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1 Geologisch-Palaontologisches Institut und Museum der Universitat Kiel, Olshausenstrasse 40, D-2300 Kiel, Germany
2 British Geological Survey, Keyworth, Nottingham NG12 5GG, UK
Garnet compositions from sandstones of the Middle Jurassic Brent Group of the Oseberg Field, northern North Sea, have been treated statistically in order to assess objectively their value in stratigraphic classification and grouping and for provenance analysis. The data set consists of the compositions of 1550 garnet grains from three wells, as determined by electron microprobe analysis. The statistical techniques used include summary statistics, exploratory data analysis, analysis of correlation structure and of subcompositions, discriminant analysis and fuzzy clustering. General univariate statistics provide the characteristic properties of the data distribution pattern. Almandine is the prevailing component, followed by pyrope, grossular and spessartine. Variation in the bulk data is generally low except for many high spessartine outliers. Stepwise linear discriminant analysis is the first step in stratigraphic grouping of the samples and in end-member modelling. Using all 1550 garnet grains, group classification and separation is efficient for the Tarbert Formation and the Etive-Oseberg interval, but not for the Ness Formation. End-member analysis by fuzzy c-means clustering generates similar stratigraphic garnet logs to those generated by discriminant analysis, the advantage of the method being that fuzzy clustering allows a dynamic interpretation by assuming that the calculated cluster centres represent the garnet compositions of source rocks or source areas. There is an overall increase in almandine with time: the Etive-Oseberg interval is characterized by high pyrope contents: the Ness Formation has high grossular and spessartine contents and depletion of pyrope: and the Tarbert Formation is depleted in grossular. Therefore multivariate end-member modelling of garnet compositions has provided objective criteria for classifying and differentiating samples. The resulting grain and sample distribution patterns provide a clearer picture of the stratigraphic variations than those obtained by using the geochemically-defined garnet end members.
