Special Seminar in Applied Mathematics

The mechanical deformation of rocks is ruled by a stick-slip behavior in the brittle crust, while plastic flows mostly accommodate strain within weaker layers. The style of slip is inherently related to both fault strength and topology and rock rheology, so that the nature of the coupling between fractured and ductile regions and its associated transition zone play a crucial role in the dissipation of stress accumulated over time in the adjoining volumes. The observational evidence suggests that the transition is spread over a relatively wide range of depths, and it is affected by several parameters such as the strain rate, rock rheology, temperature, and pore pressure even during the different stages of seismic activity. Consequently, understanding how stress could be released using a universal physical mechanism, being feasible a priori the whole range of fault slip styles - from aseismic creep to regular earthquakes - may allow a comprehensive explanation of several apparently disconnected phenomena. Among them, the difference between deep and crustal earthquakes, the temporal dependency of the seismogenic thickness during the various stages of seismic activity and the impact of focal depth on the statistical properties of seismicity. The seminar is devoted to discussing the topic in the framework of turbulent transitions. The approach is suitable for several applications ranging from geothermal environments to subduction zone modelling. Moreover, it might be useful to unveil severe hazard potential in regions featured by long earthquake recurrences.