• Corpus ID: 118888449

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

  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},
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… 

Figures and Tables from this paper

Calculating the constant in the Hurst index for the time series

In this paper, the problem of precise determination of the constant value of the Hurst fractal index for the time series is considered and a proposed method for determining this indicator is presented.

Micro-scale, mid-scale, and macro-scale in global seismicity identified by empirical mode decomposition and their multifractal characteristics

It is shown that when using the mid-scale time-series only, it can obtain results similar to those obtained by the natural time analysis of global seismicity when focusing on the prediction of earthquakes with M ≥ 8.4.



Nonextensivity and natural time: The case of seismicity.

Natural time analysis reveals that the nonextensivity parameter q, in contrast to some published claims, cannot be considered as a measure of temporal organization, but the Tsallis formulation does achieve a satisfactory description of real seismic data for Japan for q=1.66 when supplemented by long-range temporal correlations.

Nonlinear Time Series Analysis of Sunspot Data

This article deals with the analysis of sunspot number time series using the Hurst exponent. We use the rescaled range (R/S) analysis to estimate the Hurst exponent for 259-year and 11 360-year

Rescaled range (R/S) analysis on seismic activity parameters

The rescaled range (R/S) analysis, proposed by Hurst, is a new statistical method. Being different from traditional statistical method, R/S analysis can provide the information of maximum fluctuation


The present work reports on the discovery of three stars that we have identified to be rotating Sun-like stars, based on rotational modulation signatures inferred from light curves from the CoRoT

Nonextensive triplet in a geological faults system

The values obtained reveal that the -Gaussian behavior of the aforementioned data exhibit long-range temporal correlations and exhibits quasi-monofractal behavior with a Hurst exponent of 0.87.

Fractals and Multifractals in Ecology and Aquatic Science

Introduction About Geometries and Dimensions From Euclidean to Fractal Geometry Dimensions Self-Similar Fractals Self-Similarity, Power Laws, and the Fractal Dimension Methods for Self-Similar

Second-order moving average and scaling of stochastic time series

Abstract:Long-range correlation properties of stochastic time series y(i) have been investigated by introducing the function σ2MA = [y(i) - (i)]2, where (i) is the moving average of y(i), defined as

An Asperity Model of Large Earthquake Sequences

The variation in maximum rupture extent of large shallow earthquakes in circum-Pacific subduction zones is interpreted in the context of the asperity model of stress distribution on the fault plane.