An investigation has been undertaken of the effects of selective grain sorting on the ability of factor analyses to identify source end-members within heavy-mineral assemblages. Q-mode factor analysis of samples randomly collected from the beach at Otter Rock, Oregon, yielded two factors; one is dominated by augite, hornblende and hypersthene, and the second consists of garnet plus zircon. These factors correspond closely to selective-sorting patterns of minerals on this beach determined from a series of samples along a beach profile collected during a period of beach-face erosion. Factor analysis of those profile samples showed that the garnet and zircon are associated with the high-density opaques which tend to concentrate at the landward limit of wave run-up, while the lower density augite, etc., are transported to the outer surf zone. Factor analyses were also performed on a synthetic data set which simulates the along-coast mixing of mineral assemblages from four spatially distinct sources. Analyses involved pure mixtures of source end-members, mixtures where random errors were introduced to simulate counting uncertainties, and mixtures of the end-members where systematic changes were added to simulate the effects of local grain sorting. The results indicate that sorting can significantly affect the results from factor analyses, with new factors introduced and with random irregularities produced in the spatial patterns of the factors.

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