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Thermodynamic criticality in seismicity: Uniqueness of surface-energy scaling in the fragment-asperity model

O. Sotolongo-Costa, A. V. Mora-Rodríguez, M. E. Mora-Ramos

Abstract

We propose that a linear relation between the energy of stress-bearing interactions and the surface of contact within the fragment-asperity model for earthquakes. It reveals as the only one that leads to a closed elementary form for a well-defined total entropy as a function of non-extensivity parameter, $q$. By writing the total Tsallis entropy as a function of $q$, a critical range of values is identified: $1.4\lesssim q\lesssim 1.8$. Such interval of $q$-values corresponds to the strong variation of entropy and contains the most of reported results for this parameter determined for main-shocks around the world in recent decades, indicating the role of $q$ as a criticality indicator, more than just a fitting parameter.

Thermodynamic criticality in seismicity: Uniqueness of surface-energy scaling in the fragment-asperity model

Abstract

We propose that a linear relation between the energy of stress-bearing interactions and the surface of contact within the fragment-asperity model for earthquakes. It reveals as the only one that leads to a closed elementary form for a well-defined total entropy as a function of non-extensivity parameter, . By writing the total Tsallis entropy as a function of , a critical range of values is identified: . Such interval of -values corresponds to the strong variation of entropy and contains the most of reported results for this parameter determined for main-shocks around the world in recent decades, indicating the role of as a criticality indicator, more than just a fitting parameter.
Paper Structure (6 sections, 22 equations, 1 table)

This paper contains 6 sections, 22 equations, 1 table.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Results and discussion
  4. Conclusions
  5. Uniqueness of the relation $\varepsilon \propto \sigma$ for a well-defined total entropy
  6. Alternative derivation of the $b(q)$ relation