Complex events in a fault model with interacting asperities

The dynamics of a fault with heterogeneous friction is studied by employing a discrete fault model with two asperities of different strengths. The average values of stress, friction and slip on each asperity are considered and the state of the fault is described by the slip deficits of the asperities as functions of time. The fault has three different slipping modes, corresponding to the asperities slipping one at a time or simultaneously. Any seismic event produced by the fault is a sequence of n slipping modes. According to initial conditions, seismic events can be different sequences of slipping modes, implying different moment rates and seismic moments. Each event can be represented geometrically in the state space by an orbit that is the union of n damped Lissajous curves. We focus our interest on events that are sequences of two or more slipping modes: they show a complex stress interchange between the asperities and a complex temporal pattern of slip rate. The initial stress distribution producing these events is not uniform on the fault. We calculate the stress drop, the moment rate and the frequency spectrum of the events, showing how these quantities depend on initial conditions. These events have the greatest seismic moments that can be produced by fault slip. As an example, we model the moment rate of the 1992 Landers, California, earthquake that can be described as the consecutive failure of two asperities, one of which has a double strength than the other, and evaluate the evolution of stress distribution on the fault during the event.