Positive feedback, memory, and the predictability of earthquakes

We review the "critical point" concept for large earthquakes and enlarge it in the framework of so-called "finite-time singularities." The singular behavior associated with accelerated seismic release is shown to result from a positive feedback of the seismic activity on its release rate. The most important mechanisms for such positive feedback are presented. We solve analytically a simple model of geometrical positive feedback in which the stress shadow cast by the last large earthquake is progressively fragmented by the increasing tectonic stress.