  Event correlation between aftershocks in the coherent noise model is studied
by making use of natural time, which has recently been introduced in complex
time-series analysis. It is found that the aging phenomenon and the associated
scaling property discovered in the observed seismic data are well reproduced by
the model. It is also found that the scaling function is given by the
$q$-exponential function appearing in nonextensive statistical mechanics,
showing power-law decay of event correlation in natural time.
