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| Titel |
Multidimensional earthquake frequency distributions consistent with self-organization of complex systems: The interdependence of magnitude, interevent time and interevent distance |
| VerfasserIn |
A. Tzanis, F. Vallianatos |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250069146
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| Zusammenfassung |
| It is well known that earthquake frequency is related to earthquake magnitude via a simple linear relationship of the form logN = a – bM, where N is the number of earthquakes in a specified time interval; this is the famous Gutenberg – Richter (G-R) law. The generally accepted interpretation of the G-R law is that it expresses the statistical behaviour of a fractal active tectonic grain (active faulting) – the relationship between the constant b and the fractal dimension of the tectonic grain has been demonstrated in various ways.
The story told by the G-R law is, nevertheless, incomplete! It is now accepted that the active tectonic grain comprises a critical complex system, although it hasn’t yet been established whether it is stationary (Self-Organized Critical), evolutionary (Self-Organizing Critical), or a time-varying blend of both. At any rate, critical systems are characterized by strong interactions between near and distant neighbours. This, in turn, implies that the self-organization of earthquake occurrence should be manifested by certain statistical behaviour of its temporal and spatial dependence.
A measure of temporal dependence is the time lapsed between consecutive events above a magnitude threshold over a given area (interevent time). A measure of spatial dependence is the hypocentral distance between consecutive events above a magnitude threshold over a given area (interevent distance). The statistics of earthquake frequency – interevent times have been studied by several researchers, albeit frequently on the basis of different definition for the interevent time. The statistics of earthquake frequency – interevent distance is still terra incognita.
Herein we present a multidimensional analysis of the statistical behaviour of frequency – magnitude – interevent time, frequency – magnitude – interevent distance and frequency – interevent time – interevent distance. We demonstrate that earthquake frequency is multiply related, not only to magnitude as the G-R law predicts, but also to the interevent time and distance by means of well defined power-laws. We also demonstrate that interevent time and distance are not independent of each other, but also interrelated by means of well defined power-laws. We argue that these relationships are universal and valid for both local and regional tectonic grains and seismicity patterns.
Eventually, we argue that the four-dimensional hypercube formed by the joint distribution of earthquake frequency, magnitude, interevent time and interevent distance comprises a generalized distribution of the G-R type which epitomizes the temporal and spatial interdependence of earthquake activity, consistent with expectation for a stationary or evolutionary critical system. Finally, we attempt to discuss the emerging generalized frequency distribution in terms of non-extensive statistical physics.
Acknowledgments. This work was partly supported by the THALES Program of the Ministry of Education of Greece and the European Union in the framework of the project "Integrated understanding of Seismicity, using innovative methodologies of Fracture Mechanics along with Earthquake and Non-Extensive Statistical Physics – Application to the geodynamic system of the Hellenic Arc - SEISMO FEAR HELLARC". |
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