A model for migration of aftershocks driven by afterslip

Abstract

Aftershocks region have been extensively reported to expand logarithmically with time. The associated migration velocity is typically of the order of several km/decade but can be much larger, especially when observing early aftershock sequences, seismic swarms, or tremors. We present here a model for the expansion of aftershock zones based on the idea that aftershocks are triggered as afterslip grows with time along the fault. One of the model assumptions is that aftershocks are triggered when a critical level of afterslip is reached. We predict that the migration velocity $V_p$ at time $t$ following the mainshock is given by $V_p = ζ fracA’δτtimes fracct$, where $A’$ is a frictional parameter, $δτ$ a characteristic value for the stress perturbation, $c$ the radius of the stress perturbation, and $ζ$ a constant of order unity. The scaling $V_p = 1/t$ implies a logarithmic expansion of the aftershock zone with time. The migration velocities predicted by our model are in quantitative agreement with the observations reported following aftershock sequence of small and large earthquakes in various tectonic settings, seismic swarms, and tremor sequences.