Metoda biplot w interpretacji danych złożonych (CDA) w geologii

Krzysztof Labus, Małgorzata Labus


The biplot method in Compositional Data Analysis (CDA) in geology.
A b s t r a c t. 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, SO42–, HCO3-. 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 SO42– and HCO3- fractions.

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