Nonlinear Processes in Geophysics
www.nonlin-processes-geophys.net
1023-5809
1607-7946
9
5/6
2002
10.5194/npg-9-453-2002
http://www.nonlin-processes-geophys.net/9/453/2002/
http://www.nonlin-processes-geophys.net/9/453/2002/npg-9-453-2002.html
http://www.nonlin-processes-geophys.net/9/453/2002/npg-9-453-2002.pdf
453
461
0000-00-00
A simple model for the earthquake cycle combining self-organized complexity with critical point behavior
W. I. Newman
D. L. Turcotte
Departments of Earth and Space Sciences, Physics and Astronomy, and Mathematics, University of California, Los Angeles, CA 90095, USA
Department of Earth and Atmospheric Sciences, Snee Hall, Cornell University, Ithaca, NY 14853, USA
We
have studied a hybrid model combining the forest-fire
model with the site-percolation model in order to better
understand the earthquake cycle. We consider a square array
of sites. At each time step, a "tree" is dropped on a randomly
chosen site and is planted if the site is unoccupied. When
a cluster of "trees" spans the site (a percolating cluster),
all the trees in the cluster are removed ("burned") in
a "fire." The removal of the cluster is analogous to a characteristic
earthquake and planting "trees" is analogous to
increasing the regional stress. The clusters are analogous to
the metastable regions of a fault over which an earthquake rupture
can propagate once triggered. We find that the frequency-area
statistics of the metastable regions are power-law with
a negative exponent of two (as in the forest-fire model).
This is analogous to the Gutenberg-Richter distribution of
seismicity. This "self-organized critical behavior" can be
explained in terms of an inverse cascade of clusters. Small clusters
of "trees" coalesce to form larger clusters. Individual trees
move from small to larger clusters until they are destroyed. This
inverse cascade of clusters is self-similar and the
power-law distribution of cluster sizes has been shown to have
an exponent of two. We have quantified the forecasting of
the spanning fires using error diagrams. The assumption that
"fires" (earthquakes) are quasi-periodic has moderate predictability.
The density of trees gives an improved degree
of predictability, while the size of the largest cluster of
trees provides a substantial improvement in forecasting a "fire."</font