Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Multidecadal variation of the Earth’s inner-core rotation

An Author Correction to this article was published on 31 January 2023

This article has been updated


Differential rotation of Earth’s inner core relative to the mantle is thought to occur under the effects of the geodynamo on core dynamics and gravitational core–mantle coupling. This rotation has been inferred from temporal changes between repeated seismic waves that should traverse the same path through the inner core. Here we analyse repeated seismic waves from the early 1990s and show that all of the paths that previously showed significant temporal changes have exhibited little change over the past decade. This globally consistent pattern suggests that differential inner-core rotation has recently paused. We compared this recent pattern to the Alaskan seismic records of South Sandwich Islands doublets going back to 1964 and it seems to be associated with a gradual turning-back of the inner core relative to the mantle as a part of an approximately seven-decade oscillation, with another turning point in the early 1970s. This multidecadal periodicity coincides with changes in several other geophysical observations, especially the length of day and magnetic field. These observations provide evidence for dynamic interactions between the Earth’s layers, from the deepest interior to the surface, potentially due to gravitational coupling and the exchange of angular momentum from the core and mantle to the surface.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Seismic raypaths used in the study.
Fig. 2: Examples highlighting a pattern change in the inner-core temporal changes in the recent decade.
Fig. 3: S of the inner-core waves from two subsets of doublets.
Fig. 4: Global temporal change of DF’s travel time (dt) and the comparison with the ΔLOD.

Similar content being viewed by others

Data availability

The digital waveform data in this study are openly available from the Incorporated Research Institutions for Seismology Data Management Center ( and Canadian National Seismograph Network ( The analogue waveforms from the station COL were collected and manually digitized by ref. 7, and those of the SSI doublets are available at The yearly averaged LOD measurements and the daily Earth Orientation Parameters series (EOPC04) are freely downloaded from the International Earth Rotation and Reference Systems (

Code availability

The codes used in this study are available upon request.

Change history


  1. Buffett, B. A. Earth’s core and the geodynamo. Science 288, 2007–2012 (2000).

    Article  Google Scholar 

  2. Gubbins, D. Rotation of the inner core. J. Geophys. Res. Solid Earth 86, 11695–11699 (1981).

    Article  Google Scholar 

  3. Glatzmaier, G. A. & Roberts, P. H. A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle. Phys. Earth Planet. Inter. 91, 63–75 (1995).

    Article  Google Scholar 

  4. Glatzmaier, G. A. & Roberts, P. H. Rotation and magnetism of Earth’s inner core. Science 274, 1887–1891 (1996).

    Article  Google Scholar 

  5. Vidale, J. E. & Earle, P. S. Fine-scale heterogeneity in the Earth’s inner core. Nature 404, 273–275 (2000).

    Article  Google Scholar 

  6. Creager, K. C. Inner core rotation rate from small-scale heterogeneity and time-varying travel times. Science 278, 1284–1288 (1997).

    Article  Google Scholar 

  7. Song, X. Joint inversion for inner core rotation, inner core anisotropy, and mantle heterogeneity. J. Geophys. Res. Solid Earth 105, 7931–7943 (2000).

    Article  Google Scholar 

  8. Attanayake, J., Thomas, C., Cormier, V. F., Miller, M. S. & Koper, K. D. Irregular transition layer beneath the earth’s inner core boundary from observations of antipodal PKIKP and PKIIKP waves. Geochem. Geophys. Geosyst. 19, 3607–3622 (2018).

    Article  Google Scholar 

  9. Tanaka, S. & Hamaguchi, H. Degree one heterogeneity and hemispherical variation of anisotropy in the inner core from PKP(BC)–PKP(DF) times. J. Geophys. Res. Solid Earth 102, 2925–2938 (1997).

    Article  Google Scholar 

  10. Niu, F. & Wen, L. Hemispherical variations in seismic velocity at the top of the Earth’s inner core. Nature 410, 1081–1084 (2001).

    Article  Google Scholar 

  11. Sun, X. & Song, X. Tomographic inversion for three-dimensional anisotropy of Earth’s inner core. Phys. Earth Planet. Inter. 167, 53–70 (2008).

    Article  Google Scholar 

  12. Buffett, B. A. Gravitational oscillations in the length of day. Geophys. Res. Lett. 23, 2279–2282 (1996).

    Article  Google Scholar 

  13. Buffett, B. A. & Creager, K. C. A comparison of geodetic and seismic estimates of inner-core rotation. Geophys. Res. Lett. 26, 1509–1512 (1999).

    Article  Google Scholar 

  14. Buffett, B. A. & Glatzmaier, G. A. Gravitational braking of inner-core rotation in geodynamo simulations. Geophys. Res. Lett. 27, 3125–3128 (2000).

    Article  Google Scholar 

  15. Aurnou, J. & Olson, P. Control of inner core rotation by electromagnetic, gravitational and mechanical torques. Phys. Earth Planet. Inter. 117, 111–121 (2000).

    Article  Google Scholar 

  16. Davies, C. J., Stegman, D. R. & Dumberry, M. The strength of gravitational core–mantle coupling. Geophys. Res. Lett. 41, 3786–3792 (2014).

    Article  Google Scholar 

  17. Song, X. & Richards, P. G. Seismological evidence for differential rotation of the Earth’s inner core. Nature 382, 221–224 (1996).

    Article  Google Scholar 

  18. Vidale, J. E., Dodge, D. A. & Earle, P. S. Slow differential rotation of the Earth’s inner core indicated by temporal changes in scattering. Nature 405, 445–448 (2000).

    Article  Google Scholar 

  19. Zhang, J. et al. Inner core differential motion confirmed by earthquake waveform doublets. Science 309, 1357–1360 (2005).

    Article  Google Scholar 

  20. Yang, Y. & Song, X. Temporal changes of the inner core from globally distributed repeating earthquakes. J. Geophys. Res. Solid Earth 125, e2019JB018652 (2020).

    Article  Google Scholar 

  21. Poupinet, G., Ellsworth, W. L. & Frechet, J. Monitoring velocity variations in the crust using earthquake doublets: an application to the Calaveras Fault, California. J. Geophys. Res. Solid Earth 89, 5719–5731 (1984).

    Article  Google Scholar 

  22. Wen, L. Localized temporal change of the Earth’s inner core boundary. Science 314, 967–970 (2006).

    Article  Google Scholar 

  23. Yao, J., Tian, D., Sun, L. & Wen, L. Temporal change of seismic Earth’s inner core phases: inner core differential rotation or temporal change of inner core surface? J. Geophys. Res. Solid Earth 124, 6720–6736 (2019).

    Article  Google Scholar 

  24. Yao, J., Tian, D., Sun, L. & Wen, L. Comment on “Origin of temporal changes of inner-core seismic waves” by Yang and Song (2020). Earth Planet. Sci. Lett. 553, 116640 (2021).

    Article  Google Scholar 

  25. Yang, Y. & Song, X. Origin of temporal changes of inner-core seismic waves. Earth Planet. Sci. Lett. 541, 116267 (2020).

    Article  Google Scholar 

  26. Yang, Y. & Song, X. Reply to Yao et al.’s comment on “Origin of temporal changes of inner-core seismic waves”. Earth Planet. Sci. Lett. 553, 116639 (2021).

    Article  Google Scholar 

  27. Wang, W. & Vidale, J. E. Earth’s inner core rotation, 1971 to 1974, illuminated by inner-core scattered waves. Earth Planet. Sci. Lett. 577, 117214 (2022).

    Article  Google Scholar 

  28. Zhang, J., Richards, P. G. & Schaff, D. P. Wide-scale detection of earthquake waveform doublets and further evidence for inner core super-rotation. Geophys. J. Int. 174, 993–1006 (2008).

    Article  Google Scholar 

  29. Cao, A., Masson, Y. & Romanowicz, B. Short wavelength topography on the inner-core boundary. Proc. Natl Acad. Sci. USA 104, 31–35 (2007).

    Article  Google Scholar 

  30. Song, X. & Dai, W. Topography of Earth’s inner core boundary from high-quality waveform doublets. Geophys. J. Int. 175, 386–399 (2008).

    Article  Google Scholar 

  31. Yao, J., Sun, L. & Wen, L. Two decades of temporal change of Earth’s inner core boundary. J. Geophys. Res. Solid Earth 120, 6263–6283 (2015).

    Article  Google Scholar 

  32. Efron, B. & Tibshirani, R. J. An Introduction to the Bootstrap (Chapman and Hall/CRC, 1994).

  33. Tkalčić, H., Young, M., Bodin, T., Ngo, S. & Sambridge, M. The shuffling rotation of the Earth’s inner core revealed by earthquake doublets. Nat. Geosci. 6, 497–502 (2013).

    Article  Google Scholar 

  34. Wang, W. & Vidale, J. E. Seismological observation of Earth’s oscillating inner core. Sci. Adv. 8, eabm9916 (2022).

    Article  Google Scholar 

  35. Yang, Y. & Song, X. Inner core rotation captured by earthquake doublets and twin stations. Geophys. Res. Lett. 49, e2022GL098393 (2022).

  36. Braginsky, S. I. Torsional magnetohydrodynamic vibrations in the Earth’s core and variations in day length. Geomagn. Aeron. 10, 1–8 (1970).

    Google Scholar 

  37. Roberts, P. H., Yu, Z. J. & Russell, C. T. On the 60-year signal from the core. Geophys. Astrophys. Fluid Dyn. 101, 11–35 (2007).

    Article  Google Scholar 

  38. Hide, R. Interaction between the Earth’s liquid core and solid mantle. Nature 222, 1055–1056 (1969).

    Article  Google Scholar 

  39. Jault, D. in Earth’s Core and Lower Mantle (eds Jones, C. A. et al.) 73–95 (CRC Press, 2003).

  40. Ding, H., Jin, T., Li, J. & Jiang, W. The contribution of a newly unraveled 64 years common oscillation on the estimate of present‐day global mean sea level rise. J. Geophys. Res. Solid Earth 126, e2021JB022147 (2021).

  41. Zatman, S. & Bloxham, J. Torsional oscillations and the magnetic field within the Earth’s core. Nature 388, 760–763 (1997).

    Article  Google Scholar 

  42. Zatman, S. in Earth’s Core: Dynamics, Structure, Rotation (eds Dehant, V. et al.) 233–240 (American Geophysical Union, 2003).

  43. Schlesinger, M. E. & Ramankutty, N. An oscillation in the global climate system of period 65–70 years. Nature 367, 723–726 (1994).

    Article  Google Scholar 

  44. Gervais, F. Anthropogenic CO2 warming challenged by 60-year cycle. Earth-Sci. Rev. 155, 129–135 (2016).

    Article  Google Scholar 

  45. Scafetta, N., Milani, F. & Bianchini, A. A 60‐year cycle in the meteorite fall frequency suggests a possible interplanetary dust forcing of the Earth’s climate driven by planetary oscillations. Geophys. Res. Lett. 47, e2020GL089954 (2020).

    Article  Google Scholar 

  46. Zotov, L., Bizouard, C. & Shum, C. K. A possible interrelation between Earth rotation and climatic variability at decadal time-scale. Geod. Geodyn. 7, 216–222 (2016).

    Article  Google Scholar 

  47. Ding, H. & Chao, B. F. A 6-year westward rotary motion in the Earth: detection and possible MICG coupling mechanism. Earth Planet. Sci. Lett. 495, 50–55 (2018).

    Article  Google Scholar 

  48. Dumberry, M. & Bloxham, J. Variations in the Earth’s gravity field caused by torsional oscillations in the core. Geophys. J. Int. 159, 417–434 (2004).

    Article  Google Scholar 

  49. Greff-Lefftz, M., Pais, M. A. & Mouël, J.-L. L. Surface gravitational field and topography changes induced by the Earth’s fluid core motions. J. Geod. 78, 386–392 (2004).

    Article  Google Scholar 

  50. Sambridge, M. Geophysical inversion with a neighbourhood algorithm—I. Searching a parameter space. Geophys. J. Int. 138, 479–494 (1999).

    Article  Google Scholar 

  51. Stephenson, J., Tkalčić, H. & Sambridge, M. Evidence for the innermost inner core: robust parameter search for radially varying anisotropy using the neighborhood algorithm. J. Geophys. Res. Solid Earth 126, e2020JB020545 (2021).

    Article  Google Scholar 

Download references


We acknowledge the support from the National Key R&D Program of China (grant no. 2022YFF0800601 to X.S.), the National Natural Science Foundation of China (grant no. U1939204 to X.S. and grant no. 42104096 to Y.Y.) and China Postdoctoral Science Foundation (grant no. 2021M690203 to Y.Y.). The discussions with H. Ding and J. Chen helped improve our manuscript.

Author information

Authors and Affiliations



X.S. and Y.Y. conceived the study; Y.Y. processed the seismic data; Y.Y. and X.S. analysed the data and wrote the manuscript together.

Corresponding author

Correspondence to Xiaodong Song.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Geoscience thanks Severine Rosat, Susini De Silva, Thanh-Son Phạm and Januka Attanayake for their contribution to the peer review of this work. Primary Handling Editor: Louise Hawkins, in collaboration with the Nature Geoscience team.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Waveform comparisons of the multiplets of all the eight paths.

Each row with two panels side by side shows the waveforms from the same multiplet, with the path number labeled in between. The left panels show pairs from the relatively old time period with the earlier event in the 1990s or early 2000s, while the right panels show pairs from the relatively recent time period with both events in the late 2000s or even later. The waveform plots and notations follow the same style as in Fig. 2.

Extended Data Fig. 2 Comparison of global similarity (S) measurements between two time periods.

The S measurements and their corresponding uncertainty ranges (circles and vertical bars of ±σs) of the inner-core waves along all the eight different paths are plotted but only from doublets with lapse over 3.5 years and the most recent data (year 2020 and after) are not included. In each path-bin, the horizontal position of each measurement represents the lapse of the doublet, which is normalized by an interval of 3.0 to 12.0 years. If a doublet belongs to a multiplet, we use solid circles to distinguish.

Extended Data Fig. 3 All the S measurements of the inner-core waves in this study.

The light gray line segments and error bars (±σs) are plotted in the same way as in Fig. 3. The measurements from the doublets with both events before 2009 (blue) or after 2009 (red) are also shown in Fig. 3. The other doublets (gray) have one event before 2009 and the other event after 2009.

Extended Data Fig. 4 Temporal changes of DF’s travel time along the 6 paths at the BC distance range.

In each panel, the best-fitting curve (solid blue line) is the path-dependent factor (pn) multiplied by the same cubic spline from the joint inversion (Methods). The dt segment of each doublet is plotted in the same way as in Fig. 4. The uncertainty of each measurement (±σt) is plotted at the end of the segment, and large ddt measurements over 2σt are marked in red (others in gray). The histograms represent the distributions of the normalized ddt measurements and residuals, similar to those in Fig. 4.

Extended Data Fig. 5 Comparison of the best-fitting two-piece uniform spline with other models.

(a) Other uniform splines with more knots. Here, we show the best-fitting 3-piece and 5-piece uniform splines. The circles with corresponding colors are the knots of the splines searched out in the inversion (Methods). (b) A model with two connected linear segments and its uncertainty from bootstrapping. Note that the mean values of the models in (a) and (b) have been removed.

Extended Data Fig. 6 Comparison of the ddt measurements between the early lower-quality SSI doublets sampling the 1960s and the later doublets.

In each panel, the doublet on top covers the time period of the 1960s and early 1970s and has a much larger lapse (labeled in the paratheses) but smaller or comparable ddt than that of the bottom doublet. Note that the labeled ddt measurements have been corrected for the small difference in the epicentral distance of the two doublet events, as indicated by the relative time shift between the outer-core BC and AB arrivals (Methods). The waveform plots and the notations follow the same style as in Fig. 2c.

Extended Data Fig. 7 Reverse of the length of day variations (-LOD).

The gray line shows the daily EOPC04 series, which is available in the time span of 1962 to the present day from the International Earth Rotation and Reference Systems (IERS). The yearly averaged -LOD measurements (the circles connected by a solid black line) before 2008 are directly obtained from the IERS, and those after 2008 are computed from the daily EOPC04 series. The dotted line is the 65-year component of the -LOD extracted by Ding et al.40 using wavelet decomposition.

Extended Data Fig. 8 A possible resonance Earth system with a period of 6–7 decades across different layers from the inner core to surface.

The question marks indicate uncertain physical mechanisms yet. New observations of this study are highlighted in red.

Supplementary information

Supplementary Information

Detailed descriptions of the doublet datasets, Supplementary Figs. 1 and 2.

Supplementary Table 1

Information of the high-quality SSI doublets.

Supplementary Table 2

Information of the high-quality non-SSI doublets.

Supplementary Table 3

Measurements of the waveform similarity along all the paths.

Supplementary Table 4

Measurements of the double differential time along the paths in the BC group.

Supplementary Table 5

Information of the additional SSI doublets and their double differential time measurements.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, Y., Song, X. Multidecadal variation of the Earth’s inner-core rotation. Nat. Geosci. 16, 182–187 (2023).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing