Quantifying a soil pore distribution from 3D images: Multifractal spectrum through wavelet approach

Knowledge on soil pore geometry is important for understanding soil processes as it controls the movement and storage of fluids on various scales. With the advent of modern non-destructive tomography techniques there have been many attempts made to analyze pore space features mainly concentrating on the visualization of soil structure. Multifractal formalism or the wavelet transform has been revealed as a useful tool in these cases where highly complex and heterogeneous media are studied. The field of 3D pore space analysis opens a challenging opportunity to develop techniques for quantifying and describing pore space properties. One of these quantifications can be the maximum depth pore network (MD), analogous as the quantification of the preferential flow paths. In this paper, a variation of the wavelet transform modulo maxima (WTMM) method used to compute multifractal behavior is presented. As a wavelet transform analysis (WTA), it allows us to focus on every scale which can be useful to select the range of scales where multifractal analysis (MFA) can be applied, revealing the MD global scaling patterns. In addition, the proposed method does not make any global estimate, so it can also be used to focus on local distribution of singularities. So, in the context of multiscaling structure analysis, the proposed wavelet-based method can complement box-counting analysis in order to statistically describe preferential flow path geometry and flow processes. The methodology is applied to determine the multifractal behaviour of 3D images of soil samples with 45.1 µm resolution (256 × 256 × 256 voxels) with closer porosities (ranging from 12% to 14%) and different spatial arrangements.