Self organized criticality in an improved Olami-Feder-Christensen model

TL;DR

This paper introduces an improved Olami-Feder-Christensen model demonstrating power-law avalanche distributions, q-Gaussian return distributions, and scaling relations, supporting the idea that earthquake magnitudes are inherently unpredictable.

Contribution

The study presents an enhanced model capturing avalanche size differences and return distributions, extending understanding of self-organized criticality in earthquake dynamics.

Findings

Avalanche size distribution follows power-law and finite size scaling.

Return distributions approach q-Gaussian shapes in the thermodynamic limit.

Waiting time distribution exhibits scaling behavior.

Abstract

An improved version of the Olami-Feder-Christensen model has been introduced to consider avalanche size differences. Our model well demonstrates the power-law behavior and finite size scaling of avalanche size distribution in any range of the adding parameter $p_{add}$ of the model. The probability density functions (PDFs) for the avalanche size differences at consecutive time steps (defined as returns) appear to be well approached, in the thermodynamic limit, by q-Gaussian shape with appropriate q values which can be obtained a priori from the avalanche size exponent $\tau$. For the small system sizes, however, return distributions are found to be consistent with the crossover formulas proposed recently in Tsallis and Tirnakli, J. Phys.: Conf. Ser. 201, 012001 (2010). Our results strengthen recent findings of Caruso et al. [Phys. Rev. E 75, 055101(R) (2007)] on the real earthquake data which support the hypothesis that knowing the magnitude of previous earthquakes does not make the magnitude of the next earthquake predictable. Moreover, the scaling relation of the waiting time distribution of the model has also been found.