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| Titel |
Recurrence and interoccurrence behavior of self-organized complex phenomena |
| VerfasserIn |
S. G. Abaimov, D. L. Turcotte, R. Shcherbakov, J. B. Rundle |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 14, no. 4 ; Nr. 14, no. 4 (2007-08-02), S.455-464 |
| Datensatznummer |
250012244
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| Publikation (Nr.) |
 copernicus.org/npg-14-455-2007.pdf |
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| Zusammenfassung |
| The sandpile, forest-fire and slider-block models are
said to exhibit self-organized criticality. Associated natural phenomena
include landslides, wildfires, and earthquakes. In all cases the
frequency-size distributions are well approximated by power laws (fractals).
Another important aspect of both the models and natural phenomena is the
statistics of interval times. These statistics are particularly important
for earthquakes. For earthquakes it is important to make a distinction
between interoccurrence and recurrence times. Interoccurrence times are the
interval times between earthquakes on all faults in a region whereas
recurrence times are interval times between earthquakes on a single fault or
fault segment. In many, but not all cases, interoccurrence time statistics
are exponential (Poissonian) and the events occur randomly. However, the
distribution of recurrence times are often Weibull to a good approximation.
In this paper we study the interval statistics of slip events using a
slider-block model. The behavior of this model is sensitive to the stiffness
α of the system, α=kC/kL where kC is the spring constant
of the connector springs and kL is the spring constant of the loader plate
springs. For a soft system (small α) there are no system-wide events and
interoccurrence time statistics of the larger events are Poissonian. For a
stiff system (large α), system-wide events dominate the energy dissipation
and the statistics of the recurrence times between these system-wide events
satisfy the Weibull distribution to a good approximation. We argue that this
applicability of the Weibull distribution is due to the power-law (scale
invariant) behavior of the hazard function, i.e. the probability that the
next event will occur at a time t0 after the last event has a power-law
dependence on t0. The Weibull distribution is the only distribution that
has a scale invariant hazard function. We further show that the onset of
system-wide events is a well defined critical point. We find that the number
of system-wide events NSWE satisfies the scaling relation NSWE
∝(α-αC)δ where αC is the critical value
of the stiffness. The system-wide events represent a new phase for the
slider-block system. |
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