A simple but effective cellular automaton for earthquakes

The physics of fractures, which forms the basis of seismic faulting, is not very amenable to simple deterministic differential equations. For this reason a different approach, aimed at reproducing the statistical mechanical properties of earthquakes, has attracted progressively increasing interest. A variety of models have been presented but there seems to be little that can be done to ascertain the merits and defects of each. We set the clock back and attempt to derive a dynamically evolving automation that is as simple as possible and that incorporates all the basic ingredients and includes strain diffusion, a process often disregarded in simple models in spite of its crucial importance. Our automaton is based on a homogeneous grid of cells and its rupturing is controlled by a generalized local threshold. The automation also considers local dissipation of energy and time-dependent strain applications. This simple model is capable of reproducing earthquake dynamics, including the effects due to transient loads such as those imposed by elastic waves, with an efficiency superior to that of the most complicated automata and with less stringent assumptions.