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1 Lamont-Doherty Earth
Observatory
61 Route 9W
Palisades, New York
10964
agnes{at}ldeo.columbia.edu
(A.H.)
2 Department of Earth and Space
Sciences
University of California
Los Angeles, California
90095-1567
djackson{at}ucla.edu
ykagan{at}ucla.edu
(D.D.J.,
Y.Y.K.)
We have initially developed a time-independent forecast for southern
California by smoothing the locations of magnitude 2 and larger earthquakes. We
show that using small m 
2 earthquakes gives a reasonably good
prediction of m 5 earthquakes. Our forecast outperforms other
time-independent models
(Kagan and Jackson, 1994;
Frankel et al., 1997),
mostly because it has higher spatial resolution. We have then developed a method
to estimate daily earthquake probabilities in southern California by using the
Epidemic Type Earthquake Sequence model
(Kagan and Knopoff, 1987;
Ogata, 1988;
Kagan and Jackson, 2000). The
forecasted seismicity rate is the sum of a constant background seismicity,
proportional to our time- independent model, and of the aftershocks of all past
earthquakes. Each earthquake triggers aftershocks with a rate that increases
exponentially with its magnitude and decreases with time following Omori's
law. We use an isotropic kernel to model the spatial distribution of aftershocks
for small (m 
5.5) mainshocks. For larger events, we smooth the
density of early aftershocks to model the density of future aftershocks. The
model also assumes that all earthquake magnitudes follow the Gutenberg-Richter
law with a uniform b-value. We use a maximum likelihood method to
estimate the model parameters and test the short-term and time-independent
forecasts. A retrospective test using a daily update of the forecasts between 1
January 1985 and 10 March 2004 shows that the short-term model increases the
average probability of an earthquake occurrence by a factor 11.5 compared with
the time-independent forecast.
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