Least-squares self-coherency analysis of superconducting gravimeter records in search for the Slichter triplet

Spiros D. Pagiatakis*, Hui Yin, Mahmoud Abd El-Gelil

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


We develop a new approach for the spectral analysis of the superconducting gravimeter data to search for the spheroidal oscillation 1S1 of the Earth solid inner core. The new method, which we call least-squares (LS) self-coherency analysis, is based on the product of the least-squares spectra of segments of the time series under consideration. The statistical foundation of this method is presented in the new least-squares product spectrum theorem that establishes rigorously confidence levels for detecting significant peaks. We apply this approach along with a number of other innovative ideas to a 6-year long gravity series collected at the Canadian Superconducting Gravimeter Installation (CSGI) in Cantley, Canada, by splitting it into 72 statistically independent monthly records. Each monthly record is analysed spectrally and all monthly LS spectra are multiplied to construct the self-coherency spectrum of the 6-year gravity series. The self-coherency spectrum is then used to detect significant peaks in the band 3-7 h at various significant levels with the aim to identify a triplet of periods associated with the rotational/ellipsoidal splitting of 1S1 (Slichter triplet). From all the Slichter periods predicted by various researchers so far, Smylie's triplet appears to be the most supported one, albeit very weakly, both, before and after the atmospheric pressure effect is removed from the series. Using the viscous splitting law [Smylie, D.E., 1992. The inner core translational triplet and the density near Earth's center. Science 255, 1678-1682] as guide, we can also see one interesting and statistically significant triplet with periods A = {4.261 h, 4.516 h, 4.872 h}, which changes slightly to A′ = {4.269 h, 4.516 h, 4.889 h} after the atmospheric pressure correction is applied to the gravity series.

Original languageEnglish
Pages (from-to)108-123
Number of pages16
JournalPhysics of the Earth and Planetary Interiors
Issue number2
Publication statusPublished - Feb 12 2007


  • Coherency
  • Least-squares
  • Product spectrum
  • Slichter triplet
  • Spectral analysis

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Geophysics
  • Physics and Astronomy (miscellaneous)
  • Space and Planetary Science


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