The statistical mechanics of earthquakes

Abstract

We review recent theoretical developments on the physics of earthquakes. In particular, we focus on the rise of the statistical mechanical view of earthquakes as a kind of ‘phase transition’. This view is appealing in light of the well known scaling relations such as the Gutenberg-Richter magnitude frequency and Omori's law of aftershock decay. Scaling relations such as these, which are in reality power laws, are known to be associated with dynamical systems residing near a critical point in the state space of the system. These second-order critical points are associated with second-order transitions, which are a result of gradual changes of the controlling parameters. At the same time, characteristic earthquakes, which involve the entire fault segment sliding nearly at once, are more reminiscent of a first-order transition, which is characterized by sudden widespread changes in the physical state of the system. In this paper, we review these ideas and show how recent developments are leading to a view of earthquake fault systems based on modern statistical mechanics.