  Recently, slow earthquakes (slow EQ) have received much attention relative to
understanding the mechanisms underlying large earthquakes and to detecting
their precursors. Low-frequency earthquakes (LFE) are a specific type of slow
EQ. In the present paper, we reveal the relevance of LFEs to the 2011 Great
Tohoku Earthquake (Tohoku-oki EQ) by means of cluster analysis. We classified
LFEs in northern Japan in a data-driven manner, based on inter-time, the time
interval between neighboring LFEs occurring within 10 km. We found that there
are four classes of LFE that are characterized by median inter-times of 24
seconds, 27 minutes, 2.0 days, and 35 days, respectively. Remarkably, in
examining the relevance of these classes to the Tohoku-oki EQ, we found that
activity in the shortest inter-time class (median 23 seconds) diminished
significantly at least three months before the Tohoku-oki EQ, and became
completely quiescent 30 days before the event (p-value = 0.00014). Further
statistical analysis implies that this class, together with a similar class of
volcanic tremor, may have served as a precursor of the Tohoku-oki EQ. We
discuss a generative model for these classes of LFE, in which the shortest
inter-time class is characterized by a generalized gamma distribution with the
product of shape parameters 1.54 in the domain of inter-time close to zero. We
give a possible geodetic interpretation for the relevance of LFE to the
Tohoku-oki EQ.
