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Variability in iceberg discharge and deep-ocean circulation in the North Atlantic during the last glacial period is inferred from the grain-size distribution and trace elemental composition of terrigenous sediments in a deep-sea core taken on Reykjanes Ridge, south of Iceland. End-member modeling of the grain-size distributions is used to unmix the signals of varying bottom-current speed and iceberg discharge. The size distribution within the silt fraction appears to be influenced by both factors. Based on Th-Sc-La relationship, we established that during the ice-rafted detritus events, continental material of likely Greenlandic origin increased to 87%, and that bottom-current-derived material contains to 40% mid-oceanic ridge fines, probably of Icelandic origin. Our results have important implications for the use of silt grain size as an indicator for paleocurrent speed in the glacial North Atlantic. We show that reconstructions of variations in bottom-current speed based on the raw grain-size data are opposite to inferences from the unmixed record. The latter indicates that deep-water convection decreased during periods of enhanced iceberg discharge, which is in general agreement with paleoceanographic reconstructions of the North Atlantic. Keywords: ocean circulation, iceberg discharge, brain-size distribution, end-member modeling, trace element geochemistry.

Detrital modes are the basic type of quantitative data used in sedimentary petrology. They represent estimates of the petrographic framework composition of sand or sandstone obtained by point counting of thin sections. At present, geological references from analysis of these numerical data are semi-quantitative only, because many of the data-processing methods employed in sedimentary petrology lack a firm theoretical basis. A review of existing methods reveals a number of fundamental statistical problems associated with the use of univariate statistics and the construction of so-called hexagonal fields of compositional variation. It is shown that these problems can be overcome by using multivariate methods that honour the non-negativity and unit-sum constraints on compositional data, and incorporate the covariance structure. Spread in compositional data can be modelled on two levels: (1) by regarding the grain as unit of observation, and the total point count as a sample from a multinomial distribution; (2) by regarding the total count as unit of observation, and a set of counts as a sample from an additive logistic normal distribution. Numerical methods are presented for constructing statistically rigorous confidence regions in ternary diagrams by inversion of significance tests for these two distributions. Statistical analyses of the framework composition and heavy-mineral assemblages of modern beach and river sands illustrate their use. The case histories are followed by a brief overview of popular multivariate methods for reconstructing sediment provenance. Keywords: sediment provenance; compositional data; ternary diagrams; confidence regions; multivariate statistics