Macroporosity of 2-D cross sections of soil columns via X-ray CT: multifractal statistics and long range correlations for assessing 3-D soil pore structure

摘要

Soil pore structure controls important physical and biological processes in the soil-plant-microbial systems where microbial population dynamics, nutrient cycling, diffusion, mass flow and nutrient uptake by roots take place across many orders of magnitude in length scale. Over the last decades, fractal geometry has been proposed to deal with soil pore complexity and fractal techniques have been applied. 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.