On the Choice and Implications of Rheologies That Maintain Kinematic and Dynamic Consistency Over the Entire Earthquake Cycle

Viscoelastic processes in the upper mantle redistribute seismically generated stresses and modulate crustal deformation throughout the earthquake cycle. Geodetic observations of these motions at the surface of the crust-mantle system offer the possibility of constraining the rheology of the upper mantle. Parsimonious representations of viscoelastically modulated deformation through the aseismic phase of the earthquake cycle should simultaneously explain geodetic observations of (a) rapid postseismic deformation, (b) late in the earthquake cycle near-fault strain localization. To understand how rheological formulations affect kinematics, we compare predictions from time-dependent forward models of deformation over the entire earthquake cycle for an idealized vertical strike-slip fault in a homogeneous elastic crust underlain by a homogeneous viscoelastic upper-mantle. We explore three different rheologies as inferred from laboratory experiments: (a) linear Maxwell, (b) linear Burgers, (c) power-law. The linear Burgers and power-law rheologies are consistent with fast and slow deformation phenomenology over the entire earthquake cycle, while the single-layer linear Maxwell model is not. The kinematic similarity of linear Burgers and power-law models suggests that geodetic observations alone may be insufficient to distinguish between them, but indicate that one may serve as an effective proxy for the other. However, the power-law rheology model displays a postseismic response that is non-linearly dependent on earthquake magnitude, which may offer a partial explanation for observations of limited postseismic deformation near some magnitude 6.5-7.0 earthquakes. We discuss the role of mechanical coupling between frictional slip and viscous creep in controlling the time-dependence of regional stress transfer following large earthquakes and how this may affect the seismic hazard and risk to communities living close to fault networks.