Frictional weakening and slip complexity in earthquake faults

Previous work has shown that velocity-weakening friction produces slip complexity in simple dynamical models of earthquake faults ( Carlson and Langer, 1989). Rere I show that a different type of dynamical instability, caused by slipweakening friction, also produces slip complexity. The deterministically chaotic slip complexity produced by slip-weakening friction in a simple one dimensional model is studied and the scaling of the distribution of sizes of events with the parameters in the model examined. In addition, a possible physical origin of frictional weakening is examined, through a very simplified mathematical representation of a physical process proposed by Sibson (1973), whereby frictional heating causes an increase in pore fluid temperature and pressure, thereby reducing the effective normal stress and friction. The two different types of frictional weakening are derived from two opposing limits, with slip weakening occurring when the dissipation of heating is slow compared to the rupture timescale, as Lachenbruch (1980) has shown, while velocity weakening is shown to occur when the dissipation is fast compared to the rupture timescale. Since both end-member cases of frictional weakening are seen to produce slip complexity, slip complexity is argued to be a generic feature of frictional weakening and elastodynamics on a fault.