Probability Gain due to Foreshocks following Quiescence Tested by Synthetic Catalogs

The database obtained from the observations of the Italian Seismological
Network over more than 15 yr was analyzed by a simple algorithm to determine
the rate of occurrence of major events after the precursors called foreshocks: moderate
earthquakes following a period of quiescence. The number of observed foreshocks
depends, among other factors, on the spatial (R1) and temporal (/'1) ranges of
the quiescence used to define the foreshocks. These parameters can be optimized to
get the highest value of the success rate of the precursor for a given data set. In our
case, the optimization process led to a probability gain (G) higher than 100. In order
to estimate the factors that influence the value of G, we tested our method on synthetic
catalogs obtained from the real one by randomizing the origin times of the events,
or the spatial coordinates, or both of them. The analysis showed that the apparently
high value of the probability gain obtained optimizing the parameters. R1 and T 1 is
the result of (a) shortness of the catalog, (b) uneven spatial distribution of seismicity,
and (c) real variation in time of the occurrence rate.

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In order to investigate the factors that could contribute
to the high values of the probability gain for foreshocks, we
make use of synthetic catalogs generated by a computer program
(Console et al., 1993b). The algorithm was prepared
assuming that the magnitude distribution of the synthetic
catalog should be the same as that of the real one.