Alejandro Ramírez-Rojas

The interaction between the Cocos Plate and the Caribbean and North American plates produces an extensive subduction zone associated with significant seismic activity from South of Mexico to Central America, posing a substantial seismic hazard to the region. Central America has experienced numerous earthquakes with magnitudes greater than 7.0, primarily associated with tectonic processes, particularly the subduction of the Cocos Plate. In Nicaragua, the western region is one of the country’s most seismically active areas. Here, we present a nonlinear statistical analysis of seismicity in Nicaragua based on a catalogue of seismic events recorded between January 2000 and September 2025. The study aims to characterize the seismic behavior of Nicaragua and its surrounding areas using natural time analysis (NTA), entropy fluctuations, the statistical distribution of an order parameter (OP), and non-extensive statistical analysis. These approaches are used to investigate the complex seismic dynamics primarily associated with the subduction of the Cocos Plate beneath the Caribbean Plate. The results indicate that the Nicaraguan lithosphere behaves as a complex self-organizing system. Although the region exhibits periods of apparent stability, the system continuously evolves toward states of criticality. The calculated entropic index (q = 1.84) indicates a high degree of instability and the presence of long-range correlations, suggesting that local seismicity is governed by correlated processes rather than occurring as a purely random process.

Different methodologies have been developed for the analysis and study of dynamical systems, including both theoretical models and natural systems. Examples span a wide range of applications, such as astronomy, financial and economic time series, biophysical systems, physiological phenomena, and Earth sciences, including seismicity and climatic processes. The study of these complex systems is commonly based on the analysis of the signals they generate, using mathematical tools to extract relevant information. A broad spectrum of mathematical disciplines converges in this context, including stochastic, probability and statistical theory, entropic and informational measures, fractal and multifractal analysis, natural time analysis, modeling of non-linearity and recurrence methods, generalized entropies, non-extensive systems, machine learning, and high-dimensional and multivariate complexity. Research in this area is largely focused on the characterization of complex systems, providing indicators of determinism or stochasticity, distinguishing between regularity, chaos, and noise, and identifying topological as well as disorder-regularity features. In addition, short- and long-term forecasting, together with the identification of short- and long-range correlations, play a central role in such characterization. To address these objectives, numerous mathematical tools have been developed for the analysis of time series and point processes, each designed to capture specific signal properties. In this work, many of the most important tools used in time series analysis are compiled and reviewed, highlighting their main characteristics and the different types of complex systems to which they have been applied.

Natural time analysis (NTA) provides a powerful method to uncover dynamic features hidden behind seismic catalogs and identify when the system enters a critical stage before a major earthquake. In this paper, we perform a NTA of the corrected Mexican seismic catalog, spanning the period from 7 January 2000 to 31 October 2024. The analysis is based on a novel procedure for performing the window selection of events in natural time. In this method, which we term window lengthening, the time series of seismic parameters are calculated by consecutively increasing the length of the initial window by one event so that the last window contains the entire catalog. In this way, the past seismic history is always kept in memory. This procedure reveals that fluctuations of seismic parameters, such as the order parameter of seismicity, the change of entropy under time reversal, and the complexity measure, are less sensitive to low-magnitude events, exhibit deeper and more easily identifiable extrema in the proximity of major earthquakes, and are strongly correlated. These features are desirable to distinguish between precursory and non-precursory fluctuations to strong earthquakes.

Seismicity is the result of the interaction between tectonic plates in relative motion where the underlying mechanism of earthquake generation in seismic subduction areas is stick-slip. In reality, seismicity is a complex phenomenon as it involves processes that take place from within the Earth. A thorough understanding of seismicity requires theoretical and experimental approaches. The dynamics in subduction zones occur when two tectonic plates, one on top of the other, are in relative motion where the plate below is in motion due to convective processes within the Earth. Due to the roughness of both surfaces, the underlying mechanism that gives rise to seismicity is stick-slip. In this work, an experimental stick-slip model is proposed, which simulates the relative motion of two rough surfaces by the interaction of two blocks covered by sandpaper with a certain degree of roughness. In this experimental model, the interaction between rough surfaces (sandpaper), with a relative motion in opposite directions to each other, produces stick-slip events (synthetic seismicity), which mimic real seismicity. Here we present the first analyses of synthetic seismicity by calculating the Gutenberg-Richter law, temporal correlations and characterization in terms of organization and order from the Fisher-Shannon method for each synthetic catalogue.

The Mexican Pacific coast has presented significant seismic activity due to the tectonic processes that have generated it. This coast, from Baja California until Chiapas is matched with three tectonic settings, to the north, a dispersion zone is presented in Baja California and Cortes Sea, at the middle, conforming by Jalisco, Colima and Michoacan states, La Rivera Plate is the principal source of seismicity and, finally the seismic activity in Guerrero, Oaxaca and Chiapas is driven by the Cocos Plate subduction. According with the catalogues published by the SSN, the yearly number of earthquakes occurred is very different at each zone is very different being Cocos plate the subduction zone that has produced the major number of earthquakes. We analyzed the catalogues of six zones of the Mexican Pacific coast in the period between 2000 and 2023. Based on the Tsallis q-statistical approach it is possible to assess the temporal changes of the non-extensivity by fitting the cumulative number of earthquakes with the generalized Gutenberg-Richter. Our preliminary results show differences in the fitting of the q-values for the six studied regions. These results are consistent with a pervious analysis, where it was observed that the highest q-value was obtained in Jalisco zone, while Oaxaca region reported the lowest q-value.

Mexico is a well-known seismically active country, which is primarily affected by several tectonic plate interactions along the southern Pacific coastline and by active structures in the Gulf of Baja California. In this paper we investigate this seismicity in the context of a non-extensive statistical approach based on Tsallis entropy. The analysis is performed using data from the corrected Mexican seismic catalogue provided by the National Seismic Service, spanning a period from January 2000 to October 2023. The Gutenberg-Richter law fitting to the earthquake sub-catalogues for all six regions studied indicates magnitudes of completeness between 3.30 and 3.76. All six regions display values of the entropic index in the range 1.52≲q≲1.61, which are lower than the previously estimated range 1.54≲q≲1.70 using catalogue data from 1988 to 2010. The cause of this discrepancy is certainly due to the use of modern recording devices, which are sensitive enough to detect a larger number of low-magnitude events compared to older instrumentation.

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