Noname manuscript No.

By using earthquake catalogs, previous studies have reported evidence that some changes in the spatial and temporal organization of earthquake activity are observed before and after of a main shock. These previous studies have used different approaches for detecting clustering behavior and distance-events density in order to point out the asymmetric behavior of foreshocks and aftershocks. Here, we present a statistical analysis of the seismic activity related to the M w = 8.2 earthquake that occurred on 7 September 2017 in Mexico. First, we calculated the inter-event time and distance between successive events for the period 1 January 1998 until 20 October 2017 in a circular region centered at the epicenter of the M w = 8.2 EQ. Next, we introduced the concept of pseudo-velocity as the ratio between the inter-event distance and inter-event time. A sliding window is considered to estimate some statistical features of the pseudo-velocity sequence before the main shock. Specifically, we applied the multifractal method to detect changes in the spectrum of singularities for the period before the main event on 7 September. Our results point out that the multifractality associated with the pseudo-velocities exhibits noticeable changes in the characteristics of the spectra (more narrower) for approximately three years, from 2013 until 2016, which is preceded and followed by periods with wider spectra. On the other hand, we present an analysis of patterns of seismic quiescence before the M w = 8.2 earthquake based on the Schreider algorithm over a period of 27 years. We report the existence of an important period of seismic quietude, for six to seven years, from 2008 to 2015 approximately, known as the alpha stage, and a beta stage of resumption of seismic activity, with a duration of approximately three years until the occurrence of the great earthquake of magnitude M w = 8.2 . Our results are in general concordance with previous results reported for statistics based on magnitude temporal sequences.

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.

During past decades, several studies have suggested the existence of possible seismic electric precursors associated with earthquakes of magnitude M > 7 . However, additional analyses are needed to have more reliable evidence of pattern behavior prior to the occurrence of a big event. In this article we report analyses of self-potential Δ V records during approximately two years in three electro-seismic stations in Mexico located at Acapulco, Guerrero; Petatlán, Guerrero and Pinotepa Nacional, Oaxaca. On 18 April 2014 an M s 7.2 earthquake occurred near our Petatlán station. Our study shows two notable anomalies observed in the behavior of the Fourier power spectrum of Δ V for ultra low frequency ULF-range, and the transition of the α l -exponent of the detrended fluctuation analysis of the Δ V time series from uncorrelated to correlated signals. These anomalies lasted approximately three and a half months before the main shock. We compare this electric pattern with another electric signal we reported associated with an M s 7.4 that occurred on 14 September 1995 at Guerrero state, Mexico. Our characterization of the anomalies observed in both signals point out similar features that enrich our knowledge about precursory phenomena linked to the occurrence of earthquakes of magnitude M > 7 .

We introduce a generalization of Higuchi's estimator of the fractal dimension as a new way to characterize the multifractal spectrum of univariate time series. The resulting multifractal Higuchi dimension analysis (MF-HDA) method considers the order-q moments of the partition function provided by the length of the time series graph at different levels of subsampling. The results obtained for different types of stochastic processes as well as real-world examples of word length series from fictional texts demonstrate that MF-HDA provides a reliable estimate of the multifractal spectrum already for moderate time series lengths. Practical advantages as well as disadvantages of the new approach as compared to other state-of-the-art methods of multifractal analysis are discussed, highlighting the particular potentials of MF-HDA to distinguish monofrom multifractal dynamics based on relatively short time series.