Detecting periodicities and declustering in earthquake catalogs using the Schuster spectrum, application to Himalayan seismicity

We show that the Schuster test alone does not provide a sufficient condition to assert the existence of a periodicity in an earthquake catalog. Such periodicities can be detected by computing a spectrum of Schuster p-values (the probability to observe such a level of periodic variations in a catalog occurring out of a constant seismicity rate). We show that the detection level is slightly period dependent, and we provide an analytical expression relating the amplitude of seismicity-rate variations to the confidence level at which the probability that the observed variations be due to chance can be discarded. The Schuster spectrum also provides information about the deviation from a sinusoidal function of the periodicity of the seismicity rate, and identifies an eventual imperfect declustering of the catalog, making it coincidently a potential tool to determine whether or not a catalog has been properly declustered. Applying this tool to the Nepalese seismicity, we demonstrate annual variations of the seismicity rate of amplitude up to 40%, while no other periodicity appears. In particular, no variations of seismicity at any of the tidal periods are observed, indicating that the relative amplitude response of the seismicity at these periods is less than 18%.