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Soil Mass, Surface, and Spectral Fractal Dimensions Estimated from Thin Section Photographs

Dep. of Agricultural Chemistry and Soil Science, Univ. of Sydney, NSW 2006, Australia

E. A. FitzPatrick

Dep. of Plant and Soil Science, Univ. of Aberdeen, AB9 2UE Scotland

*Corresponding author (a.anderson{at}agec.usyd.edu.au).

ABSTRACT

Aspects of fractal geometry have been used to give quantitative measurements of soil structure. Fractal dimensions measured were the mass fractal dimension (D_m), surface fractal dimension (D_s), and the spectral dimension (d). We investigated the fractal component of a computer program, STRUCTURA, which measures the fractal dimension of soil from images of soil thin sections. Six thin sections, each showing different structural characteristics, were analyzed in order to obtain a range of fractal dimensions. The dimensions, in particular D_m and d, were shown to discriminate the different structures. The values of D_m and d ranged from 1.682 to 1.852 and 1.236 to 1.668, respectively. A further objective was to use these results, together with fractal theory, to show the potential fractal geometry has in predicting physical processes such as diffusion within the soil. To assist with the interpretation of fractal dimensions, the dimensions of different soil samples with the same porosity were compared.

Received for publication March 1, 1995.

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