Fractal geometry of the fault network across the Soutpansberg Mountains, Limpopo, South Africa

Abstract

Earth systems and landforms are defined by complicated patterns and structures that hold key information for many important naturally-controlled systems (e.g. minerals, energy and natural hazards). A deeper understanding of these systems remains elusive, in part due to the complexity in defining their geometry. Fractal analysis (FA) provides a method of characterising patterns that are seemingly complicated beyond conventional geometry principles. FA has been actively applied to faulted regions in an attempt to resolve multi fracture-controlled processes. In this study we apply FA to the Soutpansberg Mountains (SM) to better characterise its extensive fracture network (most notably regional faults) covering many orders of scale, and to test whether the results mimic known geological complexities. In addition, we test whether there is any link between the fractal geometry and the occurrence of Cu-mineralisation and groundwater hot springs. We apply the box-counting technique to determine the fractal dimension (D), lacunarity (LC) to quantify the concentration (density) of fracturing, and test for multifractal (MF) affinity. The results of the FA correspond well with the known complex geology across the SM; areas with higher D-values and an affinity toward MF behaviour correspond to regions of the SM displaying at least two fault orientations with possibly two directions of shear displacement (i.e. normal and transcurrent). In addition, lower LC values correspond to regions of the SM that exhibit a greater degree of faulting. Also, regions with higher fractal complexity relate to areas with the highest concentration of Cu-mineralisation and highest-temperature hot springs. This suggests that principles of fractal geometry play a role in the interconnectivity within the brittle upper crust. We thus confirm that FA can be applied together with regional strain controls to better understand dynamics of natural and induced fracture propagation and recommend that this be further applied to exploration within the Earth’s Critical Zone.