Multifractal features of 3D macropore geometry of structured soil columns with X-ray computer tomography

Disordered media often exhibit great complexity in the way that their various elements and materials are arranged. One way of studying this complexity is to consider one type of measurable data which is related to a particular aspect, and to characterize these data by means of a suitable mathematical technique. Porous media are examples of disordered media consisting of both solid and empty parts, and where the measurement that describes the pore-space volume enclosed within a domain centered at a particular point often exhibits large variations from point to point. These variations can be characterized by a multifractal spectrum as long as suitable scalings are found; in such a case, the properties of its distribution are related to the spectrum. Multifractal analysis has been successfully applied in the characterization of soil porosity with digital 2D images acquired with a variety of methods. New technologies, such as X-ray computed tomography render 3D images of the pore space geometry of intact soil samples, and therefore offer more opportunities for analysis. The objective of this paper is two-fold. Firstly we study the appropriateness of multifractal analysis for assessing the complexity of soil macropore 3D geometry, and secondly, we describe this complexity by using entropy-based multifractal parameters.