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.
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The digital waveform data in this study are openly available from the Incorporated Research Institutions for Seismology Data Management Center (http://iris.edu) and Canadian National Seismograph Network (http://earthquakescanada.nrcan.gc.ca/stndon/CNSN-RNSC/index-en.php). The analogue waveforms from the station COL were collected and manually digitized by ref. 7, and those of the SSI doublets are available at https://doi.org/10.6084/m9.figshare.21548679.v1. The yearly averaged LOD measurements and the daily Earth Orientation Parameters series (EOPC04) are freely downloaded from the International Earth Rotation and Reference Systems (https://www.iers.org/IERS/EN/Home/home_node.html).
The codes used in this study are available upon request.
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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.
The authors declare no competing interests.
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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.
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.
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.
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Yang, Y., Song, X. Multidecadal variation of the Earth’s inner-core rotation. Nat. Geosci. 16, 182–187 (2023). https://doi.org/10.1038/s41561-022-01112-z
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