A Log-linear model of grain size influence on the geochemistry of sediments

Sediment composition is mainly controlled by the nature of the source rock(s), and chemical (weathering) and physical processes (mechanical crushing, abrasion, hydrodynamic sorting) during alteration and transport. Although the factors controlling these processes are conceptually well understood, detailed quantification of compositional changes induced by a single process are rare, as are examples where the effects of several processes can be distinguished. The present study was designed to characterize the role of mechanical crushing and sorting in the absence of chemical weathering. Twenty sediment samples were taken from Alpine glaciers that erode almost pure granitoid lithologies. For each sample, 11 grain-size fractions from granules to clay (ø grades <-1 to >9) were separated, and each fraction was analysed for its chemical composition. The presence of clear steps in the box-plots of all parts (in adequate ilr and clr scales) against ø is assumed to be explained by typical crystal size ranges for the relevant mineral phases. These scatter plots and the biplot suggest a splitting of the full grain size range into three groups: coarser than ø=4 (comparatively rich in SiO2, Na2O, K2O, Al2O3, and dominated by “felsic” minerals like quartz and feldspar), finer than ø=8 (comparatively rich in TiO2, MnO, MgO, Fe2O3, mostly related to “mafic” sheet silicates like biotite and chlorite), and intermediate grains sizes (4≤ø <8; comparatively rich in P2O5 and CaO, related to apatite, some feldspar). To further test the absence of chemical weathering, the observed compositions were regressed against three explanatory variables: a trend on grain size in ø scale, a step function for ø≥4, and another for ø≥8. The original hypothesis was that the trend could be identified with weathering effects, whereas each step function would highlight those minerals with biggest characteristic size at its lower end. Results suggest that this assumption is reasonable for the step function, but that besides weathering some other factors (different mechanical behavior of minerals) have also an important contribution to the trend. Key words: sediment, geochemistry, grain size, regression, step function

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

L'Emmagatzematge de cereals en sitges d'època ibèrica al nord-est de Catalunya

Una sitja és una cavitat subterrània destinada a emmagatzemar la collita, especialment de cereals. Amb el manteniment d'unes condicions ideal de temperatura i humitat els cereals s'hi poden conservar durant un llarg període de temps, que segons Varró podria arribar als 50 anys. Aquestes excepcionals possibilitats han possibilitat que l'emmagatzematge en sitges fos un dels mètodes de conservació de cereals a llarg termini més utilitzat en les societats pre-industrials de tot el món. La sitja estàndard del nord-est de Catalunya és aquella que era excavada a l'argila, no portava revestiment i tenia la boca en forma de tub, de 0,77 m de diàmetre màxim per 0,42 de profunditat. El perfil era de tipus còncau, amb el diàmetre màxim situat en el terç central de la sitja, i un fons indistintament còncau o pla. La profunditat i el diàmetre màxim es situarien entre 1,75 i 2 m., amb un marge de diferència reduïdíssim entre ambdues mesures. La capacitat resultant d'aquestes dimensions se situaria entre 1 i 3 tones de cereals, que en termes estàndards de producció seria el resultat de la collita d'una extensió d'entre 1,5 i 4 hectàrees de terreny. ASBTRACT: A silo is an underground cavity designed to store the harvest, especially grain. With the maintenance of ideal conditions of temperature and moisture grains can be preserved for a long period of time, according to Varró it could reach 50 years. These exceptional opportunities have enabled the storage silos to be one of the methods of long-term conservation of grain used in most pre-industrial societies around the world. The standard silo from the North-East of Catalonia was excavated in clay,it had no siding and its mouth was tube-shaped, up to 0.77 m of maximum diameter to 0.42 deep. The profile was concave, with maximum diameter located in the central third of the silo, and a background either concave or flat. The depth and maximum diameter are located between 1.75 and 2 m, with a very little margin of difference between the two measures. The capacity resulting from these dimensions would be located between 1 and 3 tons of cereals, which in terms of production standards it would mean a harvest of between 1.5 and 4 hectares of ground.