A quantitative approach to capturing the compositional variability of modern sands

摘要

The petrographic data cube (PDC) is a three-dimensional array designed to characterise compositional variability of sediments. This study focuses on point-count data of modern sands, in which compositional variability may be conveniently factorised into local and regional controls. Several terms that provide a framework for the description of compositional variability, such as transport invariance, fractionation potential and effective count length, are introduced, illustrated, and quantitatively defined. Pearson' s chi-squared statistic, a quantitative measure of compositional homogeneity, allows the efficiency of data-acquisition procedures to be statistically analysed. Analysis of replicates shows that the common strategy of counting a large number of points, designed to minimise random counting error, may ultimately lead to a paradoxical situation to which one is forced to reject the hypothesis of compositional homogeneity that should hold by definition. This apparent inconsistency may be resolved by taking into account that the spread of detrital modes is also controlled by hydrodynamic fractionation. Consequently, the actual number of points counted to arrive at estimates of detrital modes usually exceeds the estimated number of points, N (the effective count length), corresponding to the precision of replicate analyses. This implies that counting more than N points merely reduces the uncertainty in estimated compositions of (sub) specimens, but it does not lead to a better prediction of the composition of the lithosome from which the specimens are derived. Maximisation of the number of specimens is a much more effective strategy to obtain robust composition estimates, because it allows reduction of uncertainties through averaging. An extension of the method, developed to investigate the problem of compositional variability at different spatial scales, permits the length scales of compositionally homogeneous zones (petrofacies) to be characterised in a probabilistic way.