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Multifractal Characterization of Soil Pore Systems

^a International Potato Center (CIP), P.O. Box 1558, Lima 12– Perú and Universidad Mayor de San Marcos, FCF-DAFI, P.O. Box 10584, Lima 1- Perú
^b Dep. of Environmental Sciences, Rutgers Univ., 14 College Farm Road, New Brunswick, NJ 08901
^c International Potato Center (CIP), P.O. Box 1558, Lima 12– Perú
^d Dep. of Land Resource Science, Univ. of Guelph, Guelph, ON, Canada

View larger version (88K): [in a new window]   Fig. 1. Illustration of multifractal theory applied to a binary image. (a) binary image of Soil 7 (500 x 750 pixels), spatial pattern of probabilities Pi(L) calculated with Eq. [3] using (b) L = 10 and (c) L = 50 pixels, and spatial pattern of the exponent i estimated with Eq. [4] using (d) L = 10 and (e) L = 50 pixels.

View larger version (14K): [in a new window]   Fig. 2. Examples of application of (a) Eq. [12], and (b) Eq. [13] to the binary image of Soil 7 for selected q values. Values of f(q) and (q) were obtained from the slope of plots similar to those in (a) and in (b), respectively. The plot of (q = -1.0) illustrates data that resulted in R2 = 0.88, one of the lowest found in this study (R2 for the rest of the plots can be found in Table 3).

View larger version (11K): [in a new window]   Fig. 3. Example of f(q) and (q) functions estimated in the range of q values in which the numerators of Eq. [12] and [13] were linear with log L (see Fig. 2).

View larger version (67K): [in a new window]   Fig. 4. Binary images of the studied soil thin sections separated in groups of similar pore properties.

View larger version (31K): [in a new window]   Fig. 5. Selected cumulative distributions of pore area measured on binary images.

View larger version (11K): [in a new window]   Fig. 6. f()-spectra for soils in (a) Group 1, (b) Group 2, and (c) Group 3, as shown in Fig. 4.

View larger version (12K): [in a new window]   Fig. 7. Plots of (a) (0) vs. D0 and (b) widths of -intervals: (0) - (qi,+) vs. (qi,-) - (0) for soils in the three groups considered. The numerical values of qi,+ and qi,- were the same and equal to the smallest of the two values defining a q interval (see Table 3). Proximity to the 1:1 line implies (a) more homogeneous distributions, or (b) more symmetric f()-spectra. In plot (b) two soils of Group 2 had identical values and show as one point in the graph.