Nonextensive models for earthquakes

TL;DR

This paper revisits a nonextensive statistical model for earthquakes, proposing a new energy distribution function and validating it with seismic data, highlighting differences from previous models in physical quantities.

Contribution

It introduces a modified energy distribution function based on Tsallis statistics and tests its validity with real earthquake data, differing from prior models.

Findings

New energy distribution function differs significantly from previous models.

Both models yield similar nonextensive parameter q values.

Physical quantities like energy density differ by orders of magnitude.

Abstract

We have revisited the fragment-asperity interaction model recently introduced by Sotolongo-Costa and Posadas (Physical Review Letters 92, 048501, 2004) by considering a different definition for mean values in the context of Tsallis nonextensive statistics and introducing a new scale between the earthquake energy and the size of fragment $\epsilon \propto r^3$. The energy distribution function (EDF) deduced in our approach is considerably different from the one obtained in the above reference. We have also tested the viability of this new EDF with data from two different catalogs (in three different areas), namely, NEIC and Bulletin Seismic of the Revista Brasileira de Geof\'{\i}sica. Although both approaches provide very similar values for the nonextensive parameter $q$, other physical quantities, e.g., the energy density differs considerably, by several orders of magnitude.