A Complexity View into the Physics of the Accelerating Seismic Release Hypothesis: Theoretical Principles

Area of Science:

• Geophysics and Statistical Physics
• Seismology and Complex Systems

Background:

• Observational data suggest large earthquakes often follow accelerating-decelerating seismic release patterns.
• These patterns are frequently modeled using power law time-to-failure relationships.

Purpose of the Study:

• To develop a unified theoretical framework for seismic release rates.
• To integrate non-extensive statistical physics and energy conservation principles.
• To analyze earthquake precursors and their relationship to fault system dynamics.

Main Methods:

• Defined a generalized Benioff strain function (Ωξ(t)) incorporating earthquake energy (E) and a parameter (ξ).
• Derived a time-to-failure power-law for fault systems obeying hierarchical distribution laws from Tsallis entropy.
• Analyzed a common exponent (mξ) as a function of the non-extensive entropic parameter (q) and the Gutenberg-Richter b-value.

Main Results:

• Demonstrated the existence of a common exponent (mξ) dependent on the Tsallis entropic parameter (q).
• Derived an analytic expression connecting mξ, q, and the Gutenberg-Richter b-value.
• Identified ranges of q and b values associated with accelerating seismic stages and failure, including precursory variations in mξ.

Conclusions:

• The study provides a new theoretical perspective on empirical earthquake laws.
• Calculations based on Tsallis entropy and energy conservation link model parameters to expected main shock magnitudes.
• The framework offers insights into the average generalized Benioff strain rate during accelerating periods.