Clays and Clay Minerals, Vol. 56, No. 3, 389–395, 2008.
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Authors
Martin, Miguel Angel
Garcia-gutierrez, Carlos
Issue Date
2008
Type
Article
Language
Keywords
Periodicals , Geology , Fractals , Fragmentation , Iterated Function Systems , Log-selfsimilarity , Particle-size Distribution , Random Cascades , Soil
Alternative Title
Log Selfsimilarity Of Continuous Soil Particle-size Distributions Estimated Using Random Multiplicative Cascades.
Abstract
Particle-size distribution (PSD) is a fundamental soil property usually reported as discrete clay, silt, and sand percentages. Models and methods to effectively generate a continuous PSD from such poor descriptions using another property would be extremely useful to predict and understand in fragmented distributions, which are ubiquitous in nature. Power laws for soil PSDs imply scale invariance (or selfsimilarity), a property which has proven useful in PSD description. This work is based on two novel ideas in modeling PSDs: (1) the concept of selfsimilarity in PSDs; and (2) mathematical tools to calculate fractal distributions for specific soil PSDs using few actual texture data. Based on these ideas, a random, multiplicative cascade model was developed that relies on a regularity of scale invariance called ‘logselfsimilarity.’ The model allows the estimation of intermediate particle size values from common texture data. Using equivalent inputs, this new modeling approach was checked using soil data and shown to provide greatly improved results in comparison to the selfsimilar model for soil PSD data. The Kolmogorov-Smirnov D-statistic for the log-selfsimilar model was smaller than the selfsimilar model in 92.94% of cases. The average error was 0.74 times that of the selfsimilar model. The proposed method allows measurement of a heterogeneity index, H, defined using Ho¨ lder exponents, which facilitates quantitative characterization of soil textural classes. The average H value ranged from 0.381 for silt texture to 0.838 for sandy loam texture, with a variance of <0.034 for all textural classes. The index can also be used to distinguish textures within the same textural class. These results strongly suggest that the model and its parameters might be useful in estimating other soil physical properties and in developing new soil PSD pedotransfer functions. This modeling approach, along with its potential applications, might be extended tofi ne-grained mineral and material studies.
Description
Clays and Clay Minerals, Vol. 56, No. 3, 389–395, 2008. Log Selfsimilarity Of Continuous Soil Particle-size Distributions Estimated Using Random Multiplicative Cascades. Miguel Angel Martin; Carlos Garcia-gutierrez. DOI: 10.1346/CCMN.2008.0560308. Copyright © 2008, The Clay Minerals Society.
Citation
Clays and Clay Minerals, Vol. 56, No. 3, 389–395, 2008.
Publisher
The Clay Minerals Society
License
Copyright © 2006-2018, The Clay Minerals Society