Vörös A. szerk.: Fragmenta Mineralogica Et Palaentologica 14. 1989. (Budapest, 1989)

FRAGMENTA MINERALOGICA ET PALAEONTOLOGICA 14. BUDAPEST, 1989 p --»-16 Multivariate mathematical methods in the study of a single volcanic suite By SZ. HARANGI (Received December 1, 1988) Abstract : Application of multivariate mathematical methods proved to be effective on the petrochemical study of a volcanic suite without a priori information about the mineralogy and petrography. This paper attempts to give some guidelines to the use of a few such techniques of these mathematical methods. Classification of the main rock types can be achieved by the use of cluster analysis. Euclidean distance with raw data and cosine theta coefficient are recommended to use as a similarity measure, while among the linkage methods the weighted-pair group average proved to be most efficient. To check the clustering non-linear mapping is an excellent technique. Principal component analysis can be applied to the study of the processes affected on the chemistry of the volcanics: differentiation, subsequent alteration. Such a complex study can lead to setting up a working-hypothesis for the following investigation. INTRODUCTION Increase in the volume of geochemical data has required the use of various multivariate mathematical statistical methods. Appearance and spreading of the computers in the geosciences have allowed the application of these techniques to the geological study. Processing the recent and previous data sets could lead new results not only in the geochemical exploration, but in the petrochemical and paleontological researches as well. A comprehensive study of the mathematical statistical techniques in the geosciences was reviewed by DAVIS (1973) and HOWARTH (1983), statistical evaluating of petrochemical data was discussed by LE MAITRE (1982). As he remarked "the petrologist of today not only has to be a master of the petrological microscope but also has to be numerate to interpret the increasing amounts of data produced by modern analytical equipment". Interpretations of the vast quantity of petrochemical data using conventional methods prove to be more and more difficult. Variation diagrams like the rectilinear and triangular plots utilize only a few oxides at a time, consequently there is a loss of information content. Ternary petrologic variation diagrams may result spurious trends of an igneous rock suite due to the closed data effect (BUTLER 1979). There are a number of petrochemical .classification schemes (e.g. TAS diagram, R1-R2 plot) for clustering igneous rocks but the results of these methods are ambiguous and subjective (HARANGI 1988). To overcome these difficulties it is necessitated to call multivariate mathematical methods to help. Statistical techniques can be applied for a wide range of petrological problems, CHAYES and VELDE (1965) revealed the compositional differences of the orogen and oceanisland type basalts by means of discriminant factors. Study of the chemical variation within volcanic suites using principal component analysis led to the conclusion that the differentiation processes within the alkali- and sub-alkali volcanic series must be fundamentally dif-