An attempt for the multiscale modelling of rheological parameters from the laboratory to fault systems

Faults usually showcase an intermittent slip activity featured by slowly creeping or almost locked phases alternated with sudden peaks called earthquakes. The recurrence time of seismic events on individual faults is highly variable with clustered occurrences often in the order of a few thousand years. The limited duration of recordings and data promoted the development of analogous models to supply information about earthquake physics and preparatory processes. Therefore, lab experiments have been playing an important role in advancing our knowledge of seismic phenomena. Nevertheless, it is quite clear that a straightforward application of lab observations to natural fault system is not possible, and the effect of both temporal and spatial scale difference should be painstakingly evaluated. Among the most pressing issues there is the role of mechanical parameters (e.g., fault friction, with coefficients on fault smaller than expected from laboratory studies) and how they affect physical mechanisms behind seismic activity. Here, we propose a theoretical approach to investigate this topic. We set up a model for earthquake occurrence grounded on basic principles of fracture mechanics and in agreement with laboratory and seismological evidence. The success of such a scale-linking approach is demonstrated by the successful reproduction of several statistical features of seismic activity (e.g., the Gutenberg-Richter law and its scaling exponent variability). We show that earthquakes can be interpreted as fracture avalanches whose properties are mainly controlled by the joint distribution of fault strength and shear stress through the definition of asperity breaking conditions. In this framework, static friction coefficients can be interpreted as self-averaging effective properties of interfaces where no dominant effect is played by individual asperities. However, our model suggests that earthquakes tend to nucleate nearby the regions features by the extreme values of the strength distribution. Then, the larger the scale, the higher the probability to find a weaker segment, so that the macroscopic static friction coefficient decreases with the spatial scale of investigation from the usually measured values in the lab, mostly in the range 0.4−0.7, to μ≈ 0.1 at natural scales. Conversely, dynamic friction coefficients are expected to be roughly the same regardless of the scale.