An R-Based Function for Modeling of End Member Compositions
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An R-Based Function for Modeling of End Member Compositions Martin Seidel1 · Mario Hlawitschka2
Received: 15 May 2014 / Accepted: 17 July 2015 © International Association for Mathematical Geosciences 2015
Abstract Clastic sediment grains have been exposed to numerous physical and chemical processes during erosion, transport and accumulation. It is widely accepted that weathering and sorting processes are strongly controlled by climate, making grain-size distributions a potential recorder for paleoenvironmental conditions. Polymodal grainsize distributions of sediments are in general a result of mixing of unimodal grain-size distributions (end members) from different sources. Thus, unmixing of polymodal grain-size distributions into their unimodal end member compositions (end member modeling) provides a powerful method for revealing sediment sources and environmental conditions of the past. Since the early 1960s, several algorithms for unmixing of such compositional data were published. However no source code is available in a modern open access programming language. This study provides an algorithm and some additional functions for the decomposition of compositional data into endmember compositions based on a free available statistical programming language. The source code is provided as supplementary materials. To prove the functionality of the algorithm, end member models of sandstone compositions and grain-size distributions were calculated. Keywords
End member modeling · Unmixing · Grain size distribution · R
Electronic supplementary material The online version of this article (doi:10.1007/s11004-015-9609-7) contains supplementary material, which is available to authorized users.
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Martin Seidel [email protected]
1
Institute of Geophysics and Geology, Leipzig University, Talstrasse 35, 04103 Leipzig, Germany
2
Department of Computer Science, Leipzig University, Augustusplatz 10, 04109 Leipzig, Germany
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Math Geosci
1 Introduction Sorting and mixing of particles are crucial geological processes in nature. Sorting occurs during the transport of erosional products from its source area toward the site of deposition and is a function of particle size, flow velocity, and transport medium (Hjulström 1935; Pye 1987; Sundborg 1967). When erosional products from different origin and/or transport processes are deposited at the same site, different unimodal grain-size populations, so-called end members, are mixed together and may lead to polymodal grain-size distributions with each mode representing different transport or depositional processes (Folk and Ward 1957; Tanner 1964). Since erosion, sediment transport, and sediment deposition are linked to climatic conditions, paleoenvironmental information may be recorded in grain-size distributions. Grain-size distributions as well as many other geological data are compositional data. Compositional data of single samples can be interpreted as a nonnegative vector whose components (variables) are a proportion of a whole, summarizing to a constant sum
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