A scale‐invariant cellular‐automata model for distribited seismicity

Abstract

In the standard cellular‐automata model for a fault an element of stress is randomly added to a grid of boxes until a box has four elements, these are then redistributed to the adjacent boxes on the grid. This redistribution may result in one or more of these boxes having four or more elements in which case further redistributions are required. On the average added elements are lost from the edges of the grid. We have modified this model so that the boxes have a scale‐invariant distribution of sizes. The objective is to model a scale‐invariant distribution of fault sizes. When a redistribution from a box occurs it is equivalent to a characteristic earthquake on the fault. A redistribution from a small box (a foreshock) may trigger an instability in a large box (the main shock). A redistribution from a large box always triggers many instabilities in the smaller boxes (aftershocks). The frequency‐size statistics for both main shocks and aftershocks satisfy the Gutenberg‐Richter relation with b = 0.835 for main shocks and b = 0.635 for aftershocks. Model foreshocks occur 28% of the time.