Critical behaviour and the evolution of fault strength during earthquake cycles

The problem of how fault rheology and heterogeneity interact to produce the observed scaling of earthquakes (such as the power-law moment–frequency relationship) remains largely unsolved. Rock friction experiments have elucidated the properties of smooth faults1,2,3, but seem insufficient to explain the observed complexity of real fault dynamics4,5. The recognition of a connection between fault-related processes and critical phenomena in other physical systems, together with numerical models of repeated earthquakes, have resulted in significant progress in the theoretical interpretation of earthquake scaling4,5,6,7,8,9,10,11,12,13,14. But fault rheology and heterogeneity have so far been treated separately. Here I attempt to unify the requirements of fault rheology and heterogeneity using numerical calculations of quantized slip in an elastic continuum. I show that cyclical fault strength evolves naturally by means of a statistical selection for high-strength fault patches (asperities), resulting in the accumulation and eventual failure of those asperities. The applicability of these results to real fault systems is supported by a recent analysis of time-dependent earthquake statistics15. These results imply that self-similarity and criticality on a fault emerge during an earthquake cycle, and suggest that the character of local seismicity can be useful in earthquake forecasting by revealing how advanced a fault is within its cycle.