The time dependence of the parameter of the Gutenberg-Richter (GR)
magnitude distribution is computed for foreshock sequences of earthquakes,
correlated with the main shock, by using the geometric-growth model
of earthquake focus, the magnitude distribution of correlated earthquakes
and the time-magnitude correlations, derived recently. It is shown
that this parameter decreases in time in the foreshock sequence, from
the background values down to the main shock. If correlations are
present, this time dependence and the time-magnitude correlations
provide a tool of monitoring the foreshock seismic activity. We discuss
the relevance of such an analysis for the occurrence moment and the
magnitude of a main shock. The discussion is applied to a few Vrancea
main shocks and the precursory seismic activity of the l'Aquila earthquake.
The limitations of such an analysis are discussed.
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