Keywords:X-ray computed tomography of soil Image analysis Soil pore space Soil spatial variability Long-range dependence Multifractal analysis Hurst exponent A correct statistical model of soil pore structure can be critical for understanding flow and transport processes in soils, and creating synthetic soil pore spaces for hypothetical and model testing, and evaluating similarity of pore spaces of different soils. Advanced visualization techniques such as X-ray computed tomography (CT) offer new opportunities of exploring heterogeneity of soil properties at horizon or aggregate scales. Simple fractal models such as fractional Brownian motion that have been proposed to capture the complex behavior of soil spatial variation at field scale rarely simulate irregularity patterns displayed by spatial series of soil properties. The objective of this work was to use CT data to test the hypothesis that soil pore structure at the horizon scale may be represented by multifractal models. X-ray CT scans of twelve, water-saturated, 20-cm long soil columns with diameters of 7.5 cm were analyzed. A reconstruction algorithm was applied to convert the X-ray CT data into a stack of 1480 grayscale digital images with a voxel resolution of 110 microns and a cross-sectional size of 690 x 690 pixels. The images were binarized and the spatial series of the percentage of void space vs. depth was analyzed to evaluate the applicability of the multifractal model. The series of depth-dependent macroporosity values exhibited a welldefined multifractal structure that was revealed by singularity and Rényi spectra. The long-range dependencies in these series were parameterized by the Hurst exponent. Values of the Hurst exponent close to one were observed indicating the strong persistence in variations of porosity with depth. The multifractal modeling of soil macropore structure can be an efficient method for parameterizing and simulating the vertical spatial heterogeneity of soil pore space.
In this paper, several features of pore-size soil distribution are first analyzed, suggesting that they are closer to those of singular measures than to those of distributions with smooth density. In a second step, the weighted singularity strength of an experimental measure obtained by image analysis of soil samples is evaluated. The results of this analysis show the singular nature of pore-size distribution. Finally, the distribution is characterized by means of a spectrum of entropies computed on distorted measures associated with the original experimental measure.
Abstract. The notion of representative elementary area (REA) developed to address heterogeneity and scale problems in quantitative soil pedology comes from the notion of representative elementary volume of fluid dynamics in porous media. The REA allows the identification of the minimum area of a soil block section that is required to represent the pedofeature of interest based on its distribution in soil space. In this paper eight samples were imaged with two different techniques: the confocal microscope and the conventional film camera. These techniques provided information about pore sizes between 3.62 µm and 161.98 µm, and between 39.72 µm and 1776.34 µm, respectively. Sixteen of the resulting digital images were then analyzed to investigate the representative elementary area of the multifractal patterns of the spatial distribution of voids related to the micro and macroporosity by means of the entropy dimension. Our results permit the location of the REA region over the domain of the microstructures rendered by the analysis of the microscope images. They also suggest that this region seemingly spans scales of the macrostructures as revealed by the analysis of the camera pictures.
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