Aging in coherent noise models and natural time

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.