Fractal and multifractal analysis of pore-scale images of soil

We examine critically the fractal and multifractal analysis of two-dimensional images of soil sections. We demonstrate that, dependent on the porosity displayed in the image, both a fractal dimension and a multifractal spectrum can be extracted from such images irrespective of whether these images exhibit fractal structures and multifractal scaling of local density and porosity. We suggest ways to transform the data arising from the analysis in order to differentiate better between fractal and non-fractal images. We examine three soil images and conclude that there is no compelling evidence of scaling properties associated with mass fractal and multifractal structures. Our results point to a need for alternative methods for characterizing soil pore structures and to extend our modelling of complex and multiscale porous media to cases where scaling symmetries are relaxed.