Multivariate analyses of Erzgebirge granite and rhyolite composition: implications for classification of granites and their genetic relations
Introduction
The Erzgebirge metallogenic province of Germany and the Czech Republic is located at the northwest edge of the Bohemian Massif. In a small area of about 6000 km2, there occurs a unique assemblage of compositionally heterogeneous granitic and volcanic rocks of late Carboniferous/early Permian age which were generated in the geologically short time of 35 million years between about 325 and 290 Ma (Förster et al., 1998). The Erzgebirge is characterized by highly differentiated felsic systems which form multi-phase plutons possessing either transitional I-S-, S- or aluminous A-type affinities Förster and Tischendorf, 1994, Förster et al., 1995.
Geochemical, mineralogical and geochronological data from recent studies require that previous granite classifications (e.g. Tischendorf and Förster, 1990) be revised. The revision results in a subdivision of the granites into five major groups that are genetically distinct (Förster et al., 1998). The groups, whose extents are shown on the map in Fig. 1, are:
- 1.
Transitional I-S-type low-F biotite granites.
- 2.
Transitional S-I-type low-F two-mica granites.
- 3.
S-type high-F, high-P2O5 Li-mica granites.
- 4.
Aluminous A-type high-F, low-P2O5 Li-mica granites.
- 5.
Aluminous A-type high-F, low-P2O5 biotite granites.
Groups 1 and 4 are assemblages of granitic rocks having somewhat different geologic histories which can be recognized as sub-groups. Kirchberg and Niederbobritzsch granites are thought to represent sub-groups of the transitional I-S-type biotite granite group and the Seiffen, Markersbach and the Schellerhau suite granites are sub-groups of the aluminous A-type Li-mica granite group. Group 3 granites (Eibenstock, Tellerhäuser, Annaberg, Pobershau and Satzung) are nearly identical in composition except for easily mobilized components such as Rb, Li, Cs, U and F. Group 2 is represented by only a single massif (Bergen), as is Group 5 (Gottesberg).
The Erzgebirge granites were divided into major groups and sub-groups on the basis of empirically selected compositional variables, especially elements that have been used traditionally in petrology, such as F, P, Li, Ba, Th, U and the rare earths (Förster et al., 1995, Förster et al., 1998). However, the variables chosen did not permit perfect discrimination between all groups. Magma differentiation is believed to be the most important cause of incorrect classifications because differentiation may result in depletion or enrichment of elements in highly fractionated granites. In extreme cases, evolved granites of one group may have trace element patterns similar to `primitive' granites of another group. Another complication arises because some granites have undergone late- to post-magmatic alteration which caused local redistribution of some mobile elements (F, Li, Ba, U) used as discriminants. Altered samples from cogenetic, well-characterized large plutons can be correctly classified in spite of such changes in element concentrations but the effects may be more troublesome in smaller-sized bodies whose intrusive histories are not completely understood. Exposures often are inadequate to resolve the relationships between these smaller bodies, which simply may be spatially displaced intrusions of larger neighboring plutons.
Although a five-group classification seems consistent with current geological knowledge, a statistical examination of geochemical analyses from the Erzgebirge might confirm the validity or indicate shortcomings in the classification. This statistical study uses multivariate canonical analysis to address several major questions about the Erzgebirge granites and associated rhyolites:
- 1.
Is the subdivision of the Erzgebirge granites into five major groups justified on the basis of geochemical composition?
- 2.
Are there significant differences between granites considered to be members of a single group?
- 3.
What are the affinities of other Variscan silicic igneous rocks that have not yet been assigned to a major group?
- 4.
Which geochemical variables are most effective in classifying Erzgebirge granites?
Question (3) will be illustrated for a population of `unclassified' rhyolitic dikes in the western Erzgebirge. These rocks either crosscut `classified' granite plutons or occur in their immediate neighborhood (Fig. 1). Detailed petrographic analyses are not yet available for these fine-grained porphyritic rocks. Statistical analyses also will be used to determine the likely affinities of small granite bodies within the Aue-Schwarzenberg granite zone which were either unclassified or whose classification was based on a limited number of samples. These granites will be the subject of a separate paper.
Section snippets
The data base
Powdered rock samples were analyzed for the minor and trace elements Li, Be, Sc, Zn, Ga, Rb, Sr, Y, Zr, Nb, Sn, Cs, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta, W, Pb, Th and U by inductively coupled plasma-mass spectrometry, inductively coupled plasma-atomic emission spectrometry and, to a lesser extent, by instrumental neutron activation analysis. Analyses of most trace elements by different methods allowed the checking of dissolution procedures and inter-technique
Multivariate canonical approach
Because the relationships to be explored are complex and the data are highly multivariate, there is no `off-the-shelf' or prescribed statistical procedure for addressing these questions. However, a generalized canonical approach will incorporate all of the variables simultaneously, taking into account interactions between all possible pairs of variables (Krzanowski, 1988). Canonical discriminant analysis can utilize the prior information available about the relationships between some of the
Interpretation of loadings
The scores of observations on a canonical axis are determined by multiplying each variable by the corresponding element of the eigenvector. This suggests that an element of the eigenvector (or the loading of the variable on the canonical axis) should reflect the relative importance of the variable which it represents. However, this is true only indirectly, because the numerical values of the loadings also reflect the measurement units of the variables. If a variable is expressed in percent, its
Interpretation of scores
Once the original variables have been combined into canonical scores, the scores can be treated exactly like any other variable. Along with the individual observations on the scatter plot, the centroid of a group can be shown enclosed in a circle indicating the bivariate standard error of the centroid (Krzanowski, 1988). The cloud of individual observations in a group can be enclosed in a probability ellipse by assuming that the observations follow a bivariate normal density distribution.
Fig. 3
Answers to the initial questions
From Fig. 3, we can answer two of the four questions initially posed. First, ``Is the subdivision of the Erzgebirge granites into five major groups justified on the basis of geochemical composition?''. Fig. 3 demonstrates that the five-group classification is valid and there is very little overlap between the groups. We can quantitatively assess the distinction between the groups by counting the misclassifications resulting from the canonical analysis (Table 1). The misclassification rate is
Selecting the best variables
The question of the most effective geochemical variables for classifying Erzgebirge granites cannot be derived from either Fig. 2, Fig. 3 because the answer is presupposed in the selection of the 10 variables used in the canonical analysis. Selecting the appropriate variables for canonical analysis is difficult because the variables interact in unpredictable ways so it is not possible to determine a unique, optimal combination of variables using stepwise procedures analogous to those of
Effectiveness of variables
The final canonical analysis was preceded by a series of more limited statistical studies; the results of these provide additional insight into the information content of the geochemical data available for the Erzgebirge magmatites. Each major category of variable (major oxide, trace element and ratio variable) was analyzed separately to determine how effectively the major groups could be distinguished. The results are essentially equivalent, suggesting that multivariate statistical
Comparison with traditional variables
The geochemical variables selected for this study have been chosen entirely on the basis of statistical considerations, without regard to geological processes, petrochemical relationships or the traditional use of certain geochemical measurements. The question naturally arises as to how well the statistically selected suite of variables performs in comparison to a more traditional selection of variables such as that on which the current classification of the Erzgebirge was based. Since the
Conclusions
Multivariate statistical techniques, particularly canonical discriminant analyses of compositional data, have proved useful in distinguishing the granite plutons of the Erzgebirge region. Graphical plots of observations on the first two canonical axes allow relationships between plutons to be inferred and permit the assignment of rhyolite specimens of unknown affiliation to the major plutonic classes.
For mathematical reasons, it is not possible to select an unambiguously `best' combination from
Note on software
Most statistical calculations for this study were made using JMP v. 3.2, an interactive data analysis package for Macintosh computers. Because the full data set contained more variables than could be accommodated by JMP, stepwise analyses were made using the STEPDISC procedure in SAS/STAT v. 6.0 on a UNIX workstation. Both software products are from SAS Institute, Cary, NC.
Acknowledgements
The authors would like to thank R. Naumann, P. Dulski, M. Zimmer, H.-G. Plessen and E. Kramer (all GFZ Potsdam) for performing the geochemical analyses and G. Bohling for helping with computations on a UNIX workstation.
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