  A prominent feature of earthquakes is their empirical laws including memory
(clustering) in time and space. Several earthquake forecasting models, like the
EpidemicType Aftershock Sequence (ETAS) model, were developed based on
earthquake empirical laws. Yet, a recent study showed that the ETAS model fails
in reproducing significant long-term memory characteristics found in real
earthquake catalogs. Here we modify and generalize the ETAS model to include
short- and long-term triggering mechanisms, to account for the short- and
long-time memory (exponents) recently discovered in the data. Our generalized
ETAS model reproduces accurately the short- and long-term/distance memory
observed in the Italian and South California earthquake catalogs. The revised
ETAS model is also found to significantly improve earthquake forecasting.
