Hölder spectrum of dry grain volume-size distributions in soil

Abstract

Fractal parameters have been applied before to describe number and mass size distributions of particles and aggregates through power scaling laws. Exponents such as the fragmentation fractal dimension, D f, represent rough estimates of the scale dependence present in the number or mass accumulated with respect to length scale. However, a deeper and more accurate study of these distributions may be done using multifractal analysis techniques when a large enough amount of data is available. The light scattering method and the multifractal analysis enable the study of these distributions in scales not very often explored. In the present work, attention is focused on the Hölder exponents spectrum, α( q), and its capability to characterize dry grain volume-size distributions in soil. Twenty samples were analyzed by laser diffraction and Hölder spectrum analyses, showing a great variability in Hölder exponent results. Coefficients of determination have been considered to study and characterize scalings achieved. Hölder spectrum analysis revealed to be useful in the characterization of these distributions as they showed suitable scaling properties in general, producing the best fits for the entropy dimension ( D 1). Thus, the combination of laser diffraction and Hölder spectrum analyses is a potential tool for detecting changes in soil grain distributions due to physical or degradation processes. The similarity of these results to those obtained from mathematical multifractal measures suggests that this way of characterizing dry soil grain distributions may be used to simulate empirical data by means of mathematical algorithms based in fractal geometry (Iterated Function Systems and related ones).