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The paper considers the application of the Tsallis q-statistics based on the principles of non-extensive statistical physics to the analysis of seismic events and man-made impacts. Non-extensive statistical physics (NESP) is based on the concept of entropy, which was introduced in 1988 by Constantino Tsallis as a generalization of the standard Boltzmann–Gibbs entropy. NESP is used to describe complex dynamic systems that demonstrate the interaction of system elements with their nearest neighbors and with the entire system as a whole, as well as memory effects. Such systems are characterized by a large range of spatio-temporal correlations. The Tsallis parameter q can be used as a measure of the correlation of the system. The probability density function of the difference in magnitude between successive tectonic earthquakes is more realistically described by the q-Gaussian distribution than by the normal distribution. To describe the probability density function, elements of the so-called q-algebra are used: the q-exponent and the q-logarithm. The frequency distributions of time and distance between successive events are adequately approximated by the q-exponent. The distribution of earthquakes by energy is approximated by an analytical curve with the calculated value of the Tsallis parameter q. The determination of the Tsallis parameter q by different methods for catalogues of tectonic earthquakes and industrial explosions demonstrates the varying degree of correlation of the systems considered. Based on the studies of two seismically active regions of the Altai-Sayan Mountain Region (ASR) and Sakhalin Island, it is shown that the earthquake flow is a system with memory and long-range spatial correlations, and the obtained values of the Tsallis parameter q ~ 1.5 practically coincide with the values calculated for the magnitudes of the catalogs of various seismically active regions. At the same time, series of industrial explosions occurring in the same regions are not processes with memory and long-range correlations, as indicated by the reduced values of the Tsallis parameter q.

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Analysis of Tectonic Earthquakes and Industrial Explosions from the Point of Non-extensive Statistical Physics

  • 会议论文

  • 发表日期：

    2026年

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  • V. N. Sychev,
  • N. A. Sycheva

摘要

The paper considers the application of the Tsallis q-statistics based on the principles of non-extensive statistical physics to the analysis of seismic events and man-made impacts. Non-extensive statistical physics (NESP) is based on the concept of entropy, which was introduced in 1988 by Constantino Tsallis as a generalization of the standard Boltzmann–Gibbs entropy. NESP is used to describe complex dynamic systems that demonstrate the interaction of system elements with their nearest neighbors and with the entire system as a whole, as well as memory effects. Such systems are characterized by a large range of spatio-temporal correlations. The Tsallis parameter q can be used as a measure of the correlation of the system. The probability density function of the difference in magnitude between successive tectonic earthquakes is more realistically described by the q-Gaussian distribution than by the normal distribution. To describe the probability density function, elements of the so-called q-algebra are used: the q-exponent and the q-logarithm. The frequency distributions of time and distance between successive events are adequately approximated by the q-exponent. The distribution of earthquakes by energy is approximated by an analytical curve with the calculated value of the Tsallis parameter q. The determination of the Tsallis parameter q by different methods for catalogues of tectonic earthquakes and industrial explosions demonstrates the varying degree of correlation of the systems considered. Based on the studies of two seismically active regions of the Altai-Sayan Mountain Region (ASR) and Sakhalin Island, it is shown that the earthquake flow is a system with memory and long-range spatial correlations, and the obtained values of the Tsallis parameter q ~ 1.5 practically coincide with the values calculated for the magnitudes of the catalogs of various seismically active regions. At the same time, series of industrial explosions occurring in the same regions are not processes with memory and long-range correlations, as indicated by the reduced values of the Tsallis parameter q.