Regional strain derived from fractal analysis applied to strike-slip fault systems in NW Sicily

Deformation related to brittle structures can be expressed by the geometric moment, a purely kinematic parameter obtained from the product of the area of a fault surface and the amount of displacement. A geological-structural survey has been carried out on Messinian to Lower Pliocene fault systems along the Tyrrhenian coast in northwestern Sicily. Data pertaining to the kinematics and linear lengths of the faults as well as to the average displacement amounts of each fault have been gathered. The analysed structures, which lie in a context of dextral transcurrent tectonics, with a master fault oriented approximately NW-SE, which is associated with Messinian to Lower Pliocene dextral and sinistral strike-slip faults trending N140°E and N30°-50°E, respectively. The fractal geometry of the structures studied in this area of NW Sicily allows to calculate the total strain responsible for the faulting. Besides, considering the strain as being fractal, it has been possible to evaluate the deformation on the whole, which is due either to the master fault or to the associated minor faults. The calculated geometric moments M_g furthermore present a relationship between the number of faults with a geometric moment ≥ M_g, and M_g of the type N(M_g) = M_g^-β similar to the relationship N(M₀)=M₀^-B between the number N of earthquakes with a seismic moment ≥ M₀ and M₀. The angular coefficient β, can be considered analogous, kinematic, to the exponent B, thus becoming a strain index.