Numerical
modeling has become a powerful tool in several fields of geosciences,
but a comprehensive model to describe the composition of clastic
sediments is still lacking. This project aims at developing a
numerical-statistical model
that allows for describing quantitatively the
petrographic, chemical, and granulometric changes related to the
overall transfer of material from the original source rock to the
sediment at the final site of deposition. These relative changes of
sediment composition (as compared to the initial source) are largely
controlled by tectonics, physiography, climate, and transport energy.
The model is intended for both inductive and deductive approaches.
Potential applications of the model might be, for example, the
prediction of sediment composition under well-known geologic
conditions and the reconstruction of sediment provenance based on
final composition. To achieve this general goal, we are working in
two subgoals: (1) the broadening of our
theoretical understanding of so-called *multi-way
compositions *(e.g., data sets
simultaneously reporting grain size, chemistry, *and*
mineralogy of sediment samples) and (2) modelling
of multi-way compositional change in several case studies.

**Keywords**: compositional data analysis,
diagenesis, log-linear models, quantitative provenance analysis,
weathering.

- Basics about compositional data analysis: Compositional data in a nutshell

. Blatt, Middleton and Murray (1972) published a plot where they conveyed "the probable relationship between grain size and detrital fragment composition, based on the limited data currently available". The plot gives, for the range of grain sizes occurring in nature, the composition on five parts (rock fragments, poly-crystalline quartz, mono-crystalline quartz, feldspar and mica). Our goal here is to fit an Aitchison (1986) trend to this data, by means of regression of a composition on grain size. The theory underlying the solution to this problem is available here, and a nice presentation here. A paper (under revision) has been accepted in**A global model of evolution of sediment lithic composition with grain size variations***Mathematical Geosciences*.-
. Granulometric curves (equivalent to probability densities) can be treated within the framework of the Hilbert space structure proposed and developed by Egozcue and Diaz-Barrero (CoDaWork'03), and by van den Boogaart (CoDaWork'05). One takes logs of the measured density curve, and regresses the result against a (low) number of orhonormal polynomials. The chosen polynomials should be orthogonal with respect to a given reference density (**Exploring the geometry of granulometric curves***exponential*if the dominant process is comminution,*normal*if the dominant process is sorting vs. mixture,*uniform*for unknown dominant process). A preliminary talk is available here, and a more evolved material will be presented at CoDaWork'08. -
. That the geochemistry of a sediment depends on its grain size is a well-known fact. The factors underlying that control are also quite known, but nevertheless still poorly**A local model of dependence of geochemistry on grain size***quantified*. Of goal here is to derive a predictive model, able to tell us what should we expect to find when measuring the geochemistry of a sediment given its grain size fraction (and explain why). The data set used was obtained from moraines and streams of a glacial area in the Alps (in a granitic/granodioritic massif): samples were sieved in 11 one-unit-phi intervals, and each fraction was analysed for major oxide and trace element concentrations. Results suggest that the strongest control in this case is the inherited characteristic crystal size of each mineral in the parental rock. No chemical weathering is observed, as the resulting geochemical evolution can be perfectly explained by invoking three main characteristic crystal sizes (from -1 to 4, from 4 to 7 and finer than 7 phi) and a slight difference on the mechanical properties of phyllosilicates against other components. This material will be presented at CoDaWork'08. The necessary theory regarding regression of compositional responses has been submitted to Computers & Geosciences.