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

Abstract

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 q , 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 T , q r 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 E parameter. Our analysis provides the triplet (q E , q T , q r ) 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 E throughout the Yellowstone park volcanic area is presented and correlated with the existence of the regional hydrothermal features.

Complexity of Fracturing in Terms of Non-Extensive Statistical Physics: From Earthquake Faults to Arctic Sea Ice Fracturing

“…Abe and Suzuki [ 25 , 50 ] showed that the cumulative distribution functions (CDFs) of inter-event distances P (> r ) and inter-event times P (> T ) between successive earthquakes in California and Japan scale according to the q -exponential distribution (Equation (8)), for q -values of q r < 1 and q T > 1, respectively. These results were further tested and verified in acoustic emissions recorded in laboratory experiments [ 51 ], in aftershock sequences [ 52 ], volcanic seismicity [ 36 , 38 ] and earthquake swarms [ 53 , 54 ], as well as in regional [ 34 , 35 , 37 , 55 , 56 , 57 ] and global seismicity [ 40 , 58 ]. In Figure 3 we show the CDFs P (> T ) and P (> r ) of inter-event times and distances, respectively, during the 2008–2009 Yellowstone Lake earthquake swarm and the corresponding fits according to the q -exponential distribution (after [ 38 ]).…”

“…If N (> M ) is the cumulative distribution of the number of earthquakes N with magnitude greater than M , then the derived model, as was later revised by [ 31 , 32 ], reads as: where M 0 is the minimum earthquake magnitude in the dataset, a M a model parameter that expresses the proportionality between the released seismic energy and the size of the fragments and q M the entropic index. The fragment-asperity model has found various applications in regional and local seismicity, as well as in volcanic seismicity [ 33 , 34 , 35 , 36 , 37 , 38 ]. In Figure 1 we show the application of the model to the 1996–2016 earthquake activity in the Yellowstone volcanic field (after the work of [ 38 ]).…”

“…The fragment-asperity model has found various applications in regional and local seismicity, as well as in volcanic seismicity [ 33 , 34 , 35 , 36 , 37 , 38 ]. In Figure 1 we show the application of the model to the 1996–2016 earthquake activity in the Yellowstone volcanic field (after the work of [ 38 ]). Generally, the results of the aforementioned studies suggest that the fragment-asperity model can adequately describe the frequency-magnitude distribution of earthquakes in a broader range of scales compared to the G-R relation.…”

Regional Seismic Information Entropy to Detect Earthquake Activation Precursors

“…Here, each earthquake in the time series is addressed as a microstate. In the context of Tsallis Entropy [ 62 , 63 , 64 , 65 , 66 , 67 ], the entropic index q that expresses the degree of non-extensivity of the system has been shown to represent the magnitude-frequency distribution, the spatiotemporal properties of earthquake swarms, asperities, and the existence of regional hydrothermal features. Natural time analysis revealed that the Tsallis formulation achieves a satisfactory description of real seismic data for Japan when the index is supplemented by long-range temporal correlations [ 63 ].…”

Seismicity Pattern Changes Prior to the 2008 Ms7.3 Yutian Earthquake

“…Among the above reported changes possibly associated with earthquakes, seismicity changes may provide some useful information for intermediate-term forecasts of earthquakes [ 8 ], as even earthquake forecasting has been a controversial issue for a long time [ 8 , 9 , 10 , 11 ]. It is noteworthy that recently, analyses of seismicity based on information entropy (e.g., [ 12 ]), Tsallis entropy (e.g., [ 13 ]), and natural time entropy (e.g., [ 14 ]) have provided interesting results towards intermediate-term and short-term forecasting.…”