Metoda biplot w interpretacji danych złożonych (CDA) w geologii

• Autorzy: Labus K. , Labus M.

Warianty tytułu

EN

The biplot method in Compositional Data Analysis (CDA) in geology

• Języki publikacji: PL

Abstrakty

EN

Compositional data consist of compositions of parts summing to some whole (e.g.: 100%, 1). Such "closed" data are very popular in geochemistry, sedimentology, hydrogeology and environmetrics. This paper presents the data visualization method by means of the biplot method - a statistical technique widely applied in Compositional Data Analysis. This method enables a graphical display of observations and variables on the same chart, in a way that approximates their correlation. In a biplot the observations are marked with points, and variables - by rays emanating from the origin. Both their lengths and directions are important to the interpretation. The paper presents two examples of implementation of biplots in analysis of hydrogeological and petrological data. The first example concerns petrological data set for pores and skeleton grains of different Polish sandstones. The biplot visualization unveiled a possible independence of subcompositions of transitional pores (T) and macropores (R), as well as submacropores (S) and skeleton grains (Re). The use of this method made it also possible to demonstrate the rule according to which the share of transitive pores decreases at the advantage of real macropores from younger to older rocks, what is related to diagenesis processes. The second example concerns interpretation of hydrological data on chemistry of mine water of the "Rydułtowy" coal mine. In this case the graphical interpretation of biplot revealed large relative variation between HCO₃ ^–-Cl^–, HCO₃^–-I – and HCO₃^–-Na+. Besides, on the same basis, possible independence between the ion couples: HCO₃^--Br^–, Ca²⁺-Na⁺, HCO₃^–-Cl^–, Br-Na⁺, HCO₃^–-Cl^–and Ca₂₊-K⁺ was identified and consequently verified using statistical tests. Additionally, taking into account geometrical features of the relevant biplot, a formula was proposed for defining relationships between shares of ions: Ca²⁺, Mg²⁺, Na⁺ and Cl^{–<.sup>, SO}₄^2–, HCO>sub>3^–. These relationships are most apparent for poly-ion groundwater of the active exchange zone, where the ratios of the above mentioned components are similar to each other, despite a slight predominance of SO₄^2– and HCO₃^– fractions.

Słowa kluczowe

PL

interpretacji danych złożonych; CDA; biplot; skład chemiczny wód podziemnych; porowatość skały

EN

Compositional Data Analysis; biplot; CDA; rock porosity; groundwater chemical composition

• Wydawca: Państwowy Instytut Geologiczny - Państwowy Instytut Badawczy
• Czasopismo: Przegląd Geologiczny
• Rocznik: 2010
• Tom: Vol. 58, nr 5
• Strony: 436--442
• Opis fizyczny: Bibliogr. 11 poz., ta., wykr.

Twórcy

autor

Labus K.

autor

Labus M.

• Wydział Górnictwa i Geologii, Politechnika Śląska, ul. Akademicka 2, 44-100 Gliwice,

Bibliografia

• AITCHISON J. 1986 - The Statistical Analysis of Compositional Data, Monographs on Statistics and Applied Probability. Chapman and Hall, London.
• AITCHISON J. 2003a - The Statistical Analysis of Compositional Data. Blackburn Press, New Jersey.
• AITCHISON J. 2003b - A Concise Guide to Compositional Data Analysis. CDA Workshop, Girona.
• AITCHISON J. & GREENACRE M. 2002 - Biplots of Compositional Data. Appl. Statist.,51: 375- 382.
• GABRIEL K.R. 1971 - The biplot display of matrices with application to principal components analysis. Biometrika, 58: 453-467.
• LABUS K. 2007 - Identyfikacja procesów formujących chemizm wód podziemnych w warunkach drenażu górniczego, w południowo- zachodniej części Górnośląskiego Zagłębia Węglowego. Zesz. Nauk. PŚl. Gór., 281: 1-247.
• LABUS M. 2005 - Compositional data analysis as a tool for interpretation of rock porosity parameters. Geol. Quart., 49, 3: 347-354.
• LABUS K. & LABUS M. 2006 - Zastosowanie analizy danych złożonych (CDA) w geologii. Gosp. Sur. Min., 22, 2: 39-52.
• PAWLOWSKY-GLAHN V. & BUCCIANTI A. 2002 - Visualization and modeling of sub-populations of compositional data: statistical methods illustrated by means of geochemical data from fumarolic fluids. Int. J. Earth Sci., 91: 357-368
• THIÓ-HENESTROSA S. & MARTÍN-FERNÁNDEZ J.A. 2005 - Dealing with compositional data: the freeware CoDaPack. Math. Geol., 37, 7: 773-793.
• UDINA F. 2005 - Interactive Biplot construction. J. Stat. Softw., 13, 3: 1-16; http://www.jstatsoft.org/.