The critical slip distance for seismic faulting

Abstract

Experimentally based friction laws^1,2 have been found to predict virtually the entire range of observed behaviour of natural faults^3,4. These laws contain a critical slip distance, L, which plays a key role in determining the degree of fault instability, the size of the zone of earthquake nucleation, the frictional breakdown width, and the proportion of pre- and post-seismic slip to co-seismic slip. In laboratory measurements L is found to be about 10⁻⁵m, but modelling results show that it must be about 10⁻²m if natural earthquake behaviour is to be simulated. The discovery that fault surfaces are fractal over the scale range 10⁻⁵–10⁵ (refs 5,6), even for faults with large net slip, has confused the problem of scaling this parameter from laboratory experiments to natural faults, because fractal surfaces have no characteristic length. Here I show that geometrically unmated fractal surfaces, when in contact under a normal load, develop a characteristic length in their contact because long-wavelength apertures close under load whereas short-wavelength apertures may remain open. This critical distance may be identified with L, and calculations based on fault topography data show that at seismogenic depths it will be in the range anticipated from the earthquake modelling studies.