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

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

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

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
Volume160
Issue number2
DOIs
Publication statusPublished - Feb 12 2007

Fingerprint

gravimeters
inner core
gravity
gravitation
atmospheric pressure
solid Earth
pressure effect
pressure effects
products
Canada
spectral analysis
installing
spectrum analysis
confidence
theorems
oscillation
analysis
time series
oscillations

Keywords

  • 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

Cite this

Least-squares self-coherency analysis of superconducting gravimeter records in search for the Slichter triplet. / Pagiatakis, Spiros D.; Yin, Hui; El-Gelil, Mahmoud Abd.

In: Physics of the Earth and Planetary Interiors, Vol. 160, No. 2, 12.02.2007, p. 108-123.

Research output: Contribution to journalArticle

@article{d23c9cdc4e044bf7823667fa312473c9,
title = "Least-squares self-coherency analysis of superconducting gravimeter records in search for the Slichter triplet",
abstract = "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.",
keywords = "Coherency, Least-squares, Product spectrum, Slichter triplet, Spectral analysis",
author = "Pagiatakis, {Spiros D.} and Hui Yin and El-Gelil, {Mahmoud Abd}",
year = "2007",
month = "2",
day = "12",
doi = "10.1016/j.pepi.2006.10.002",
language = "English",
volume = "160",
pages = "108--123",
journal = "Physics of the Earth and Planetary Interiors",
issn = "0031-9201",
publisher = "Elsevier",
number = "2",

}

TY - JOUR

T1 - Least-squares self-coherency analysis of superconducting gravimeter records in search for the Slichter triplet

AU - Pagiatakis, Spiros D.

AU - Yin, Hui

AU - El-Gelil, Mahmoud Abd

PY - 2007/2/12

Y1 - 2007/2/12

N2 - 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.

AB - 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.

KW - Coherency

KW - Least-squares

KW - Product spectrum

KW - Slichter triplet

KW - Spectral analysis

UR - http://www.scopus.com/inward/record.url?scp=33845752148&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845752148&partnerID=8YFLogxK

U2 - 10.1016/j.pepi.2006.10.002

DO - 10.1016/j.pepi.2006.10.002

M3 - Article

VL - 160

SP - 108

EP - 123

JO - Physics of the Earth and Planetary Interiors

JF - Physics of the Earth and Planetary Interiors

SN - 0031-9201

IS - 2

ER -