  It has been observed that the earthquake events possess short-term memory,
i.e. that events occurring in a particular location are dependent on the short
history of that location. We conduct an analysis to see whether real-time
earthquake data also possess long-term memory and, if so, whether such
autocorrelations depend on the size of earthquakes within close spatiotemporal
proximity. We analyze the seismic waveform database recorded by 64 stations in
Japan, including the 2011 "Great East Japan Earthquake", one of the five most
powerful earthquakes ever recorded which resulted in a tsunami and devastating
nuclear accidents. We explore the question of seismic memory through use of
mean conditional intervals and detrended fluctuation analysis (DFA). We find
that the waveform sign series show long-range power-law anticorrelations while
the interval series show long-range power-law correlations. We find
size-dependence in earthquake auto-correlations---as earthquake size increases,
both of these correlation behaviors strengthen. We also find that the DFA
scaling exponent $\alpha$ has no dependence on earthquake hypocenter depth or
epicentral distance.
