Multifractal analysis of particle size distributions in soil

Power-law scaling of particle size distributions in air, water, and soil have been frequently reported and are sometimes interpreted in the context of a fractal dimension to yield estimates of the geometrical characteristics of particles and aggregates such as their density or porosity. However, the underlying process leading to a measure of particle size distribution suggests that, in general, particle size distributions in natural systems should not conform to a simple power law. Rather, measures on a fractal object such as a particle aggregate give rise to a very different type of scaling known as multifractal. In this paper, data on soil grain size distributions obtained from soil horizons composed predominantly of clay and silt are analyzed to illustrate the inappropriateness of a simple power law interpretation in this case and to demonstrate the theoretically anticipated multifractal behavior.