Multifractal Analysis of Soil Porosity Based on Mercury Injection and Nitrogen Adsorption

Pore-size distributions (PSD) determined by different methods across various ranges of equivalent pore radius have shown multifractal characteristics. Here, the multifractal formalism was employed to describe both mercury injection porosimetry (MIP) and nitrogen adsorption isotherms (NAI) curves, measured in a Mollisol and in a Vertisol. Four different soil use intensities and three replicate samples per treatment were analyzed. Mercury injection and nitrogen adsorption were used to measure PSDs for equivalent pore radii 150 to 0.005 µm and 0.1 to 0.001 µm, respectively. The scaling properties of all the Hg injection curves and N2 adsorption isotherms could be fitted reasonably well with multifractal models. A generalized dimension spectrum, D(q), led to a better definition of multifractal scaling than a singularity spectrum, f(α). Parameters derived from these two functions showed highly significant differences between MIP and NAI in both soil types. Thus, mean values of entropy dimension, D1, and correlation dimension, D2, were significantly higher for mercury injection than for nitrogen adsorption. On the contrary, Hölder exponents of order zero, α(0), were on average significantly higher for nitrogen adsorption. Also, mean widths of the f(α) spectra were much larger for nitrogen adsorption. These results indicate heterogeneity due to the presence of different porous domains at the scale of primary soil aggregates. The multifractal approach was useful to characterize the heterogeneity of the soil pore system and to distinguish between different patterns of PSD corresponding to various degrees of clustering.