Relationship between the fractal dimension anisotropy of the spatial faults distribution and the paleostress fields on a Variscan granitic massif (Central Spain): the F-parameter

Abstract

The spatial distribution of faults is usually described as a fractal set characterised by the fractal dimension. In this work, we have filtered fault patterns interpreted from digital elevation models, aerial photographs and field maps, by using structural geological parameters of the stress ellipsoid (stress tensor direction and stress ratio R′) and age of deformation. From these filtered structural maps, we have obtained the fractal dimension associated with the fracture patterns developed during Permo-Triassic and Alpine tectonic events on a Variscan granitic massif located in the Spanish Central System. Oriented fractal dimensions were calculated on several transects crossing the fault-filtered maps. The fractal dimension ( D), calculated by 1-D box-counting, describes an ellipse on a polar plot with the short axis as the minimum value ( D Hmin) and the long axis as the maximum value ( D Hmax) of the fractal dimensions measured. From these analyses, we have defined the F-parameter as a function of the maximum value, minimum value and vertical value of fractal dimension ( D z), F=( D z− D Hmin)/( D Hmax− D Hmin). Finally we have established, from a local scale analysis, a perpendicular relationship between the principal axes of the ellipse of the fractal spatial anisotropy of fractures and the principal axes of the stress tensor ( σ Hmax, σ Hmin and σ z) that generates this dynamic pattern of fractures. Furthermore, the F-parameter and the stress ratio R′ are equivalents and, applied in this area, both show a triaxial extension.