MÈTODOS DE REDES COMPLEXAS MONO E MULTICAMADAS APLICADOS À SISMOLOGIA

Abstract

In this work, we studied real and synthetic earthquake data from the viewpoint of Complex Networks and Nonextensive Statistical Mechanics (NESM). Through the analysis of spatial and temporal probability distributions between successive earthquakes, the behavior of complex systems in the seismological phenomenon was investigated, being observed agreement between these distributions and non-traditional functions, q-exponential, present in the theory of NESM. These functions arise in systems that have strong long-range temporal and spatial correlations between their elements, and have been found in previous works for regional and global earthquakes. In addition, we found relationships that provided scale invariance in the observed and simulated seismic events, being one more evidence of the presence of complex characteristics in the seismological phenomenon. Furthermore, complex networks of epicenters were constructed using two approaches: monolayer and multilayer. In the first case, we considered two models of connection, successive and time window, to establish relationships between different locations in the world. Through the analysis of topological properties of the created networks, such as the degree correlation function and the degree correlation coefficient, it was revealed that shallow earthquakes (depth of up to 70 km) has assortative behavior, which means regions where occurred earthquakes with great magnitude are strongly correlated to each other. In contrast, networks of deep earthquake (depth greater than 70 km) exhibit neutral (random) behavior with no specific correlation between them. We also created temporal multiplex networks of successive connections for global earthquakes, and they revealed unique properties in earthquake networks that were not visible in simple networks. We observed the distributions of strength of these networks follow a power law with exponential cutoff behavior. The global clustering coefficient of the multiplex networks of shallow earthquakes presents scale invariance, while networks of deep events exhibit behavior similar to random networks. The results indicate similarities and differences between shallow and deep earthquakes in various contexts. Furthermore, they strengthen the hypothesis that the Earth is in a critical state and the possible existence of relationships between spatially and temporally distant events.