Alex George Lipp , Oliver Shorttle , Frank Syvret, Gareth G Roberts 

The elemental composition of a sediment is set by the composition of its protolith
and modified by weathering, sorting, and diagenesis. An important problem is deconvolving these contributions to a sediment’s composition to arrive at information about processes
that operate on the Earth’s surface. We approach this problem by developing a predictive and
invertible model of sedimentary major-element composition. We compile a dataset of sedimentary rock, river sediment, soil, and igneous rock compositions. Principal component
analysis of the dataset shows that most variation can be simplified to a small number of variables. We thus show that any sediment’s composition can be described with just two vectors
of igneous evolution and weathering. We hence define a model for sedimentary composition
as a combination of these processes. A 1:1 correspondence is observed between predictions
and independent data. The log-ratios ln(K 2 O/MgO) and ln(Al 2 O 3 /Na 2 O) are found to be
simple proxies for respectively the model’s protolith and weathering indices. Significant deviations from the model can be explained by sodium-calcium exchange. Using this approach,
we show that the major-element composition of the upper continental crust has been modified by weathering and we calculate the amount of each element that it must have lost to
modify it to its present composition. By extrapolating modern weathering rates over the age
of the crust we conclude that it has not retained a significant amount of the necessarily produced weathering restite. This restite has likely been subducted into the mantle, indicating a
crust-to-mantle recycling rate of 1.33 ± 0.89 × 10 13 kg yr −1 .