Viscous flow in the deep crust and uppermost mantle can contribute to the accumulation of strain along seismogenic faults in the shallower crust1. It is difficult to evaluate this contribution to fault loading because it is unclear whether the viscous deformation occurs in localized shear zones or is more broadly distributed2. Furthermore, the rate of strain accumulation by viscous flow has a power law dependence on the stress applied, yet there are few direct estimates of what the power law exponent is, over the long term, for active faults. Here we measure topography and the offset along fault surfaces created during successive episodes of slip on seismically active extensional faults in the Italian Apennines during the Holocene epoch. We show that these data can be used to derive a relationship between the stress driving deformation and the fault strain rate, averaged over about 15 thousand years (kyr). We find that this relationship follows a well-defined power law with an exponent in the range of 3.0–3.3 (1σ). This exponent is consistent with nonlinear viscous deformation in the deep crust and, crucially, strain localization promoted by seismogenic faulting at shallower depths. Although we cannot rule out some distributed deformation, we suggest that fault strain and thus earthquake recurrence in the Apennines is largely controlled by viscous flow in deep, localized shear zones, over many earthquake cycles.
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