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Garnet chemistry provides a well-established tool in the discrimination and interpretation of sediment provenance. Current discrimination approaches, however, (i) suffer from using less variables than available, (ii) subjective determination of discrimination fields with strict boundaries suggesting clear separations where in fact probabilities are converging, and (iii) significant overlap of compositional fields of garnet from different host-rock groups. The new multivariate discrimination scheme is based on a large database, a hierarchical discrimination approach involving three steps, linear discriminant analysis at each step, and the five major host-rock groups to be discriminated: eclogite-(A), amphibolite-(B) and granulite-(C) facies metamorphic rocks as well as ultramafic (D) and igneous rocks (E). The successful application of statistical discrimination approaches requires consideration of the a priori knowledge of the respective geologic setting. This is accounted for by the use of prior probabilities. Three sets of prior probabilities (priors) are introduced and their advantages and disadvantages are discussed. The user is free to choose among these priors, which can be further modified according to the specific geologic problem and the level of a priori knowledge. The discrimination results are provided as integrated probabilities of belonging to the five major host-rock groups. For performing calculations and results a supplementary Excel® spreadsheet is provided. The discrimination scheme has been tested for a large variety of examples of crystalline rocks covering all of the five major groups and several subgroups from various geologic settings. In most cases, garnets are assigned correctly to the respective group. Exceptions typically reflect the peculiarities of the regional geologic situation. Evaluation of detrital garnets from modern and ancient sedimentary settings of the Western Gneiss Region (Norway), Eastern Alps (Austria) and Albertine Rift (Uganda) demonstrates the power to reflect the respective geologic situations and corroborates previous results. As most garnet is derived from metamorphic rocks and many provenance studies aim at reconstructing the tectonic and geodynamic evolution in the source area, the approach and the examples emphasize discrimination of metamorphic facies (i.e., temperature-pressure conditions) rather than protolith composition.

Detrital zircon U-Pb age distributions derived from samples representing ancient or relatively young large

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