Investigation of heterogeneous scaling intervals exemplified by sutured quartz grain boundaries

Quartz grain boundaries from metamorphic and igneous rocks may emphasize a complex geometry, characterized by self-similarity over one to two orders of magnitude. Their fractal analysis highlights scaling sub-domains, i.e. scale intervals with a particularly good correlation. Given the importance of these aspects for the deciphering of geological microstructures, the paper is dedicated to the detection and the objective depiction of the features of heterogeneous scaling intervals. A fractal analysis based on the divider method was followed by processing methods that (i) offer a global evaluation of the curve geometry from the point of view of the correlation sub-domains, and (ii) allow a local characterization of the curves in terms of scale, with special concern for the scaling intervals heterogeneity. The application of the proposed approach was exemplified both on natural and synthetic curves. On one hand, the grain boundary analysis highlighted scaling sub-domains most obviously in the case of microstructures that were subject to overprinting, due to successive processes. On the other hand, a pattern superposition in the case of the synthetic curves strongly emphasized scaling sub-domains, as compared to the unperturbed (recursively generated) curve geometry. These aspects were expressed quantitatively and highlighted in more detail on isocorrelation maps. The importance of a rigorous characterization of these sub-domains and, eventually, the detection of pattern overprinting phenomena in geological microstructures emphasize the relevance of such an approach.