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

Abstract

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.

Multifractal analysis of vertical profiles of soil penetration resistance at the field scale

“…Pachespsky et al, 1996) or multifractal techniques (e.g. Tarquis et al, 2003;Paz-Ferreiro et al, 2010;San José Martínez et al, 2010). Likewise, soil surface microrelief has been described using fractal models (e.g.…”

“…More recently, it has been also recognized that a large class of multifractal processes could be approximated by the multifractal Brownian motion (mBm) models, based on the fact that the power law behaviour of second-order statistics allows estimation of a generalized Hurst scaling function (e.g. Leland et al, 1994;San José Martínez et al, 2010). It is worth nothing that, similar to the Hurst exponent, the generalized Hurst scaling function can be categorized into three types, i.e.…”

“…Thus, the total profile depth was subdivided into subintervals of equal length, δ (e.g. Miranda et al, 2006;San José Martínez et al, 2010), obtained with 1 ≤ k ≤ 5. Then, the distribution of the studied data series was normalized by introducing a new variable, the probability mass function, µ i (δ).…”

“…a zero mean and first and second moments that do not change over position). In this particular case the Hurst exponent measures the power law behaviour of the autocorrelation function: ρ(k) ∝ k 2H −2 (Leland et al, 1994;San José Martínez et al, 2010). Thus, the scaling exponent provides information about long-term memory of the spatial or temporal series of interest.…”

“…The Hurst exponent, H , identifies persistence or long-range autocorrelation (e.g. Pérez et al, 2010;San José Martínez et al, 2010), so low H means a weak persistence and vice versa. Great α 0 values and wide (D −8 − D 8 ) spectra are characteristic of a high heterogeneous measure.…”