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SPACE-TIME POINT-PROCESS MODELS FOR

EARTHQUAKE OCCURRENCES

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YOSIHIKO OGATA

*The Institute of Statistical Mathematics, Minami-Azabu 4-6-7,*

Minato-ku, Tokyo 106-8569, Japan
(Received January 19, 1996; revised May 9, 1997)

**Abstract.**
Several space-time statistical
models are constructed based on both classical empirical
studies of clustering and some more speculative
hypotheses. Then we discuss the discrimination between
models incorporating contrasting assumptions concerning
the form of the space-time clusters. We also examine
further practical extensions of the model to situations
where the background seismicity is spatially
non-homogeneous, and the clusters are non-isotropic. The
goodness-of-fit of the models, as measured by AIC values,
is discussed for two high quality data sets, in different
tectonic regions. AIC also allows the details of the
clustering structure in space to be clarified. A
simulation algorithm for the models is provided, and used
to confirm the numerical accuracy of the likelihood
calculations. The simulated data sets show the similar
spatial distributions to the real ones, but differ from
them in some features of space-time clustering. These
differences may provide useful indicators of directions
for further study.

*Key words and phrases*:
Centroid of
aftershock epicenters, ETAS model, inverse power laws,
maximum likelihood estimates, magnitude based clustering
(MBC) algorithm, modified Omori formula, thinning
simulation.

**Source**
( TeX ,
DVI ,
PS )