Earthquake magnitude distribution and aftershocks: a statistical geometry explanation

TL;DR

This paper explains earthquake energy distribution and aftershock patterns using statistical mechanics and geometric models of stress fields, providing predictions consistent with observed laws like Gutenberg-Richter and Omori.

Contribution

It introduces a geometric and statistical mechanics framework to explain earthquake magnitude distribution and aftershock behavior, linking stress field properties to empirical laws.

Findings

Predicted the Gutenberg-Richter law exponent from stress field models.

Provided a mechanism for aftershock occurrence consistent with the Omori law.

Validated predictions through comparison with empirical data.

Abstract

The emergence of a power-law distribution for the energy released during an earthquake is investigated in several models. Generic features are identified which are based on the self-affine behavior of the stress field prior to an event. This field behaves at large scale as a random trajectory in 1 dimension of space and a random surface in 2 dimensions. Using concepts of statistical mechanics and results on the properties of these random objects, several predictions are obtained and verified, in particular the value of the power-law exponent of the earthquake energy distribution (the Gutenberg-Richter law) as well as a mechanism for the existence of aftershocks after a large earthquake (the Omori law).