Why do we need new models of earthquake occurrence?

While modelling the coseismic phase is relatively simple, a comprehensive, effective theory of seismic occurrence is difficult because of strongly nonlinear long-range interactions taking place in the brittle crust, so that fault systems cannot be reduced to simple non-interacting «planes of slip». Moreover, earthquake dynamics not only depends on the rheological properties of rocks, but also on their structural complexity and on intricate stress patterns inside the crustal volumes. Therefore, seismicity showcases different behaviours depending on the spatial and temporal scales of investigation because each level of complexity of the seismogenic source is associated with emergent properties that cannot be derived from the elementary laws ruling the system at a fundamental level. So, we need to set up new models able to reproduce well-known results and having predictive power. Here, we introduce a simple toy model to embrace some crucial features of seismicity at both coseismic and seismic-sequence scales. The key paradigm of our model is that seismicity is driven by the optimization of energy needed to mobilize crustal volumes given some mechanical constraints (i.e., strain rate and physical properties of rocks). Our model can reproduce several properties of seismicity such as the dependence of b-value of the Gutenberg-Richter law on the tectonic setting, spatial and temporal clustering of large and small events and the statistical differences between in-fault and off-fault seismicity, being the first featured by lower b-value, fractal dimension of spatial time series and higher seismogenic potential. Differences between tectonic settings are described using the same framework. Our approach can provide information about the long-term seismic behaviour of fault systems, which may be of interest in regions equipped with recently developed seismic networks and where paleo-recordings are poorly constrained.