Grain-Size Control on Petrographic Composition of Sediments: Compositional Regression and Rounded Zeros

Abstract

It is well-known that sediment composition strongly depends on grain size. A number of studies have tried to quantify this relationship focusing on the sand fraction, but only very limited data exists covering wider grain size ranges. Geologists have a clear conceptual model of the relation between grain size and sediment petrograpic composition, typically displayed in evolution diagrams. We chose a classical model covering grain sizes from fine gravel to clay, and distinguishing five types of grains (rock fragments, poly-and mono crystalline quartz, feldspar and mica/clay). A compositional linear process is fitted here to a digitized version of this model, by (i) applying classical regression to the set of all pairwise log-ratios of the 5-part composition against grain size, and (ii) looking for the compositions that best approximate the set of estimated parameters, one acting as slope and one as intercept. The method is useful even in the presence of several missing values. The linear fit suggests that the relative influence of the processes controlling the relationship between grain size and sediment composition is constant along most of the grain size spectrum.

Time-Based Data in Occupational Studies: The Whys, the Hows, and Some Remaining Challenges in Compositional Data Analysis (CoDA)

“…Since then, CoDA has become an established framework of how to handle compositional data in, e.g. nutritional epidemiology ( Leite, 2016 ), geology ( Tolosana-Delgado and von Eynatten, 2009 ), and chemistry ( Buccianti and Pawlowsky-Glahn, 2005 ). However, in public and occupational health sciences, CoDA has gained attention only recently ( Pedišić, 2014 ; Chastin et al , 2015 ; Pedisic et al , 2017 ; Dumuid et al , 2018b ; Foley et al , 2018 ; Bauman et al , 2019 ), with few papers devoted to exposures at work ( Gupta et al , 2018a , 2019 ; Rasmussen et al , 2018 ; Hallman et al , 2019 ; Coenen et al , 2020 ).…”

Occurrence of palygorskite and sepiolite in upper Paleocene–middle Eocene marine deep sediments of the Lagonegro Basin (Southern Apennines—Italy): Paleoenvironmental and provenance inferences

“…A useful tool to deal with problems related to the interaction among different source compositions, weathering history and diagenesis, is the principal component analysis (PCA). In this analysis we have taken into account the specific nature of compositional data (e.g., Aitchison, 1986Filzmoser et al, 2010;Montero-Serrano et al, 2009;Tolosana-Delgado and von Eynatten, 2010;Weltje, 1997), i.e., the fact that each variable is non-negative and that all variables sum to a constant c (Aitchison, 1986 Prior to the analysis the data were transformed using isometric logratio (ilr) to apply methods based on standard robust covariance estimators (Filzmoser et al, 2009 and references therein). In order to explore the dataset we used the biplot, a joint graphical representation of variables and cases, projected onto principal-component planes.…”

A geological delayed response model for stratigraphic reconstructions

“…hence the partial derivative ∂u ∂t is underestimated by a limit erosion velocity E = E (t, x), depending on the climate and the age of the sediments; significantly, the erosion velocity increases with decreasing grainsize (according to the Hjulström-Sundborg diagram [6] which shows several key concepts about empirical relationships between erosion, transportation and deposition; see also [37]). One is led to the inequality with a moving obstacle ∂u ∂t + E ≥ 0 a.e.…”