authors use, in the vast majority, senseless rock names for their entries and order them by alphabets of natural languages. Qualifiers of rocks by mineral composition do not exist at all. Objective. To provide a method for encoding the mineral composition of crystalline rocks as a basis for development of a unified system of rock compositions in the form of conceptual codes and creation of comprehensive databases that ensure searching rock names by their composition, including information on genetic, structural, and other features of specific objects in their descriptions. Addressing the conceptual coding of crystalline rock compositions. A version of a "general classification for geochemical systems" using RHA method [4], which enables to order

2 the diversity of not only "geochemical" but all "chemical" systems, was offered in 1971 in St. Petersburg (then - Leningrad) University. Moreover, it was said at the end of the paper, "The above method of reducing redundant information on the system, a special case of the use of which was a proposal to construct the classification of rocks and ores, equally relates to description and classification of probabilistic systems of any other nature. Such systems may be rocks and other mixtures, for which we know the distribution of molecular concentrations (mineralogical classification of rocks)". It didn t cause a reaction. In the subsequent years, the authors of the publication and their collaborators have focused efforts on the development of the method, deepening of the scientific base, and expansion of the application areas. Terminology. Since the geological language does not always have the definiteness of the computer science language (in the broad sense of the word) adopted for the implementation of the method, let us define the concepts. Crystalline rocks: here all rocks, whose composition is presented (or may be presented) by a crystalline substance in the form of a list of mineral names and their contents. Coding procedure identifying characters or groups of characters in one code with characters or groups of characters in another code. Here, mineral composition acts as a source code, and as a resulting code a set of rank formula R, information entropy H (En), and anentropy A (An) [4-7]. Rank formula R a sequence of minerals by decrease of their contents. Information entropy H a negative sum of products of component contents by their logarithms a measure of system composition complexity (entropy is mentioned in [4]). Normalized to the interval 0-1 entropy is denoted by En. Anentropy A a negative mean of content logarithms a measure of composition purity. Alphabet a linearly ordered set of mutually distinguishable characters (letters, numbers, special and service marks). N-alphabet and A-alphabet are distinguished as alphabets of natural and artificial languages, respectively. Construction of information language describing a system of rock compositions The basis of systematization is coding of mineral composition as a material basis for identification of crystalline rocks. Such coding automatically considers in crystalline rock composition hydrogen, carbon, fluorine, sulphur present in more than half of all the minerals in the world but ignored when classifying and, subsequently, in chemical analyses [9]. Further addons, namely structure, assessed objectively, age and genesis, as interpretation products at the reached scientific level, are included in the object description. RHA coding of composition is made in three stages. 1) Construction of a rank formula of composition. The issue of measurement units for mineral contents in composition is solved taking into account the purpose of the database (vol. % are used for visual calculations in samples, thin sections, or crushed samples; wt. % - to assess the effectiveness of extraction, beneficiation, transportation, mole % - in physical-chemical modeling). The simpler tasks, the less information is required, the smaller the length n of rank

3 formula may be considered sufficient. To identify rocks with medium complexity, determination of 3-4 minerals is enough. For relatively complex rocks n can reach 5-7 or more. 2) Calculation of entropy the measure of composition complexity. The lower the entropy, the closer the composition to mono-mineral (H min = 0). The higher H, the closer the composition to the same contents of all minerals (H Max = lnn). 3) Calculation of anentropy A the measure of composition purity. Typically, there is an inverse correlation between H and A, but there are cases with positive. A-alphabetic ordering of RHA-representations of composition. For a uniform ordering of mineral compositions of rocks, rank formula is taken for the "word", in which symbols of minerals, or their names are playing the role of "letters". Mineral symbols begin with capital letters; therefore one can do without spaces or other signs between designations of minerals, as is customary when describing altered rocks. A sequence of rank formulas of minerals in [8] is taken for the A-alphabet of names (and their equivalent characters). All the procedures after the input of source materials in the intended for this software Petros3 are made automatically, including ordering [9] Example of coding mineral compositions of rocks and their systematization is given in the table. As on can see, the most complex rock is tinguaite, the least complex, almost monomineral, anorthosite. In a single sequence, at the beginning of the table are carbonatites, at the end, the ore that is incapable of traditional classification methodology in petrography. Discussion. The above method of coding and systematization is suitable for all, without exception, rocks, for which the analysis of their mineral composition is available. The result is a self-organizing system with the properties of linearity, hierarchicity, periodicity with automatic grouping and close arrangement of identical and similar compositions. Preserving knowledge of rocks in the form of a composition associated with the RHA code and included in the A- alphabetic system is more reliable than under the guise of its meaningless and changing over time name in N-alphabetical dictionary. Work according to the method for small amounts of material can be carried out using Excel. The above method of encoding (description) and systematization was implemented repeatedly for chemical and mineral compositions [10], crystal-chemical formulas [11]. It should be noted that as close as possible to the proposed by us [4-7] solution of the problem was A.H. Mitchell, who proposed "to replace the historical names... with compositional ones, based on the predominance of minerals in rock". The proposal was repelled as giving excessively complicated description. [3 p.153]. Let us register as very important in considering the proposal that the method formalizes conventional, traditionally formed "importances" when naming rocks, more specifically: naming rocks after the principal minerals (reflected in rank formula), taking into account complexity of mineral composition of rocks, naming of the simplest (with low H) rocks by slightly changed name of the principal mineral for example, apatitolite, olivinite, pyroxenite, etc. Using the proposed method enables to start compilation of a Qualifier of crystalline rocks by their mineral composition. Among the preliminary work are: development of a list of abbreviations of names of rock-forming minerals for the entire spectrum of crystalline rocks, standardization of the code length, as well as choice of the most convenient sequence of features, properties, characteristics, coordinates of the object given in the description of rocks when codes with complete descriptions are arranged in a column.

4 Table. REnAn of mineral compositions of rocks (source data in modal Vol.%) Ранговые формулы En An Description Calc Aegn Apat Biot carbonatite Aegn Calc Apat Phlg Oliv carbonatite Calc Oliv Crtl DiHe Magt olivinite Pyrx Oliv Augt Magt Apat peridotite Neph Aegn Biot Micr ijolite Neph Aegn Magt Biot urtite Neph Micr Aegn Biot juvite Quar Ands Biot Almn gneiss BiotGranKyan Quar Micr Albt Musc granite Fspt alc Biot= Aegn= Micr Natr tinguaite Augt Hbld Magt Labr pyroxenite Olig= Micr Quar Biot adamellite Ands Quar Biot Musc tonalite Labr Augt Oliv Trem gabbro Oliv Labr Augt Oliv= Magt anorthosite Labr Micr DiHe Biot plagioclasite Labr Micr= Augt Oliv essexite Micr Quar Albt Biot alaskite Micr Albt Biot Magt syenite alkaline Micr Augt Magt Biot akerite Micr Olig Quar Biot adamellite Micr Olig Quar Hbld adamellite Micr Apat Augt Hbld pulaskite Mell Neph Trem Phlg okaite Mell DiHe Andr Phlg uncompahgrite Magt Phlg Calc Apat ore MagtPhlgCalc

5 References 1. Le Maitre, R.W. (Ed.). Igneous Rocks. A Classification and Glossary of Terms. 2nd edition. Cambridge University Press, Cambridge pp. 2. Le Bas, M.J. & Streckeisen, A., The IUGS Systematics of Igneous Rocks // RMS Proceedings Vol.120. No.4. Pp Petrographic Code. St. Petersburg. VSEGEI p. 4. Petrov T.G. Substantiation of a version of general classification of geochemical systems. // LSU Bulletin. No P Petrov T.G. Information language for description of compositions of polycomponent objects // Scientific - Technical Information. Ser. 2, N. 3, pp Petrov T.G., Farafonova O.I. Information-Component Analysis. RHA Method. (Study guide). St. Petersburg p. 7. Petrov Tomas G., Moshkin Sergey V. RHA (T) -System for Coding of Discrete Distributions and Their Alteration Processes. Proc. The 3rd International Multi-Conference on Complexity, Informatics and Cybernetics IMCIC pp Petrov T.G., Krasnova N.I. R-Dictionary of Chemical Compositions of Minerals. St. Petersburg: Nauka. 152 p. 9. Petrov T.G., Moshkin S.V. RHA method and its implementation in Petros-3 software system. Computations in Geology. 2011, No.1, pp T. G. Petrov, A. A. Andriyanets-Buyko, and S. V. Moshkin. A Two-Parameter Alphabet for Coding Structural Chemical Information and its Systematization (Using the Example of Tourmaline).// Aut. Doc. and Math. Ling, 2012, Vol. 46, No. 1, pp