Statistical and fractal properties of the spatial distribution of earthquakes in the central zone of Chile are studied. In particular, data are shown to behave according to the well-known Gutenberg-Richter law. The fractal structure is evident for epicenters, not for hypocenters. The multifractal spectrum is also determined, both for the spatial distribution of epicenters and hypocenters. For negative values of the index of multifractal measure q, the multifractal spectrum, which usually cannot be reliably found from data, is calculated from a generalized Cantor-set model, which fits the multifractal spectrum for q>0, a technique which has been previously applied for analysis of solar wind data.

We introduce a new method of characterizing the seismic complex systems using a procedure of transformation from complex networks into time series. The undirected complex network is constructed from seismic hypocenters data. Network nodes are marked by their connectivity. The walk on the graph following the time of succeeding seismic events generates the connectivity time series which contains, both the space and time, features of seismic processes. This procedure was applied to four seismic data sets registered in Chile. It was shown that multifractality of constructed connectivity time series changes due to the particular geophysics characteristics of the seismic zones—it decreases with the occurrence of large earthquakes—and shows the spatiotemporal organization of these seismic systems.

Four geographical zones are defined along the trench that is formed due to the subduction of the Nazca plate underneath the South American plate; they are denoted A, B, C and D from north to south; zones A, B and D had a major earthquake after 2010 (magnitude over 8.0), while zone C has not, thus offering a contrast for comparison. For each zone, a sequence of intervals between consecutive seisms with magnitudes greater than or equal to 3.0 is set up and then characterized by Shannon entropy and mutability. These methods show a correlation after a major earthquake in what is known as the aftershock regime but show independence otherwise. Exponential adjustments to these parameters reveal that mutability offers a wider range for the parameters to characterize the recovery compared to the values of the parameters defining the background activity for each zone before a large earthquake. It is found that the background activity is particularly high for zone A, still recovering for zone B, reaching values similar to those of zone A in the case of zone C (without recent major earthquake) and oscillating around moderate values for zone D. It is discussed how this can be an indication of more risk of an important future seism in the cases of zones A and C. The similarities and differences between Shannon entropy and mutability are discussed and explained.

The mechanical description of the seismic cycle has an energetic analogy in terms of statistical physics and the second law of thermodynamics. In this context, an earthquake can be considered a phase transition, where continuous reorganization of stresses and forces reflects an evolution from equilibrium to non-equilibrium states, and we can use this analogy to characterize the earthquake hazard of a region. In this study, we used 8 years (2007–2014) of high-quality Integrated Plate Boundary Observatory Chile (IPOC) seismic data for > 100 000 earthquakes in northern Chile to test the theory that Shannon entropy, H, is an indicator of the equilibrium state of a seismically active region. We confirmed increasing H reflects the irreversible transition of a system and is linked to the occurrence of large earthquakes. Using variation in H, we could detect major earthquakes and their foreshocks and aftershocks, including the 2007 M_w 7.8 Tocopilla earthquake, the 2014 M_w 8.1 Iquique earthquake, and the 2010 and 2011 Calama earthquakes (M_w 6.6 and 6.8, respectively). Moreover, we identified possible periodic seismic behaviour between 80 and 160 km depth.