After a major earthquake, there is always a regional increase in seismic activity in the form of multiple, potentially destructive aftershocks, as they arrive in areas that may already have been severely impacted by the main earthquake, even if their magnitudes are generally lower. This rate of aftershocks is observed to decrease over time, but the origin of this decrease is still debated today, more than 130 years after it was discovered by the Japanese seismologist Fusakichi Omori (1868-1923). Time-dependent mechanisms are generally invoked to explain their existence: post-seismic slip, viscoelastic stress increase at fault level, decrease in slip resistance over time, increase in interstitial liquid pressure in the fault core, etc.

Recently, laboratory experiments conducted by physicists on sheared granular media have made it possible to reproduce the entire phenomenology characterizing earthquake statistics. Indeed, a shear band in a granular medium appears like a miniature replica of a seismic fault, and the relative displacement between different parts of the granular medium is in fact the result of the accumulation of local plastic events analogous to very small earthquakes taking place along the band. The study of the statistical properties of these events shows that they obey the empirical laws observed in seismology, both in terms of their size distribution and the spatio-temporal fluctuations in their frequency. A collaboration between physicists and geophysicists has enabled a quantitative step forward in the comparison between these systems. 

In their study, researchers have shown that, contrary to what intuition suggests, time is not the relevant variable for describing the decrease in aftershock rate observed in the two systems. To this end, the researchers have developed an analytical method for quantitatively comparing catalogs of natural and laboratory earthquakes, the difficulty lying in developing relevant observables common to systems differing by several orders of magnitude in terms of length and time scales. This unified approach shows that the evolution of the aftershock rate, measured in these different systems, is described by a general law if we consider that the variable governing the dynamics is deformation and not time. As shown in the figure, it is in fact the fault deformation rate that sets the time scale in all these systems, from the laboratory fault obtained in a model granular medium to terrestrial seismic faults: the curve on the right shows a superposition of the correlation of aftershock density as a function of total cumulative deformation since the earthquake was triggered, reflecting the universality of the phenomenon when considered as deformation-dependent (by comparison, the same curves as a function of time, on the left of the figure, are completely dispersed). This approach leads to a simple, natural rationalization of phenomena occurring on extraordinarily different scales. This possibility of spatially and temporally scaling the complex dynamics of earthquakes will enable further study of their dynamics and the parameters that influence them, and provides a framework for developing minimal models to explain the origin of aftershocks. These results are published in Geophysical Research Letters.