the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
The possible 5.9 years oscillation identification from superconducting gravimeter observations
Abstract. Surface gravity changes aroused by the periodic ∼5.9 years oscillation (referred to as SYO) are important for understanding its origin and may further constrain Earth’s deep interior dynamics, but such signals have not been directly observed. In this study, we combine multiple spectra methods to analyze six usable superconducting gravimeter (SG) residual series in Western Europe, Canada, and Australia between 1996 and 2019; and try to extract the possible SYO signals from surface gravity observations. The amplitudes of the recovered possible SYO gravity changes vary from 0.5 to 0.9 μGal at different observatories. Comparisons with a derived timeâvarying gravity model indicate that the phases of gravity SYO may also have a spherical harmonic Y22 spatial distribution. The corresponding amplitude transform factors δ/h between the observed and modeled signals for different SG stations are about 2.9, greater than the ratio of ~1.9 for the corresponding tidal Love numbers. The observed amplitudes are also quite different from the predictions of the possible mechanisms suggested by previous studies. Although the SYO is believed to have originated from core motions, our findings mean that the potential physical mechanism should be much more complicated than any existing one. We suggest that the MAC waves arising from the interplay between Magnetic, Archimedes, and Coriolis forces could be a possible excitation source of the SYO. We believe our gravity observation results should help interpret the SYO in the future.
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Interactive discussion
Status: closed
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CC1: 'Comment on egusphere-2023-202', Paul PUKITE, 15 Mar 2023
I understand that the signal being analyzed is a residual of the original meaurement after removal of tidal etc. effects. Yet, a 6 year period does appear in tidal harmonics. As an integer it aligns as a multiple of the annual cycle and with the wavenumber=0 symmetry of the lunar nodal cycle Tn=27.2122 days interfering with the lunar anomalistic cycle Ta=27.5545 days. So that 1/Tn - 1/Ta = 1/ (6 y), to close precision assuming 365.25 days -- ~5.99 years. What does this imply? As a longitidudinally independent measure it can describe a point in the Moon's orbit whereby the Moon's declination and distance wrt to the Earth are extremes (as well as the Sun given the annual multiple alignment), implying a cyclical extreme torque applied to the axis.
The other near 6 year conection pertains to the Chandler wobble, whereby the lunar nodal cycle synchronizes with a semi-annual impulse with an envelope of ~6.4 years, according to modular arithmetic mod(365.25/ 27.2122, 0.5) = 1/433d (Chandler wobble cycle) and so beat envelope of 1/433d - 1/365.25d = 1/6.4y when mixed with the annual cycle. This value is observed in all Chandler wobble measurements when the Chandler wobble is mixed with and thus interferes with the annual wobble, see e.g. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JB02527
Neither of these alignments are often invoked in the literature, as the nodal or draconic cycle is largely dismissed in favor of the tropical or synodic lunar cycle of 27.32 days , which is a longitudinally-centric measure, and thus irrelevant to the spherical symmetry of the Earth's mantle, atmosphere, and axis of rotation inertial moment. See Mathematical Geoenergy (Wiley/AGU, 2018).
Citation: https://doi.org/10.5194/egusphere-2023-202-CC1 -
AC1: 'Reply on CC1', Wei Luan, 14 Apr 2023
We thank you for providing two sets of evidence that attempt to explain the 6-year oscillation (SYO) from different perspectives. The following two points, however, require emphasis:Â
(1) Based on the equation 1/Tn - 1/Ta = 1/6 (yr), the beating period in the first alignment you provided is 6 years. However, numerous actual detection evidence places the SYO period between 5.7 and 5.9 years. The spectral analysis on the length of day variation (ÎLOD), for instance, gave the SYO period of 5.9Âą0.06yr (Ding & Chao, 2018, EPSL), 5.85Âą0.03yr (Ding, 2019, EPSL), 5.85Âą0.06yr (Ding et al., 2021, JGR solid Earth), ~5.8yr (Liao & Greiner-Mai, 1999, JG), ~5.9yr (Hsu et al. 2021, JG), or 5.8Âą0.08yr (Mound & Buffett, 2006, EPSL). The sectoral Stokes coefficients of the Earthâs gravitational field derived from the satellite laser ranging (SLR) measurements showed the SYO period of ~5.7yr (Chao & Yu, 2021, EPSL). The power spectrum analysis on the polar motion observation yielded a period of ~5.9yr for the SYO (Chen et al., 2019, JGR). Please consult our manuscript for details on citations.
(2) In light of the time series, the superposition of near-periodic signals is prone to beat (or say the the synthetic amplitude varies periodically), such as the two possible alignments you mentioned, i.e., 1) Tn=27.2122d (lunar nodal month) and Ta= 27.5545d (Mm tide); 2) TICW=433d (Chandler wobble) and TAW=365.25d (annual wobble). The superposition of these two sets of periodic signals with clear physical interpretation will lead the envelope lines to clear 6yr and 6.4yr periodic oscillations, respectively. Gibert et al. (1998) used wavelet analysis to analyze the polar motion time series, and their Figs. 2 and 3 provide clear examples of this beating phenomena. When superimposing two prograde oscillating signals with respective periods 365 and 435 mean solar days, âthe modulus of the wavelet transform oscillates with a beating period of 6 yearsâ, as the authors put it (see the caption of their Fig. 2). However, general spectrum analysis readily reveals no beat frequency from near-periodic signals presents in the Fourier spectra. Besides, the ~18 years data length we used is long enough to distinguish the above two sets of near-periodic signals. Â
Here we illustrate this point through two simple signal synthesis experiments. Please check out the attachment.
Â
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AC1: 'Reply on CC1', Wei Luan, 14 Apr 2023
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RC1: 'Comment on egusphere-2023-202', Anonymous Referee #1, 29 Mar 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-202/egusphere-2023-202-RC1-supplement.pdf
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AC2: 'Reply on RC1', Wei Luan, 28 May 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-202/egusphere-2023-202-AC2-supplement.pdf
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RC2: 'Reply on RC1', Anonymous Referee #1, 13 Jun 2023
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AC3: 'Reply on RC2', Wei Luan, 15 Jun 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-202/egusphere-2023-202-AC3-supplement.pdf
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RC3: 'Reply on AC3', Anonymous Referee #1, 16 Jun 2023
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AC5: 'Reply on RC3', Wei Luan, 17 Jul 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-202/egusphere-2023-202-AC5-supplement.pdf
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AC5: 'Reply on RC3', Wei Luan, 17 Jul 2023
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RC3: 'Reply on AC3', Anonymous Referee #1, 16 Jun 2023
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AC3: 'Reply on RC2', Wei Luan, 15 Jun 2023
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AC2: 'Reply on RC1', Wei Luan, 28 May 2023
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RC4: 'Comment on egusphere-2023-202', Anonymous Referee #2, 19 Jun 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-202/egusphere-2023-202-RC4-supplement.pdf
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AC4: 'Reply on RC4', Wei Luan, 17 Jul 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-202/egusphere-2023-202-AC4-supplement.pdf
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AC4: 'Reply on RC4', Wei Luan, 17 Jul 2023
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EC1: 'Comment on egusphere-2023-202', Elias Lewi, 27 Jul 2023
Dear Wei Luan,
Based on the discussions so far, I found that there are several flaws in the manuscript and there are many concerns by the reviewers that are not fully addressed. Therefore, I recommend that you withdraw the paper and I will encourage you to address the questions, concerns, and comments by the reviewers as most of the comments are valuable. IWhen you are fully able to show that the 5.9-year signal is indeed related to the core dynamics and has less to do with surface phenomena it will be a manuscript worth giving attention to.
Thank you for your submission, and please consider the withdrawal of your paper. I will encourage you to resubmit this article after fully addressing issues raised during the discussions.
Citation: https://doi.org/10.5194/egusphere-2023-202-EC1
Interactive discussion
Status: closed
-
CC1: 'Comment on egusphere-2023-202', Paul PUKITE, 15 Mar 2023
I understand that the signal being analyzed is a residual of the original meaurement after removal of tidal etc. effects. Yet, a 6 year period does appear in tidal harmonics. As an integer it aligns as a multiple of the annual cycle and with the wavenumber=0 symmetry of the lunar nodal cycle Tn=27.2122 days interfering with the lunar anomalistic cycle Ta=27.5545 days. So that 1/Tn - 1/Ta = 1/ (6 y), to close precision assuming 365.25 days -- ~5.99 years. What does this imply? As a longitidudinally independent measure it can describe a point in the Moon's orbit whereby the Moon's declination and distance wrt to the Earth are extremes (as well as the Sun given the annual multiple alignment), implying a cyclical extreme torque applied to the axis.
The other near 6 year conection pertains to the Chandler wobble, whereby the lunar nodal cycle synchronizes with a semi-annual impulse with an envelope of ~6.4 years, according to modular arithmetic mod(365.25/ 27.2122, 0.5) = 1/433d (Chandler wobble cycle) and so beat envelope of 1/433d - 1/365.25d = 1/6.4y when mixed with the annual cycle. This value is observed in all Chandler wobble measurements when the Chandler wobble is mixed with and thus interferes with the annual wobble, see e.g. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JB02527
Neither of these alignments are often invoked in the literature, as the nodal or draconic cycle is largely dismissed in favor of the tropical or synodic lunar cycle of 27.32 days , which is a longitudinally-centric measure, and thus irrelevant to the spherical symmetry of the Earth's mantle, atmosphere, and axis of rotation inertial moment. See Mathematical Geoenergy (Wiley/AGU, 2018).
Citation: https://doi.org/10.5194/egusphere-2023-202-CC1 -
AC1: 'Reply on CC1', Wei Luan, 14 Apr 2023
We thank you for providing two sets of evidence that attempt to explain the 6-year oscillation (SYO) from different perspectives. The following two points, however, require emphasis:Â
(1) Based on the equation 1/Tn - 1/Ta = 1/6 (yr), the beating period in the first alignment you provided is 6 years. However, numerous actual detection evidence places the SYO period between 5.7 and 5.9 years. The spectral analysis on the length of day variation (ÎLOD), for instance, gave the SYO period of 5.9Âą0.06yr (Ding & Chao, 2018, EPSL), 5.85Âą0.03yr (Ding, 2019, EPSL), 5.85Âą0.06yr (Ding et al., 2021, JGR solid Earth), ~5.8yr (Liao & Greiner-Mai, 1999, JG), ~5.9yr (Hsu et al. 2021, JG), or 5.8Âą0.08yr (Mound & Buffett, 2006, EPSL). The sectoral Stokes coefficients of the Earthâs gravitational field derived from the satellite laser ranging (SLR) measurements showed the SYO period of ~5.7yr (Chao & Yu, 2021, EPSL). The power spectrum analysis on the polar motion observation yielded a period of ~5.9yr for the SYO (Chen et al., 2019, JGR). Please consult our manuscript for details on citations.
(2) In light of the time series, the superposition of near-periodic signals is prone to beat (or say the the synthetic amplitude varies periodically), such as the two possible alignments you mentioned, i.e., 1) Tn=27.2122d (lunar nodal month) and Ta= 27.5545d (Mm tide); 2) TICW=433d (Chandler wobble) and TAW=365.25d (annual wobble). The superposition of these two sets of periodic signals with clear physical interpretation will lead the envelope lines to clear 6yr and 6.4yr periodic oscillations, respectively. Gibert et al. (1998) used wavelet analysis to analyze the polar motion time series, and their Figs. 2 and 3 provide clear examples of this beating phenomena. When superimposing two prograde oscillating signals with respective periods 365 and 435 mean solar days, âthe modulus of the wavelet transform oscillates with a beating period of 6 yearsâ, as the authors put it (see the caption of their Fig. 2). However, general spectrum analysis readily reveals no beat frequency from near-periodic signals presents in the Fourier spectra. Besides, the ~18 years data length we used is long enough to distinguish the above two sets of near-periodic signals. Â
Here we illustrate this point through two simple signal synthesis experiments. Please check out the attachment.
Â
-
AC1: 'Reply on CC1', Wei Luan, 14 Apr 2023
-
RC1: 'Comment on egusphere-2023-202', Anonymous Referee #1, 29 Mar 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-202/egusphere-2023-202-RC1-supplement.pdf
-
AC2: 'Reply on RC1', Wei Luan, 28 May 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-202/egusphere-2023-202-AC2-supplement.pdf
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RC2: 'Reply on RC1', Anonymous Referee #1, 13 Jun 2023
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AC3: 'Reply on RC2', Wei Luan, 15 Jun 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-202/egusphere-2023-202-AC3-supplement.pdf
-
RC3: 'Reply on AC3', Anonymous Referee #1, 16 Jun 2023
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AC5: 'Reply on RC3', Wei Luan, 17 Jul 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-202/egusphere-2023-202-AC5-supplement.pdf
-
AC5: 'Reply on RC3', Wei Luan, 17 Jul 2023
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RC3: 'Reply on AC3', Anonymous Referee #1, 16 Jun 2023
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AC3: 'Reply on RC2', Wei Luan, 15 Jun 2023
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AC2: 'Reply on RC1', Wei Luan, 28 May 2023
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RC4: 'Comment on egusphere-2023-202', Anonymous Referee #2, 19 Jun 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-202/egusphere-2023-202-RC4-supplement.pdf
-
AC4: 'Reply on RC4', Wei Luan, 17 Jul 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-202/egusphere-2023-202-AC4-supplement.pdf
-
AC4: 'Reply on RC4', Wei Luan, 17 Jul 2023
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EC1: 'Comment on egusphere-2023-202', Elias Lewi, 27 Jul 2023
Dear Wei Luan,
Based on the discussions so far, I found that there are several flaws in the manuscript and there are many concerns by the reviewers that are not fully addressed. Therefore, I recommend that you withdraw the paper and I will encourage you to address the questions, concerns, and comments by the reviewers as most of the comments are valuable. IWhen you are fully able to show that the 5.9-year signal is indeed related to the core dynamics and has less to do with surface phenomena it will be a manuscript worth giving attention to.
Thank you for your submission, and please consider the withdrawal of your paper. I will encourage you to resubmit this article after fully addressing issues raised during the discussions.
Citation: https://doi.org/10.5194/egusphere-2023-202-EC1
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