Multifractal Characterization of Soil Particle‐Size Distributions

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Abstract
A particle‐size distribution (PSD) constitutes a fundamental soil property correlated to many other soil properties. Accurate representations of PSDs are, therefore, needed for soil characterization and prediction purposes. A power‐law dependence of particle mass on particle diameter has been used to model soil PSDs, and such power‐law dependence has been interpreted as being the result of a fractal distribution of particle sizes characterized with a single fractal dimension. However, recent studies have shown that a single fractal dimension is not sufficient to characterize a distribution for the entire range of particle sizes. The objective of this study was to apply multifractal techniques to characterize contrasting PSDs and to identify multifractal parameters potentially useful for classification and prediction. The multifractal spectra of 30 PSDs covering a wide range of soil textural classes were analyzed. Parameters calculated from each multifractal spectrum were: (i) the Hausdorff dimension, f(α); (ii) the singularities of strength, α; (iii) the generalized fractal dimension, Dq; and (iv) their conjugate parameter the mass exponent, τ (q), calculated in the range of moment orders (q) of between −10 and +10 taken at 0.5 lag increments. Multifractal scaling was evident by an increase in the difference between the capacity D0 and the entropy D1 dimensions for soils with more than 10% clay content. Soils with <10% clay content exhibited single scaling. Our results indicate that multifractal parameters are promising descriptors of PSDs. Differences in scaling properties of PSDs should be considered in future studies.

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