Simulation of the long-term behaviour of a fault with two asperities

A system made of two sliding blocks coupled by a spring is employed to simulate the long-term behaviour of a fault with two asperities. An analytical solution is given for the motion of the system in the case of blocks having the same friction. An analysis of the phase space shows that orbits can reach a limit cycle only after entering a particular subset of the space. There is an infinite number of different limit cycles, characterized by the difference between the forces applied to the blocks or, as an alternative, by the recurrence pattern of block motions. These results suggest that the recurrence pattern of seismic events produced by the equivalent fault system is associated with a particular stress distribution which repeats periodically. Admissible stress distributions require a certain degree of inhomogeneity, which depends on the geometry of fault system. Aperiodicity may derive from stress transfers from neighboring faults.