Vörös A. szerk.: Fragmenta Mineralogica Et Palaentologica 14. 1989. (Budapest, 1989)
ferent (LE MAITRE 1968). Applying discriminant analysis, six tectonically-defined magma types were separated by PEARCE (1976). BERTRAND and COFFRANT (1977) pointed out the correlation of the mesozoic tholeiites from the NE American margin with the Moroccan tholeiites by means of multivariate statistical methods. Only a few examples from the wide spectrum of the application of mathematical techniques were listed here, but all of them indicated the efficiency of these methods used to igneous geochemistry. However, only a few approaches were presented to the study of a single igneous rock suite. UPADHYAYA et al. (1988) discussed the application of multivariate statistical methods to the Tavidar volcanics. At first sight these methods may seem rather complicated. There are even different algorithms and different techniques used in a single method, therefore it is necessary to have knowledge of their properties. Based on the results of previous works and our experiences, this paper attempts to give some guidelines to the geochemical investigation of a single volcanic suite without a priori information about their mineralogy and petrography, applying multivariate mathematical methods. Considering that UPADHYAYA et al. (19881 gave an efficient case study for the Tavidar volcanic suite, we concentrate on the results of various techniques of these methods in the first place. A paper with a case study for the Mecsek volcanics is in prepraration. The following issues can arise during a petrochemical study: What clusters of rocks can be separated within the suite, and how can we characterize them chemically? What is the relationship between these clusters? What processes affected the rock-chemistry ? What kind of alteration processes changed the initial, composition? What kind of differentiation trends can be recognized within the volcanic suite? Is the rock sequence cogenetic or not 9 Methods used to answer these question are: for classification: cluster analysis, non-linear mapping, principal component variation diagram; for study the processes affected the composition: principal component analysis; for revealing the chemical evolution of the suite: non-linear mapping, principal component analysis (PCA), step-wise PCA, least-squares linear regression analysis. CLUSTER ANALYSIS Cluster analysis is a popular method to the classification of samples without a priori knowledge about their properties. Based on objective criteria it reveals inherent clusters using all the available parameters of the samples. There are numerous varieties of this technique (see EVERITT 1981). In the petrology the agglomerative algorithms are generally used (DAVIS 1973, LE MAITRE 1982). Cluster analysis is not a single method but a series of procedures: possible transformation of data, computing similarity measure between the objects, linkage method for constructing a dendrogram (Table 1). In order to reveal the differences and/or the similarities of the results of various cluster analysis techniques a test was carried out. Different standardization procedures, similarity measures and linkage methods were applied to the same data set consisting of major element compositions of the Lower Cretaceous Mecsek volcanics, South Hungary. These rocks are the products of a continental rift-type volcanism. Basic, intermediate and acid volcanics were formed dominantly under submarine conditions. 67 samples and 9 variables (SÍO2, TÍO2, AI2O3, FeOtot, M9O, CaO, Na 2 0, K 2 0, P 2 0 5 ) were taken into account. Before performing a cluster analysis the variables (oxides) have to be investigated in respect of their significance. Petrological classification requires only fresh rocks to use, therefore volatile content (+H 2 0, -H 2 0, CO^ can be omitted from the data set. In order to avoid the oxidation effect, it is worth to calculate FeO as total FeO (FeOtot = FeO+0. 899 * Fe 2 03\ Variation of MnO is usually not significant in the petrological study of the volcanics, consequently it can be omitted as well. Thus, nine variables remain considering to be important. SiÖ 2 , Ti0 2 , A1 2 0 3 , FeOtot, MgO, CaO, Na 2 0, K 2 0 and P 2 05- Then it is worth to examine the data set whether there are samples containing a variable with extrem value. A simple way to check it is the produce of frequency distribution diagrams (histograms'*. In
