Single and Joint Multifractal Analysis of Soil Particle Size Distributions

It is noted that there has been little research to compare volume-based and number-based soil particle size distributions (PSDs). Our objectives were to characterize the scaling properties and the possible connections between volume-based and number-based PSDs by applying single and joint multifractal analysis. Twelve soil samples were taken from selected sites in Northwest China and their PSDs were analyzed using laser diffractometry. The results indicated that the volume-based PSDs of all 12 samples and the number-based PSDs of 4 samples had multifractal scalings for moment order −6 < q < 6. Some empirical relationships were identified between the extreme probability values, maximum probability (Pmax), minimum probability (Pmin), and Pmax/Pmin, and the multifractal indices, the difference and the ratio of generalized dimensions at q = 0 and 1 (D0- D1 and D1/D0), maximum and minimum singularity strength (αmax and αmin) and their difference (αmax- amin, spectrum width), and asymmetric index (RD). An increase in Pmax generally resulted in corresponding increases of D0-D1, αmax, αmax-amin, and RD, which indicated that a large Pmax increased the multifractality of a distribution. Joint multifractal analysis showed that there was significant correlation between the scaling indices of volume-based and number-based PSDs. The multifractality indices indicated that for a given soil, the volume-based PSD was more homogeneous than the number-based PSD, and more likely to display monofractal rather than multifractal scaling.