• Corpus ID: 118888449

On a possible fractal relationship between the Hurst exponent and the nonextensive Gutenberg-Richter index

@article{Freitas2017OnAP,
  title={On a possible fractal relationship between the Hurst exponent and the nonextensive Gutenberg-Richter index},
  author={D. B. de Freitas and Guilherme Francca and T. M. Scheerer and Carlos da Silva Vilar and R. Silva},
  journal={arXiv: Geophysics},
  year={2017}
}

• D. B. D. Freitas, G. Francca, +2 authors R. Silva
• Published 25 July 2017
• Geology
• arXiv: Geophysics

In the present paper, we analyze the fractal structures in magnitude time series for a set of unprecedented sample extracted from the National Earthquake Information Center (NEIC) catalog corresponding to 12 Circum-Pacific subduction zones from Chile to Kermadec. For this end, we used the classical Rescaled Range ($R/S$) analysis for estimating the long-term persistence signature derived from scaling parameter so-called Hurst exponent, $H$. As a result, we measured the referred exponent and obtained all values of $H>0.5$, indicating that a long-term memory effect exists. The main contribution of our paper, we found a possible fractal relationship between $H$ and the $b_{s}(q)$-index which emerges from nonextensive Gutenberg-Richter law as a function of the asperity, i.e., we show that the values of $H$ can be associated with the mechanism which controls the abundance of magnitude and, therefore, the level of activity of earthquakes. Finally, we concluded that dynamics associated with fragment-asperity interactions can be emphasized as a self-affine fractal phenomenon.