  Any periodic variations of earthquake occurrence rates in response to small,
known, periodic stress variations provide important opportunities to learn
about the earthquake nucleation process. Yet, reliable detection of earthquake
periodicity is complicated by the presence of earthquake clustering due to
aftershocks and foreshocks. Existing methods for detecting periodicity in an
earthquake catalogue typically require the prior removal of these clustered
events. Declustering is a highly uncertain process, so declustering methods are
inherently non-unique. Incorrect declustering may remove some independent
events, or fail to remove some aftershocks or foreshocks, or both. These two
types of error could respectively lead to false negative or false positive
reporting of periodic seismicity. To overcome these limitations, we propose a
new method for detecting earthquake periodicity that does not require
declustering. Our approach is to modify the existing Schuster Spectrum Test
(SST) by adapting a test statistic for periodic seismicity to account for the
presence of clustered earthquakes within the catalogue without requiring their
identification and removal.
