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| Titel |
A Hierarchical Model for Distributed Seismicity |
| VerfasserIn |
A. Tejedor, J. B. Gómez, A. F. Pacheco |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250023795
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| Zusammenfassung |
| A cellular automaton model for the interaction between seismic faults in an extended region
is presented. The model, which is called HBM, consists of a hierarchical tree structure of
levels; each level has a different number of boxes. Faults are represented by boxes, and faults
of different area are boxes with different number of sites. With respect to the organization of
the model, boxes of equal size are in the same level, and the more sites they have, the higher
they are placed in the hierarchy. Interaction between faults is also assumed to be
hierarchical.
Stress particles are randomly added to the system –simulating the action of the external
tectonic forces, in such a manner than the probability of receiving a stress particle by a
box is directly proportional to the area of that box. The particles fill progressively
the sites of the boxes. When a box is full it topples and the particles are in part
redistributed and in part lost. This process is called relaxation. A box relaxation
simulates the occurrence of an earthquake in the region. The redistribution of particles
occurs mostly in the vertical direction (upwards and downwards); however, a small
fraction of the load is transferred to the nearest neighbors in the same level of the
relaxing box to simulate long-range interactions. If particles transferred to a box
fill it, it also topples producing new relaxations. The largest box relaxed between
the external addition of two stress particles defines the magnitude of the resulting
main-shock.
This model is consistent with the definition of magnitude, i.e. earthquakes of magnitude
m take place in boxes with a number of sites ten times bigger than those responsible for
earthquakes with a magnitude m - 1, which are placed in the immediate lower level of the
hierarchy. It is assumed that the bottom level of the model contains the boxes whose
relaxation corresponds to earthquakes of magnitude m = 1. So, the number of levels of the
system is directly related to the maximum earthquake magnitude expected in the simulated
zone. The model has two parameters, c and u. Parameter c, called the coordination number, is
a geometric parameter. It represents the number of boxes in a level m connected to a box in
level m + 1; parameter u is the fraction of load that rises in the hierarchy due to a relaxation
process. Therefore, the fraction 1 - u corresponds to the load that descends in the same
process.
The only two parameters of the model are fixed taking into account three characteristics
of natural seismicity: (i) the power-law relationship between the size of an earthquake and the
area of the displaced fault; (ii) the fact, observed in Geology, that the time of recurrence of
large faults is shorter than that of small faults; and (iii) the percentages of aftershocks and
mainshocks observed in earthquake catalogs.
The model shows a self-organized critical behavior. It becomes manifest from
both the observation of a steady state around which the load fluctuates, and the
power law behavior of some of the properties of the system like the size-frequency
distribution of relaxations (earthquakes). The exponent of this power law is around -1
for values of the parameters consistent with the three previous phenomenological
observations.
Two different strategies for the forecasting of the largest earthquakes in the model have
been analyzed. The first one only takes into account the average recurrence time of
the target earhquakes, whereas the second utilizes a known precursory pattern,
the burst of aftershocks, which has been used for real earthquake prediction. The
application of the latter strategy improves significantly the results obtained with the
former.
In summary, a conceptually simple model of the cellular automaton type with
only two parameters can reproduce simultaneously several characteristics of real
seismicity, like the Gutenberg-Richter law, shorter recurrence times for big faults
compare to small ones, and percentages of aftershocks and mainshocks of around
66% and 33% respectively. Besides, a premonitory pattern has been successfully
applied. |
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