Complexity of the Yellowstone Park Volcanic Field Seismicity in Terms of Tsallis Entropy

The Yellowstone Park volcanic field is one of the most active volcanic systems in the world, presenting intense seismic activity that is characterized by several earthquake swarms over the last decades. In the present work, we focused on the spatiotemporal properties of the recent earthquake swarms that occurred on December-January 2008-2009 and the 2010 Madison Plateau swarm, using the approach of Non Extensive Statistical Physics (NESP). Our approach is based on Tsallis entropy, and is used in order to describe the behavior of complex systems where fracturing and strong correlations exist, such as in tectonic and volcanic environments. This framework is based on the maximization of the non-additive Tsallis entropy S, introducing the q-exponential function and the entropic parameter q that expresses the degree of non-extentivity of the system. The estimation of the q-parameters could be used as a correlation degree among the events in the spatiotemporal evolution of seismicity. Using the seismic data provided by University of Utah Seismological Stations (UUSS), we analyzed the inter-event time (T) and distance (r) distribution of successive earthquakes that occurred during the two swarms, fitting the observed data with the q-exponential function, resulting in the estimation of the Tsallis entropic parameters q, q for the inter-event time and distance distributions, respectively. Furthermore, we studied the magnitude-frequency distribution of the released earthquake energies E as formulated in the frame of NESP, which results in the estimation of the q parameter. Our analysis provides the triplet (q, q, q) that describes the magnitude-frequency distribution and the spatiotemporal scaling properties of each of the studied earthquake swarms. In addition, the spatial variability of q throughout the Yellowstone park volcanic area is presented and correlated with the existence of the regional hydrothermal features.