A model of interseismic stress evolution in a transcurrent shear-zone

It has been observed that most shallow earthquakes occur in a seismogenic layer which extends to a depth of a few tens of kilometres, while at greater depths the relative plate motion must take place aseismically. Such behaviour is reproduced by a model where a wide, deformed fault region is encompassed by two transcurrent plates and subjected to a constant strain rate. The shear zone is treated as a viscoelastic body, for which a power-law constitutive relation is employed. Temperature and, therefore, rheology depend on depth z. Also rigidity depends on depth. The model determines a maximum depth H for earthquake nucleation on the faults in the shear zone, if a frictional resistance linearly increasing with depth is assumed. The interseismic shear stress evolution on a vertical fault is obtained analytically for n = 1,2,3 and 4, where n is the power-law exponent. It is found that the rate of stress increase does not change appreciably as a function of n for z < H, while the effect of non-linearity becomes more sensible at larger z. Moreover, for z < H, the state of stress as obtained from this model is very different from estimates obtained from purely viscous models even for much longer times than are considered in seismology.