Kinematically consistent models of viscoelastic stress evolution

Following large earthquakes, coseismic stresses at the base of the seismogenic zone may induce rapid viscoelastic deformation in the lower crust and upper mantle. As stresses diffuse away from the primary slip surface in these lower layers, the magnitudes of stress at distant locations (> 1 fault length away) may slowly increase. This stress relaxation process has been used to explain delayed earthquake triggering sequences like the 1992 M-w = 7.3 Landers and 1999 M-w = 7.1 Hector Mine earthquakes in California. However, a conceptual difficulty associated with these models is that the magnitudes of stresses asymptote to constant values over long time scales. This effect introduces persistent perturbations to the total stress field over many earthquake cycles. Here we present a kinematically consistent viscoelastic stress transfer model where the total perturbation to the stress field at the end of the earthquake cycle is zero everywhere. With kinematically consistent models, hypotheses about the potential likelihood of viscoelastically triggered earthquakes may be based on the timing of stress maxima, rather than on any arbitrary or empirically constrained stress thresholds. Based on these models, we infer that earthquakes triggered by viscoelastic earthquake cycle effects may be most likely to occur during the first 50% of the earthquake cycle regardless of the assumed long-term and transient viscosities.