A CRACK MODEL OF AFTERSLIP EVENTS ON SHALLOW FAULTS

Post-seismic evolution of surface displacement on a strike slip fault is studied employing a linear viscous rheology for the shallow fault zone. A mathematical model is built in which the singular integral equation governing the equilibrium of cracks is transformed in an infinite-dimensional linear symmetric system whose positive eigenvalues define a sequence of characteristic relaxation times. The model lends to model vertical heterogeneities in the rheological parameters and the equations can be efficiently solved by truncation. Several specific problems are then considered in order to assess which parameters may govern the fast early relaxation observed in afterslip events in California. Neither stress heterogeneities, nor the spectral distribution of characteristic relaxation times have significant effects on surface displacement if a uniform effective viscosity is employed. Viscosity heterogeneities however, can provide fast early afterslip and, perhaps, precursory events. Post-seismic creep data following the 1966 Parkfield, the 1979 Imperial Valley and the 1987 Superstition Hill earthquakes can be fitted well with this model without resorting necessarily to non-linear rheological relations.