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

- Point out that the Schuster test cannot alone be used to unambiguously assert periodicities in a seismicity catalog.
- Provide an extended test, the Schuster spectrum, to detect periodicities in a catalog and assess a confidence level to reject the null hypothesis.
- Unbiased test: no a priori information is required on the suspected periodicity.
- Quantify the amplitude of seismicity-rate variations in Nepal: ∼40% at one year, <18% at tidal periods.
- The Schuster spectrum provides a tool to assess the quality of declustering of a catalog.

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%.