Fractal Mapping of Pore and Solid Attributes

Abstract

Soil structure depends on its genesis and consists of highly variable pore and solid networks. Several internal and external factors affect the attributes of these networks, with water being the most aggressive agent. In this study, we used selected fractal parameters (called descriptors) to quantify the basic topological attributes—compactness and connectedness—as well as lacunarity and roughness of porous materials, with special attention to sampling error and population variance dynamics. Four microhorizons were sampled from a 1.0‐ by 1.0‐ by 1.6‐m monolith during a long‐term drying period under controlled conditions. A comparative fractal analysis of selected multitemporal (11 mo) and multiscale (50×, 500×, 1000×, and 5000×) scanning electron microscopy (SEM) images was accomplished for the following layers with contrasting texture or structure: loam topsoil, pure basaltic compacted sand, and two amorphous lacustrine clays. The scale invariance (self‐similarity) of pore and solid networks was documented. A complex relationship was found between the descriptor mean values and corresponding variances. Simple power‐law relations were established between the standard deviation (and variance) and layer depth, as well as scale and sampling time. Pearson's r correlation criterion was applied to measure the degree of association between multiobjective fractal descriptors. Systematic and standardized fractal analysis of multiscale images is recommended for the statistical quantitative description of complex and dynamic pore and solid networks.