Singularity Features of Pore-Size Soil Distribution: Singularity Strength Analysis and Entropy Spectrum

Caniego, F. J.; Martı́n, Miguel Ángel; Fernando, José F.

doi:10.1142/s0218348x0100066x

Cited by 52 publications

(59 citation statements)

References 31 publications

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“…Muller and McCauley (1992) were the first to characterize the multifractal behavior of the spatial arrangements Correspondence to: F. San José Martínez (fernando.sanjose@upm.es) of pore space in sedimentary rocks. Caniego et al (2001) observed the same pattern for the soil pore size distribution.…”

Section: Introductionsupporting

confidence: 68%

“…Several works have explored the complex nature of soil porosity with multifractal analysis and they have established the suitability of this mathematical tool to characterize this highly irregular feature of soil with binarized images of sections of soil blocks (Muller and McCauley, 1996;Caniego et al, 2001;Posadas et al, 2003;Tarquis et al, 2003;García-Gutierrez and San José, 2004). Different techniques have been developed to acquire digitalized 2-D images.…”

Section: Introductionmentioning

confidence: 99%

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Representative elementary area for multifractal analysis of soil porosity using entropy dimension

Martínez

Caniego

García-Gutiérrez

et al. 2007

Nonlin. Processes Geophys.

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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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Section: Introductionsupporting

confidence: 68%

Section: Introductionmentioning

confidence: 99%

Representative elementary area for multifractal analysis of soil porosity using entropy dimension

Martínez

Caniego

García-Gutiérrez

et al. 2007

Nonlin. Processes Geophys.

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“…(3)) and the Rényi generalized dimensions D q (Eqs. (4) and (5)) (Caniego et al 2001(Caniego et al , 2003. They were estimated via linear regression analysis with the least mean-square fit applying the power laws given in expressions (2), (3), (4) and (5).…”

Section: Estimation Of Multifractal Parametersmentioning

confidence: 99%

“…Multifractal analysis can be used to characterize the heterogeneous 2-D spatial arrangement of solid and void phases (Muller and McCauley, 1992;Posadas et al, 2003;Tarquis et al, 2003;Bird et al, 2006) and the complexity of pore size distribution (Caniego et al, 2001(Caniego et al, ,2003. These two, apriori, independent aspects can be modeled as mass distributions supported at a domain at a plane or at a size interval, respectively.…”

Section: Introductionmentioning

confidence: 99%

Multifractal analysis of discretized X-ray CT images for the characterization of soil macropore structures

et al. 2010

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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.

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“…In soil science, the multifractal concept has been applied to analyze the pore size distribution and particles of soil [6][7][8], the image of a thin slice of soil [9], the structure of clay [10], the matrix pore structure of a porous medium [11], soil surface pressure [12] and soil spatial variability [13]. Muller and McCauley [4] were successful in applying the fractal method to characterize the properties of the fluid flow of sedimentary rocks.…”

Section: Introductionmentioning

confidence: 99%

Multifractal Characterization of Pore Size Distributions of Peat Soil

et al. 2016

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Abstract. This paper discusses a multifractal analysis of the microscopic structure of peat soil. The aim of this study was to apply the multifractal technique to analyze the properties of five slices of peat soil (L1-L5). Binary images (220 x 220 pixels, with a conversion value of 9.41 μm/pixel) were made from the thin slices and then analyzed. This analysis was conducted to obtain the relationship between physical parameters and complexity parameters. The results showed that the spectrum of f(α) can describe well the pore size distribution and average size of pores correlated with the value of D(0). A high value of the average pore size is followed by a low D value and vice versa.

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Singularity Features of Pore-Size Soil Distribution: Singularity Strength Analysis and Entropy Spectrum

Cited by 52 publications

References 31 publications

Representative elementary area for multifractal analysis of soil porosity using entropy dimension

Representative elementary area for multifractal analysis of soil porosity using entropy dimension

Multifractal analysis of discretized X-ray CT images for the characterization of soil macropore structures

Multifractal Characterization of Pore Size Distributions of Peat Soil

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