On the mechanics of earthquake afterslip

Abstract

We propose a model for earthquake afterslip based on rate and state variable friction laws. In the model, afterslip is attributed to the interaction of a velocity‐weakening region at depth (within which earthquakes nucleate) with an upper region of velocity‐strengthening frictional behavior. The existence of this upper region is supported by independent seismologic observations and the results of laboratory friction experiments. In our model, afterslip is the result of relaxation of a stress perturbation within the velocity‐strengthening region, which arises when an earthquake propagates into that region from below. We derive the stress perturbation and its decay from the friction constitutive law using a simple, 1 degree‐of‐freedom approximation for the elastic interaction between the fault and its surroundings. This approximation is based on thickness‐averaged displacements and slip velocities within the velocity‐strengthening region, which is assumed to slip as a rigid block. Coseismic and postseismic slip are coupled through the thickness‐averaged stiffness k of the velocity‐strengthening region. We assume k to be inversely proportional to the thickness of this region, which means that thicker velocity strengthening regions have a greater tendency to arrest coseismic slip. We model the afterslip‐time histories of the 1966 Parkfield and 1987 Superstition Hills earthquakes and relate the model parameters to physical parameters which may govern the rheologic behavior of the faults. In accord with field observations, our model predicts (1) that afterslip on some faults scales with the thickness of the (unconsolidated) sedimentary cover and (2) that proportionally more afterslip occurs for earthquakes in which coseismic surface slip is small compared with coseismic slip at depth. Velocity‐strengthening frictional behavior is to be expected for faults within poorly consolidated sediments and for those that contain significant gouge zones (about >500 m) within their shallow regions (<3–5 km). Combining our results with those of recent laboratory friction studies indicates that relatively young faults with little accumulated fault gouge should exhibit little afterslip.

Influence of anelastic surface layers on postseismic thrust fault deformation

“…An important deformation mechanism which is potentially active along with or instead of the bulk processes described here is transient afterslip on one or more discrete planes [Marone et al, 1991]. While spatial separation is probably adequate to distinguish main rupture afterslip from distributed upper crustal shear, it is more problematic to unambiguously distinguish off-rupture triggered slip.…”

Fault instability on a finite and planar fault related to early phase of nucleation

“…A considerable number of them assume a rate-and state-dependent friction law [Dieterich, 1979;Ruina, 1980] since it can represent long-term stickslip behavior with spontaneous nucleation preceding dynamic instability [Tse and Rice, 1986;Lapusta and Rice, 2003]. It can also represent slow interseismic and postseismic deformation [Marone et al, 1991;Boatwright and Cocco, 1996;Liu and Rice, 2005], as well as dynamic rupture propagation [Bizzarri et al, 2001]. Models based on the rate-and statedependent friction law have been successfully used for simulating all of the above phenomena during an earthquake cycle.…”

Postseismic quasi‐static fault slip due to pore pressure change on a bimaterial interface

“…The nonoverlapping of afterslip patches with coseismic ones [e.g., Yagi et al, 2003] suggests that afterslip is related to the frictional characteristics of this metastable region. Many researchers now tend to interpret afterslip based on rate-and state-dependent friction laws [e.g., Tse and Rice, 1986;Marone et al, 1991;Kato and Hirasawa, 1997]; the metastable region is characterized as a velocity strengthening region in such interpretation. Using the above friction law, Kato and Hirasawa [1997] numerically simulated downdip afterslip following a subduction zone earthquake.…”