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

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 Ei 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 mξ which is a function of the non-extensive entropic parameter q is demonstrated. An analytic expression that connects mξ 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 mξ 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.

Nucleation and Cascade Features of Earthquake Mainshock Statistically Explored from Foreshock Seismicity

“…We point out that our finding is consistent with the Critical Point (CP) earthquake hypothesis ([ 20 , 21 , 22 , 23 ]), where failure in the crust is a scaling up process in which stress spreads out over the entire area before the mainshock. The next step would be to apply our method to investigate the accelerating moment release and the growth of spatial correlation length with respect to their predictive power.…”

Geosystemics View of Earthquakes

“…Criticism to this method came from [ 75 ] who pointed out the arbitrariness in the critical choice of the temporal and spatial criteria for data selection, i.e., the initial precursory event of the AMR curve and the extension of the inspected region. On the other hand, [ 76 ] explained the AMR phenomenon under the view of complexity principles.…”

Case Studies of Seismic Energy Release Ahead of Underground Coal Mining Before Strong Tremors

“…The proposed approach using BSR models allowed to approximate the behaviour of the stress regime in the rock masses surrounding the studied longwall fields. Moreover, this paper discussed a study issue that could be used to better understand the Table 4 RMS values for power-law and linear fitting and curvature parameters of BSR for PMG mine data (the pillar) Guilhem et al (2013) and Vallianatos and Chatzopoulos (2018) discussed the advantages and disadvantages of BSR studies in which a number of uncertainties resulting from the nature of natural earthquakes are indicated (e.g. : whether earthquakes in pre-shock sequence concern a strong earthquake nucleation process, or what is the magnitude cut-off level, etc.).…”