Last modified: 2017-05-22

#### Abstract

The most common description of the magnitude-frequency distribution of seismic events is the exponential Gutenberg-Richter (G-R) law. Although it has been experimentally well-validated for many catalogs worldwide, it isnâ€™t yet clear at which space-time scales the G-R law still holds. For instance, in small areas where a large earthquake just happened, the probability to have another strong earthquake in a short-time interval should diminish because it takes time to recover the same level of elastic energy just released. Shortly, the magnitude-frequency law before and after a large event in small areas should be different because the energy available is different.

Our study is then aimed to propose a modification of the G-R relationship by including the dependence on an energy parameter. The new version of the magnitude distribution is such that a higher release of energy corresponds to a lower probability of strong aftershocks. In addition, we impose the new magnitude distribution to verify an invariance condition: when integrating over the energy from a minimum value to infinity, that is when integrating over large areas, the Gutenberg-Richter must be reobtained. Finally, we analyze some high quality seismic catalogs to support the above pure-modeling approach.