We present long-term and short-term forecasts for magnitude
5.8 and larger earthquakes. We discuss a method for optimizing
both procedures and testing their forecasting effectiveness
using the likelihood function. Our forecasts are expressed as
the rate density (that is, the probability per unit area and
time) anywhere on the Earth. Our forecasts are for scientific
testing only; they are not to be construed as earthquake
predictions or warnings, and they carry no official endorsement.
For our long-term forecast we assume that the rate density is
proportional to a smoothed version of past seismicity (using
the Harvard CMT catalogue). This is in some ways antithetical
to the seismic gap model, which assumes that recent earthquakes
deter future ones. The estimated rate density depends linearly
on the magnitude of past earthquakes and approximately on a
negative power of the epicentral distance out to a few hundred
kilometres. We assume no explicit time dependence, although the
estimated rate density will vary slightly from day to day as
earthquakes enter the catalogue. The forecast applies to the
ensemble of earthquakes during the test period.
It is not meant to predict any single earthquake, and no single
earthquake or lack of one is adequate to evaluate such a hypothesis.
We assume that 1 per cent of all earthquakes are surprises,
assumed uniformly likely to occur in those areas with no earthquakes
since 1977. We have made specific forecasts for the calendar
year 1999 for the Northwest Pacific and Southwest Pacific regions,
and we plan to expand the forecast to the whole Earth. We test
the forecast against the earthquake catalogue using a likelihood
test and present the results. Our short-term forecast, updated
daily, makes explicit use of statistical models describing earthquake
clustering. Like the long-term forecast, the short-term version
is expressed as a rate density in location, magnitude and time.
However, the short-term forecasts will change significantly
from day to day in response to recent earthquakes. The forecast
applies to main shocks, aftershocks, aftershocks of aftershocks,
and main shocks preceded by foreshocks. However, there is no need
to label each event, and the method is completely automatic.
According to the model, nearly 10 per cent of moderately sized
earthquakes will be followed by larger ones within a few weeks.