Stick-slip statistics for two fractal surfaces: a model for earthquakes

Following the observations of the self-similarity in various length scales in the roughness of the fractured solid surfaces, we propose here a new model for the earthquake. We demonstrate rigorously that the contact area distribution between two fractal surfaces follows a unique power law. This is then utilised to show that the elastic energy releases for slips between two rough fractal surfaces indeed follow a Guttenberg–Richter like power law.