Implications of rate and state dependent friclion for creep on shallow faults

Abstract

The aseismic sliding on shallow strike-slip faults, under the assumption of a non linear constitutive equation (velocity strengthening), is here treated as a two-dimensional quasi-static crack problem whose equations are solved numerically (boundary elements method). Results are compared with the corresponding one-dimensional («depth averaged») model by a suitable choice of the effective stiffness of the fault. In the one-dimensional case also the inertial term was taken into account in the evolutive equation. The current results are in agreement with an earlier one-dimensional model for afterslip as long as the state variable evolution is neglected a priori and friction depends only on velocity. In general, if the state variable is allowed to evolve, the previous approximation is valid for velocity strengthening slipping section of faults extending down to several kilometers in depth. For smaller sections of fault the evolution of the state variable affects the coseismic and early postseismic phase and accordingly it cannot be neglected. Moreover, in the presence of rheological heterogeneities, for fault sections shallower than 1 km depth, the comparison between the two-dimensional and one-dimensional models suggests the need to employ the two-dimensional model, possibly taking into account inertial effects.