## Earthquake statistical properties : an explanation for the distribution of magnitude and for the existence of aftershocks

Earthquakes in nature follow several statistical properties. In particular, the distribution of energy released by an earthquake (Gutenberg-Richter's law) and the frequency of aftershocks after a large event (Omori's law) are both power-laws.

By studying several earthquake models, we have shown that the Gutenberg-Richter law results from the spatial distribution of the stress field. This field is self-similar at large scale and for two dimensionnal systems can be modelled as a random surface. Using this analogy, a series of predictions is made that includes the Gutenberg-Richter law and the value of its exponent (so called b-value) together with the existence of aftershocks and their temporal distribution following Omori's law.