Multifractal statistics of discretized X-ray CT visualizations for the characterization of 3-D macropore structures

Authors: MARTIN, MIGUEL ANGEL - U. OF MADRID, SPAIN; SAN JOSE MARTINEZ, FERNANDO - U. OF MADRID, SPAIN; CANIEGO, JAVIER - U. OF MADRID, SPAIN; TULLER, MARKUS - U. OF ARIZONA; Guber, Andrey; Pachepsky, Yakov

Submitted to: Geoderma
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 8/20/2008
Publication Date: 2/7/2010
Citation: Martin, M., San Jose Martinez, F., Caniego, J., Tuller, M., Guber, A.K., Pachepsky, Y.A. 2010. Multifractal statistics of discretized X-ray CT visualizations for the characterization of 3-D macropore structures. Geoderma. 156(1-2):32-42.

Interpretive Summary: Soil pore structure controls water flow and solute transport in soils, defines the availability of water and nutrients to plants, constrains and facilitates biological activity in soil, and determines soil fertility. It is imperative to have a correct model of spatial distribution of soil voids to understand soil behavior and predict effects of management practices and environmental changes. Development of such models became possible only recently due to the introduction of the computer tomography of soils. The first step in understanding soil void structure is to develop an adequate mathematical representation of the spatial distribution of the total void area in soil crossections. In this work, the 1480 crossectional porosities were obtained for soil columns from the computer tomograms. The 20 cm-long undisturbed columns were carved from the A horizon of a floodplain loam soil in Pennsylvania, and had diameters of 7.5 cm. Dependencies of the cross-sectional porosity on depth displayed large variability. First, the spatial variations of the porosity were represented with the common monofractal model which assumes that there is a power law relationship between the large number of small soil pores vs. the small number of large soil pores. This model gave a satisfactory representation of porosity-size data, but failed to explain the relationship between variability of porosities within a size group and frequency of occurrence of this size group. We applied the multifractal model that gave the correct description of this relationship. It appears that the crossectional porosity exhibited the long range correlations that stemmed from the presence of soil macropores piercing the column. Because macropores are very important bypass conduits of water and solutes in soils, characterization of the connectivity in crossectional porosity that we have established gives important insights for further directions of using the computer tomography to characterize and parameterize soil pore space for diagnostic and prognostic purposes.

Technical Abstract: Simple fractal models such as fractional Brownian motions, that have been proposed to capture the complex behavior of soil spatial variation, often cannot simulate the irregularity patterns displayed by spatial records of soil properties. It has been reported that these spatial records exhibit a behavior close to the so-called multifractal structures. Advanced visualization techniques such as X-ray computed tomography (CT) are required to assess and characterize the multifractal behavior of soil pore space. The objective of this work was to develop the multifractal description of soil porosity values (2-D sectional porosities) as a function of depth with data from binarized 2-D images that were obtained from X-ray CT scans of 12 water-saturated 20 cm-long soil columns with diameters of 7.5 cm. 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 690x690 pixels. The series corresponding to the percentage of void space of the sectional binarized images were recorded. These series of depth-dependent macroporosity values exhibited a well defined multifractal structure that was represented by the singularity and the Rényi spectra. We also parameterized the memory, or long range dependencies, in these series using the Hurst exponent and the multifractal model. The distinct behavior of each porosity series may be associated with pore connectivity and furthermore, correlated with hydraulic soil properties. The obtained multifractal spectra were consistent with multinomial multifractal measures where larger concentrations were less diverse but more common than the smaller ones. Therefore, models to assess pore space connectivity should incorporate a multifractal random structure compatible with this multinomial structure and the long range dependences that displayed these porosity series. Parameterization of the memory in depth dependencies of 2-D porosity series yields a useful representation of complex 3-D macropore geometry and topology.