Jeffrey Howard Nussbaum

A two degree-of-freedom earthquake model with static/dynamic friction

Can a simple multi-block-spring model with total symmetry make interesting predictions for fault behaviour? Our model consists of a symmetric, slowly driven, two degree-of-freedom block-spring system with static/dynamic friction. The simple friction law and slow driving rate allow the state of this fourth order system to be described between slip events by a single variable, the difference in the stretch of the driving springs. This stretch difference measures the locked-in stress and is closely related to fault stress inhomogeneity.In general,smoothing is not observed. A spatially homogeneous stress state is found to almost always be unstable, in that the system tends toward an inhomogeneous state after many slip events. The system evolves either to a cycle that alternates between two types of earthquakes, or to a cycle with repeating but identical asymmetric earthquakes. One type of alternating earthquake solution is structurally unstable, which implies a great sensitivity to model perturbations.For this simple model, spatial asymmetry necessarily occurs, despite the symmetry in the model, thus suggesting that spatial structure in seismicity patterns may be a consequence of earthquake dynamics, not just fault heterogeneity.