Alex George Lipp , Patrice de Caritat, Gareth G Roberts 

Alluvial sediments have long been used in geochemical surveys as their compositions are assumed to be representative of areas upstream. Overbank and floodplain sediments, in particular, are increasingly used for regional to continental-scale geochemical mapping. However, during downstream transport, sediments from heterogeneous source regions are carried away from their source regions and mixed. Consequently, using alluvial sedimentary geochemical data to generate continuous geochemical maps remains challenging. In this study we demonstrate a technique that numerically unmixes alluvial sediments to make a geochemical map of their upstream catchments. The unmixing approach uses a model that predicts the concentration of elements in downstream sediments, given a map of the drainage network and element concentrations in the source region. To unmix sedimentary chemistry, we seek the upstream geochemical map that, when mixed downstream, best fits geochemical observations downstream. To prevent overfitting we penalise the roughness of the geochemical model. To demonstrate our approach we apply it to alluvial samples gathered as part of the Northern Australia Geochemical Survey. This survey gathered samples collected over a $\sim$ 500,000 km$^2$ area in northern Australia. We first validate our approach for this sample distribution with synthetic tests, which indicate that we can resolve geochemical variability at scales greater than 0.5 -- 1$^{\circ}$ in size. We proceed to invert real geochemical data from the total digestion of fine-grained fraction of alluvial sediments. The resulting geochemical maps for two elements of potential economic interest, Cu and Nd, are evaluated in detail. We find that in both cases, our predicted downstream concentrations match well against a held-out, previously `unseen' subset of the data, as well as against data from an independent geochemical survey. By performing principal component analysis on maps generated for all 46 available elements we produce a synthesis map to identify the significant geochemical domains in this part of northern Australia. This map shows strong spatial similarities to the underlying lithological map of the area. Finally, we compare the results from our approach to geochemical maps produced by interpolating alluvial geochemical data using two standard methods: kriging and inverse distance weighting. We find that, unlike the method presented here, both these methods can generate maps that are dampened relative to expected magnitude, as well as being spatially distorted. We argue that the unmixing approach is the most appropriate method for generating geochemical maps from regional-scale alluvial surveys.