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Multifractal Characterization of Soil Particle-Size Distributions

Adolfo N. D. Posadasa, Daniel Giménez*,a, Marco Bittellib, Carlos M. P. Vazb and Markus Fluryb

a Dep. of Environmental Sciences, Rutgers Univ., 14 College Farm Road, New Brunswick, NJ 08901
b Embrapa Agricultural Instrumentation Center, P.O. Box 741, 13560-970, São Paulo, S.P., Brazil



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Fig. 1. Soil textural triangle according to the Soil Survey Division Staff (1993), showing the range of soils studied. Three groups of selected soils are distinguished based on variations in the content of two soil separates while keeping the third one approximately constant. Soils in Group 1 ({circ}) vary along the silt and sand axis. Soils in Group 2 ({blacksquare}) vary along the clay and sand axis. Soils in Group 3 (•) vary along the silt and clay axis. Open squares represent all other soils in the database.

 


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Fig. 2. Plots of {sum}Ni=1 µi (q, L) log[µi (q, L)] vs. log (L) for q = 0 and q =1 for the particle-size distributions of (a) the Les Barges, and (b) the Dusk Red Latosol 1 soils. For explanation see text.

 


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Fig. 3. Example of f({alpha})-spectra for the Les Barges and Dusk Red Latosol 1 soils.

 


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Fig. 4. Plot of differences (D0 - D1) and {f[{alpha}(-1)] - D0} as a function of clay content.

 


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Fig. 5. Plots of {tau}(q) vs. q for soil groups shown in Fig. 1, (a) Group 1, (b) Group 2, and (c) Group 3. All soils with clay content <10% exhibited spectra similar to those in Group 1 (data not shown).

 


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Fig. 6. Plot of the capacity dimension, D0, the entropy dimension, D1, and the correlation dimension, D2, as a function of clay content for all soils.

 





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