A study of seismicity on the Pacific coast of the Mexican Republic using statistical and fractal methods

Digitization of information has allowed to scientists understand diverse dynamics of complex systems. In particular, earthquake catalogs are one of the main subject of study in geo-statistical science. Main contributions are characterization and classification of seismic regions, evidence of self-organized criticality of seismicity, seismic quiescences, dynamics of aftershocks, apparently precursor behaviors of great earthquakes, and more. This is a study of the seismicity in the Pacific's coast of the Mexican Republic. Calculation of the parameters a and b of the Gutenberg-Richter law and computation of the fractal dimension by box counting method are presented. The analyses and calculations are divided into two types of study: spatial and temporal. The spatial study is carried out over the entire Mexican Republic and for five regions delimited on the Pacific coast in the time interval between 1975 and 2019. On the other hand, the temporal study is carried out among diverse time periods defined according to all possible pairs of years between 1975 and 2019, giving a total of 1035 time intervals. We obtained b-value ≈ 1 for all cases of study. Also a strong linear correlation between a and b parameters is found. Finally, we obtained fractal dimension values D between 1.3-1.9 for the five regions. We conclude that there is a positive correlation between coefficients a and b, values of D agree with the spatial density of the epicenters of each region, and considerable changes in the coefficient b with respect to time periods.