Weak ductile shear zone beneath the western North Anatolian Fault Zone: inferences from earthquake cycle model constrained by geodetic observations

After large earthquakes, rapid postseismic transient motions are commonly observed. Later in the loading cycle, strain is typically focused in narrow regions around the fault. In simple two-layer models of the loading cycle for strike-slip faults, rapid post-seismic transients require low viscosities beneath the elastic layer, but localized strain later in the cycle implies high viscosities in the crust. To explain this apparent paradox, complex transient rheologies have been invoked. Here we test an alternative hypothesis in which spatial variations in material properties of the crust can explain the geodetic observations. We use a 3D viscoelastic finite element code to examine two simple models of periodic fault slip: a stratified model in which crustal viscosity decreases exponentially with depth below an upper elastic layer, and a block model in which a low viscosity domain centered beneath the fault is embedded in a higher viscosity background representing normal crust. We test these models using GPS data acquired before and after the 1999 Izmit/Duzce earthquakes on the North Anatolian Fault Zone (Turkey). The model with depth-dependent viscosity can show both high postseismic velocities, and preseismic localization of the deformation, if the viscosity contrast from top to bottom of layer exceeds a factor of about 10⁴. However, with no lateral variations in viscosity, this model cannot explain the proximity to the fault of maximum postseismic velocities. In contrast, the model which includes a localized weak zone beneath the faulted elastic lid can explain all the observations, if the weak zone extends down to mid-crustal levels and outward to 10 or 20 km from the fault. The non-dimensional ratio of relaxation time to earthquake repeat time, τ/Δt, is the critical parameter in controlling the observed deformation. In the weak-zone model, τ/Δt should be in the range 0.005 to 0.01 in the weak domain, and larger than ~ 1.0 elsewhere. This implies a viscosity in the weak zone of ~ 10^18×0.3 Pa s, and larger than ~ 10²⁰ Pa s outside this region. Models with sharp boundaries to the weak zone fit the data better than those with a smooth increase of viscosity away from the fault. Thus abrupt changes in material properties, such as those that might result from grain-size reduction, may be required in addition to any effect from shear heating. Unlike some previous models, we do not require non-linear stress-dependent viscosities. Our models imply that geodetic strain rates decay to a quasi-steady state within about 10% of the inter-earthquake period (years or decades) and that interseismic geodetic observations can therefore be used to infer the long-term geological slip rate, provided there has not been a recent earthquake. Rheologies inferred from postseismic studies alone likely reflect the rheology of the weak zone beneath the fault, and should not be used to infer the strength profile of normal lithosphere.