Fault slip distribution and fault roughness

International audienceWe present analysis of the spatial correlations of seismological slip maps and fault topography roughness, illuminating their identical self-affine exponent. Though the complexity of the coseismic spatial slip distribution can be intuitively associated with geometrical or stress heterogeneities along the fault surface, this has never been demonstrated. Based on new measurements of fault surface topography and on statistical analyses of kinematic inversions of slip maps, we propose a model, which quantitatively characterizes the link between slip distribution and fault surface roughness. Our approach can be divided into two complementary steps: (i) Using a numerical computation, we estimate the influence of fault roughness on the frictional strength (pre-stress). We model a fault as a rough interface where elastic asperities are squeezed. The Hurst exponent inline image, characterizing the self-affinity of the frictional strength field, approaches inline image, where inline image is the roughness exponent of the fault surface in the direction of slip. (ii) Using a quasi-static model of fault propagation, which includes the effect of long-range elastic interactions and spatial correlations in the frictional strength, the spatial slip correlation is observed to scale as inline image, where inline image represents the Hurst exponent of the slip distribution. Under the assumption that the origin of the spatial fluctuations in frictional strength along faults is the elastic squeeze of fault asperities, we show that self-affine geometrical properties of fault surface roughness control slip correlations and that inline image. Given that inline image for a wide range of faults (various accumulated displacement, host rock and slip movement), we predict that inline image. Even if our quasi-static fault model is more relevant for creeping faults, the spatial slip correlations observed are consistent with those of seismological slip maps. A consequence is that the self-affinity property of slip roughness may be explained by fault geometry without considering dynamical effects produced during an earthquake