Carlos García-Gutiérrez

LOG SELFSIMILARITY OF CONTINUOUS SOIL PARTICLE-SIZE DISTRIBUTIONS ESTIMATED USING RANDOM MULTIPLICATIVE CASCADES

Particle-size distribution (PSD) is a fundamental soil property usually reported as discrete clay, silt, and sand percentages. Models and methods to effectively generate a continuous PSD from such poor descriptions using another property would be extremely useful to predict and understand in fragmented distributions, which are ubiquitous in nature. Power laws for soil PSDs imply scale invariance (or selfsimilarity), a property which has proven useful in PSD description. This work is based on two novel ideas in modeling PSDs: (1) the concept of selfsimilarity in PSDs; and (2) mathematical tools to calculate fractal distributions for specific soil PSDs using few actual texture data. Based on these ideas, a random, multiplicative cascade model was developed that relies on a regularity of scale invariance called ‘log-selfsimilarity.’ The model allows the estimation of intermediate particle size values from common texture data. Using equivalent inputs, this new modeling approach was checked using soil data and shown to provide greatly improved results in comparison to the selfsimilar model for soil PSD data. The Kolmogorov-Smirnov D-statistic for the log-selfsimilar model was smaller than the selfsimilar model in 92.94% of cases. The average error was 0.74 times that of the selfsimilar model. The proposed method allows measurement of a heterogeneity index, H, defined using Hölder exponents, which facilitates quantitative characterization of soil textural classes. The average H value ranged from 0.381 for silt texture to 0.838 for sandy loam texture, with a variance of <0.034 for all textural classes. The index can also be used to distinguish textures within the same textural class. These results strongly suggest that the model and its parameters might be useful in estimating other soil physical properties and in developing new soil PSD pedotransfer functions. This modeling approach, along with its potential applications, might be extended to fine-grained mineral and material studies.

A protocol for fractal studies on porosity of porous media: High quality soil porosity images

A protocol for obtaining digital images from natural porous media with a wide range of pore sizes, intended for fractal studies of the porosity, is proposed. Soil porosity is used as paradigm of complex natural porous media in this study. The use of several imaging devices and fluorescent compounds to enhance the contrast between the solid and the pore phase is tested. Finally a protocol is reached using a photo camera and a confocal microscope. It is the first time that confocal microscopy is used for this purpose. Artificial porous images are created through random Sierpinski carpet fractals and the statistical information of real soil images. These ground truth images are used in an objective comparison of automatic segmentation algorithms for the obtained images. A statistical classification on the performance of several automatic segmentation algorithms for this type of images is reached.

Minkowski Functionals of Connected Soil Porosity as Indicators of Soil Tillage and Depth

We made use of 3D tomograms from X-ray computed tomography of soil samples from a vineyard in La Rioja (Spain), to explore the ability of Minkowski functionals of connected soil pore space to discriminate between different pore space geometries coming from soils with different management and depth and that, a priori, are expected to have some degree of dissimilarity. We estimate the volume of the connected pore space (

A Packing Computational Method Relating Fractal Particle Size Distribution and Void Fraction in Granular Media

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

), the surface of the interface soil/void (

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

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Modeling Multifractal Features of Soil Particle Size Distributions with Kolmogorov Fragmentation Algorithms

), the accumulated mean curvature of that interface (

Lacunarity of soil macropore space arrangement of CT images: Effect of soil management and depth

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On the fractal modelling of biomass distributions: An application to size class in fisheries

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On soil textural classifications and soil-texture-based estimations

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