Modelling the joint variability of grain size and chemical composition in sediments

The geochemical composition of siliciclastic sediments correlates strongly with grain size. Hence, geochemical composition may serve as a grain-size proxy. In the absence of grain-size variations, geochemical data of siliciclastic sediments may be used to characterise size-independent processes, i.e., sediment provenance, weathering, mixing, shape/density sorting and diagenesis. In general, however, geochemical data sets contain both types of information. In order to formalise interpretation of geochemical data, we propose a mathematical method to decompose the total geochemical variability of a series of genetically related specimens into a grain-size dependent (the shared signal) and a grain-size independent part (the residual signal). The former may serve as a proxy for grain size whereas the latter represents geochemical variability that would have been observed if all sediments would have had the same grain-size distribution. The two data sets are jointly decomposed by means of Partial Least Squares (PLS) and orthogonal projection. Subsequently, the presence of significant grain-size independent geochemical variability in the residual signal is determined in a statistically rigorous manner using a χ ²-test. Using a synthetic example, we show that the residual record effectively reveals an imposed provenance signal which could not have been resolved from the geochemical or grain-size data sets individually. We analysed the relation between grain size and geochemical composition in three Quaternary marine sediment cores located offshore West Africa and South America (GeoB7920-2, GeoB9508-5 and GeoB7139-2). Both sites are characterised by biogenic sediment input, in addition to fluvial and aeolian sediment input from the continent. It was found that all cores show a strong, but different correlation between the mean grain size and the bulk geochemical composition. These results demonstrate that geochemical grain-size proxies are empirical and site-specific. It was also found that the geochemical and grain-size data in cores GeoB7920-2 and GeoB7139-2 do not contain unique information, whereas in core GeoB9508-5 Ti varies independently from the grain size. This residual Ti-signal correlates with the transport mechanism, as demonstrated by statistically different values of aeolian and fluvial-dominated sediments. However, a unique interpretation of this residual signal in terms of the postulated grain-size independent mechanisms could not be provided without additional information. We conclude that the proposed model facilitates identification and validation of different element ratios as grain-size proxies and, more importantly, as proxies for size-independent processes. For this reason, the model paves the way for rigorous analysis of multi-proxy data, which are widely used in palaeoceanographic and palaeoclimatic research.