BEMMA: A Hierarchical Bayesian End-Member Modeling Analysis of Sediment Grain-Size Distributions
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BEMMA: A Hierarchical Bayesian End-Member Modeling Analysis of Sediment Grain-Size Distributions Shi-Yong Yu1,2 · Steven M. Colman2 · Linxiong Li3
Received: 31 July 2014 / Accepted: 1 August 2015 © International Association for Mathematical Geosciences 2015
Abstract Sediment grain-size distributions provide rich information about sedimentary dynamics and potentially about environmental and climatic changes. However, entrainment, transport, and deposition, as a sequence of sorting process, modify original grain-size distributions of source materials, thereby resulting in complex distribution forms that are commonly multimodal and asymmetrical. However, neither traditional descriptive statistics nor curving fitting methods are able to address this complexity fully. End-member modeling analysis, essentially based on polytope expansion, stands out as a flexible and robust method for the unmixing of sediment grain-size distributions. Yet there are still several key issues that remain unresolved. Here a hierarchical Bayesian end-member modeling analysis of grain-size distributions, fully subject to the non-negative and unit-sum constraints on the distributions, is presented. Within the Bayesian framework, the number of end members, as well as the end-member spectra and fractions can be inferred sequentially using a reversiblejump Markov chain Monte Carlo algorithm in conjunction with Gibbs samplers. Test runs using both a synthetic and a real-world dataset from a small playa located on the southern margin of the Badain Jaran Desert, NW China, reveal that this model
Electronic supplementary material The online version of this article (doi:10.1007/s11004-015-9611-0) contains supplementary material, which is available to authorized users.
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Shi-Yong Yu [email protected]
1
MOE Key Laboratory of Western China’s Environmental System, Lanzhou University, 222 South Tianshui Road, Lanzhou 730000, China
2
Large Lakes Observatory, University of Minnesota Duluth, 2205 East 5th Street, Duluth, MN 55812, USA
3
Department of Mathematics, University of New Orleans, 2000 Lakeshore Drive, New Orleans, LA 70148, USA
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Math Geosci
can yield geologically meaningful and mathematically optimal outputs, thereby providing a necessary complement and powerful alternative to the existing deterministic methods. Keywords Sediment transport · Grain-size distribution · End member · Unmixing · Markov chain · Monte Carlo
1 Introduction Sediment grain-size distributions have been commonly used to infer past environmental and climatic conditions in a wide variety of geological settings. Sediment entrainment, transport, and deposition are sorting processes (Visher 1969; Ashley 1978; McLaren and Bowles 1985; Le Roux and Rojas 2007), which may be approximated as continuous processes of fractionation both mechanically (grains may break down into smaller sizes) and dynamically (only grains with specific combination of sizes, shapes, and densities will be entrained, transported, or deposited together). Therefore, sediments associated with a specifi
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