Abstract
Observational indications support the hypothesis that many large earthquakes are preceded by accelerating-decelerating seismic release rates which are described by a power law time to failure relation. In the present work, a unified theoretical framework is discussed based on the ideas of non-extensive statistical physics along with fundamental principles of physics such as the energy conservation in a faulted crustal volume undergoing stress loading. We define a generalized Benioff strain function Ω ξ ( t ) = ∑ i = 1 n ( t ) E i ξ ( t ) , where E(i) is the earthquake energy, 0 ≤ ξ ≤ 1 . and a time-to-failure power-law of Ω ξ ( t ) derived for a fault system that obeys a hierarchical distribution law extracted from Tsallis entropy. In the time-to-failure power-law followed by Ω ξ ( t ) the existence of a common exponent m(ξ) which is a function of the non-extensive entropic parameter q is demonstrated. An analytic expression that connects m(ξ) with the Tsallis entropic parameter q and the b value of Gutenberg-Richter law is derived. In addition the range of q and b values that could drive the system into an accelerating stage and to failure is discussed, along with precursory variations of m(ξ) resulting from the precursory b-value anomaly. Finally our calculations based on Tsallis entropy and the energy conservation give a new view on the empirical laws derived in the literature, the associated average generalized Benioff strain rate during accelerating period with the background rate and connecting model parameters with the expected magnitude of the main shock.