  Around 90% of the earthquakes in the world occur at the circum-Pacific belt
referred to as the Pacific Ring of Fire exposing the countries in this region
to high risk of earthquake hazards. We model fluctuations of the different
seismic magnitudes, interevent distances, and seismic depths as a function of
earthquake occurrence from the earthquake catalogs of Chile, Mexico, Japan, New
Zealand, Philippines, and Southern California as a stochastic process with
long-term memory. We show that the fluctuations of the three seismic quantities
mentioned for all regions studied in this paper are governed by a single memory
function that is described by a memory parameter {\mu} and a decay parameter
\b{eta}. The values of {\mu} exhibit an underlying characteristic memory
behavior of seismic activities common to all the countries considered, while
the values of \b{eta} suggest a regional dependence which could be a
manifestation of different seismic dynamics in various regions. This new
perspective may provide a more versatile approach in studying the independent
datasets that may be extracted from various earthquake catalogs.
