Model quakes in the two-dimensional wave equation

This paper presents a new two-dimensional wave equation model of an earthquake fault. The model generates a complex sequence of slip events on a fault with uniform properties when there is a frictional weakening instability. Previous models of long faults in one and two dimensions had the driving in the bulk, giving the Klein-Gordon equation in the bulk. Here, I place the driving on the boundary, giving the wave equation in the bulk. The different models are, however, shown to behave similarly. I examine a whole range of frictions, with slip weakening as one end-member case and velocity weakening as the other end-member case, and show that they display a generic type of slip: complexity: there is an exponential distribution of the largest events and, for sufficient weakening, a power law distribution of small events. With the addition of a viscous-type friction term on the fault, I show that the results are independent of grid resolution, indicating that continuum limit complexity is achieved.