The elemental geochemistry of sediments is studied to understand a wide range of topics in the Earth sciences, e.g., the evolution of the continents, the history of the carbon cycle, and the location of mineral deposits. A challenge underlying all these applications is that sedimentary compositions are affected by a wide range of geochemical processes such as weathering, sorting, and mixing. These competing processes make it hard to extract useful signals from a sediment's elemental

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... . In this dissertation I will develop two predictive and invertible models for the elemental composition of a sediment. The first model describes a fine-grained sediment in terms of the composition of its protolith and the intensity of weathering it has experienced. A novel benefit of this model is that it can 'unweather' the composition of a sediment to reveal the theoretical protolith from which it derived. Using this unique approach I deduce the composition of the Archean continents from a large compilation of sedimentary rock compositions. I find the Archean exposed continents to be more silica rich than previously considered, comparable to the present day continents. The second model I develop describes fluvial sediments as a conservative mixture of the geochemistry of the sediments in their upstream drainage basin. This model is tested using a uniquely high-resolution geochemical survey covering the Cairngorms, UK, along with 67 new downstream sediment samples gathered for this dissertation. I demonstrate that the composition of these downstream sediments can be reasonably predicted assuming just conservative mixing of the upstream survey dataset. Given the success of this mixing model, I proceeed to invert it. That is, I develop a model to unmix fluvial sediments to generate a geochemical map of their source regions. I find that this unmixing model, when applied to the downstream dataset, generates upstream predictions that compare favourably to the independent survey dataset. The success of both these models sugges [...]