Analysis of Hurst exponent and the fractal dimension of seismic activity occurred in the Cocos Plate, Mexico

Julian Patiño-Ortiz, Alexander S Balankin, Miguel Patiño-Ortiz, Isaías Badillo Piña, Ricardo Carreño-Aguilera, Felipe Gayosso Martínez, Juan F Sabas G.

Abstract


Earthquakes are a natural phenomenon of great interest, know and understand the processes and mechanisms that the generated is subject of research worldwide, and it is essential to develop models that allow in the future understanding their behavior and therefore predict their occurrence.

The objective of this research is to analyze the dynamics of seismic activity occurred in the Cocos Plate - Mexico, through the evolution of the Hurst exponent and fractal dimension in 3D, in time series of seismic activity, taking the magnitude (M) as the main parameter.

In the analysis is used the methodology for the development of earthquake prediction models developed under the systems approach designed by the authors. To define the time series of seismic activity, are considered first annual intervals to find the Hurst exponent of each year since 1988 (the year in which the database is consistent) until 2012, and then it accumulates the years to find again the Hurst exponent to see the cumulative evolution of it.

In research, is analyzed the seismic activity occurred in the Cocos Plate in Mexico, in the period from January 1, 1988 to December 31, 2012. Analyses were performed following the methods proposed in this research, mainly considering that the Hurst exponent analysis provides the ability to find that the space-temporal behavior of the seismicity obey and/or can be described by parameters such as the dimension fractal and complex systems.

Keywords


Hurst coefficient, fractal, seismic activity, time series, earthquakes, earthquake prediction