Conditions for large earthquakes in a two-asperity fault model

A fault with two asperities is modelled as a system made of two blocks coupled by a spring and sliding on a plane under the same values of static and dynamic friction. An analytical solution is given for the simultaneous motion of the blocks and the corresponding orbits are plotted in the phase space. It is proven that, whichever the initial state is, the long-term behaviour of the system is one of an infinite number of limit cycles, characterized by a particular pattern of forces. The region where the system is located when the blocks are stationary can be divided into narrow stripes corresponding to different orbits of the points belonging to them. This implies that the system is sensitive to perturbations and has relevant implications for a fault, which is subject to stress transfers from earthquakes generated by neighbouring faults. In this case, the fault may experience a larger earthquake, with the simultaneous failure of the two asperities, which restores a stress distribution compatible with periodic behaviour. The seismic moment associated with simultaneous asperity failure is always greater than the maximum value that can be released in a limit cycle. For strongly coupled asperities, the moment can be several times larger.