Direction effects of the pulling force on the first order phase transition in a one block model for earthquakes

We consider a 1D spring-block model for earthquake dynamics under a modified frictional force, and examine the direction effects of a driving plate's action on these dynamics. This force deals with a frictional parameter λ₀ that takes into account the heterogeneity of the surface separating the two sides of the faults. We note that the amplitude of the motion of this block decays as the direction of the pulling force grows. Our investigations also show that the system undergoes a first order discontinuous transition from a stick-slip behavior to a creep motion as the friction parameter is varied. We establish that this phase transition is independent of the greatness of the driving plate's velocity, but depends strongly on the direction of the pulling force. It also appears from our work that the critical values of the frictional velocity and the magnitude of the earthquake depend on λ₀. (paper)