A Complexity View into the Physics of the Accelerating Seismic Release Hypothesis: Theoretical Principles
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-extens...
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MDPI AG
2018-10-01
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| Online Access: | http://www.mdpi.com/1099-4300/20/10/754 |
| _version_ | 1798002670249705472 |
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| author | Filippos Vallianatos Georgios Chatzopoulos |
| author_facet | Filippos Vallianatos Georgios Chatzopoulos |
| author_sort | Filippos Vallianatos |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T11:55:55Z |
| format | Article |
| id | doaj.art-00b2d607b0e947e8bfcf3f8ff53f5a97 |
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| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T11:55:55Z |
| publishDate | 2018-10-01 |
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| spelling | doaj.art-00b2d607b0e947e8bfcf3f8ff53f5a972022-12-22T04:25:07ZengMDPI AGEntropy1099-43002018-10-01201075410.3390/e20100754e20100754A Complexity View into the Physics of the Accelerating Seismic Release Hypothesis: Theoretical PrinciplesFilippos Vallianatos0Georgios Chatzopoulos1UNESCO Chair on Solid Earth Physics and Geohazards Risk Reduction, Technological Educational Institute of Crete, Crete 73100, GreeceUNESCO Chair on Solid Earth Physics and Geohazards Risk Reduction, Technological Educational Institute of Crete, Crete 73100, GreeceObservational 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.http://www.mdpi.com/1099-4300/20/10/754seismicity patternaccelerating seismicityTsallis entropynon extensive statistical physics |
| spellingShingle | Filippos Vallianatos Georgios Chatzopoulos A Complexity View into the Physics of the Accelerating Seismic Release Hypothesis: Theoretical Principles Entropy seismicity pattern accelerating seismicity Tsallis entropy non extensive statistical physics |
| title | A Complexity View into the Physics of the Accelerating Seismic Release Hypothesis: Theoretical Principles |
| title_full | A Complexity View into the Physics of the Accelerating Seismic Release Hypothesis: Theoretical Principles |
| title_fullStr | A Complexity View into the Physics of the Accelerating Seismic Release Hypothesis: Theoretical Principles |
| title_full_unstemmed | A Complexity View into the Physics of the Accelerating Seismic Release Hypothesis: Theoretical Principles |
| title_short | A Complexity View into the Physics of the Accelerating Seismic Release Hypothesis: Theoretical Principles |
| title_sort | complexity view into the physics of the accelerating seismic release hypothesis theoretical principles |
| topic | seismicity pattern accelerating seismicity Tsallis entropy non extensive statistical physics |
| url | http://www.mdpi.com/1099-4300/20/10/754 |
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