The 2024 Nature backtracking study established that Earth's solid inner core super-rotated from about 2003 to 2008 and then sub-rotated along the same path about 2.5 times more slowly through 2023, tracked by PKIKP waveforms (seismic compressional waves that pass through the solid inner core) from South Sandwich Islands repeating earthquakes that changed and then reverted to match earlier recordings. Several issues that study explicitly left open remain unresolved after 2024–2026 follow-ups: calibrating the absolute differential rotation rate in degrees per year, separating true rotation from near-inner-core-boundary and outer-core structural change as contributors to the waveform evolution, tracing the motion before about 2002, explaining event pairs that the reversing-rotation model predicts to match but that do not match, and building dynamical models of inner-core–outer-core–mantle coupling that reproduce the asymmetric forward/backward rates. Later work has tentatively shown that both rotation and shallow inner-core deformation contribute, and an independent group has constrained a multidecadal oscillation back to 1982, but the absolute-rate calibration, cross-path partitioning, pre-2002 backtracking history, scatterer evolution, and the rate-asymmetry mechanism all remain open.

Background

Earth's solid inner core floats within the liquid outer core and can rotate slightly relative to the crust and mantle. Song and Richards (1996) first reported seismological evidence of such differential rotation by comparing inner-core-penetrating seismic waves (PKIKP waves — compressional body waves that pass through the solid inner core, in contrast to PKiKP waves that reflect from the inner-core boundary, or ICB) from repeated nuclear explosions at the same site but recorded years apart. When a later wave is earlier or later than an earlier one, the ray has sampled a different part of the inner core's uneven (laterally heterogeneous and anisotropic) structure, implying the inner core moved. Subsequent work used repeating earthquakes (doublets and multiplets — nearly identical events rupturing the same fault patch, so that any waveform change along a fixed source–station path is attributable to the Earth's interior, not the source) recorded by seismic arrays such as Eielson (ILAR) and Yellowknife (YKA) in northern North America from South Sandwich Islands events. A competing school attributed the temporal waveform changes not to rotation but to localized structural change at or near the ICB or in the outer core, and methodological critiques (e.g., Tkalčić 2024 on data-selection traps in doublet studies) highlighted how sensitive such inferences are to event selection and clock accuracy. Yang and Song (2023) reported a multidecadal oscillation: the inner core super-rotated (rotated slightly faster than the mantle), then slowed to near zero around 2009, and they associated the oscillation with electromagnetic and gravitational coupling to the mantle. Wang, Vidale, Pang, Koper and Wang (2024, Nature 631, 340–343) advanced this decisively with a backtracking analysis: among 143 pairs of repeating earthquakes (1991–2023), many waveforms changed and later reverted to match earlier events, marking epochs when the inner core re-occupied a previously held position relative to the mantle. This showed gradual super-rotation from 2003 to 2008 followed by sub-rotation (differential rotation in the opposite direction, carrying the inner core back through the same structural path) two to three times more slowly — roughly a factor of 2.5 — through 2023. The reversal timing is broadly consistent with a multidecadal oscillation connected to tiny length-of-day variations, but the asymmetric rates do not fit a symmetric oscillation. The 2024 study itself identified what remains unresolved: absolute rotation rates cannot be extracted from the waveform-match midpoint plot alone (it constrains only the rate ratio and reversal epoch, because the mapping between waveform match and angular displacement depends on the inner core's unknown lateral seismic structure); the data cannot decisively exclude structural changes at the ICB or in the outer core as partial contributors (PKP_BC/CD waves, which turn in the outer core below the ICB, show no change, but that negative result does not rule out localized boundary or outer-core processes); motion before about 2002 cannot be traced because no matching waveforms from earlier positions were identified; some event pairs the model predicts to match do not, for which the study suggested fine time-shift measurements, beamforming (stacking array records steered to a chosen direction) to locate individual scatterers, and modelling of PKiKP/PKIKP interference; the asymmetric forward/backward rates demand new dynamical models coupling the inner core, outer core and mantle — including possible entrainment of outer-core mass in the tangent cylinder (the imaginary cylinder aligned with the rotation axis tangent to the inner core, inside which outer-core flow is dynamically distinct) — with present theory, such as the mantle–inner-core gravitational coupling mode (a normal mode in which gravitational attraction between inner-core topography and mantle density anomalies makes the inner core oscillate relative to the mantle), not constraining the mechanism; and the method should be extended to other source–station paths, further into the past and future, to test reproducibility and separate rotational from structural contributions.

Problem Statement

Determine the recent rotational and near-surface history of Earth's inner core and its physical mechanism, as left unresolved by Wang et al. (2024). Concretely: (1) calibrate the absolute differential rotation rate(s) in degrees per year of the 2003–2023 super-rotation/sub-rotation episode (the forward-then-backward differential rotation relative to the mantle) — and the rate asymmetry — independently of assumed lateral seismic-structure models of the inner core; (2) quantitatively separate rotational displacement from structural change at or near the inner-core boundary (and in the outer core) as contributors to temporal PKIKP (inner-core-penetrating seismic wave) waveform change, on more than the South Sandwich Islands–northern North America path system; (3) reconstruct the multi-decadal trajectory of inner-core differential rotation, including the period before about 2002 that waveform backtracking cannot currently reach, using earlier archives where they exist; (4) explain the event pairs whose waveforms the reversing-rotation model predicts to match but that do not; and (5) construct dynamical models coupling the inner core, outer core and mantle (including candidate mechanisms such as gravitational coupling, electromagnetic coupling, and entrainment of outer-core mass in the tangent cylinder, the imaginary cylinder aligned with the rotation axis tangent to the inner core) that reproduce the observed reversal epoch and the roughly 2.5-times asymmetry between the forward and backward rates. These components jointly serve one objective: to establish whether, how fast, in what pattern, and why the inner core has rotated relative to the mantle over recent decades.

References

  1. Wei Wang, John E. Vidale, Guanning Pang, Keith D. Koper, Ruoyan Wang (2024). Inner core backtracking by seismic waveform change reversals. Nature 631, 340–343. DOI: 10.1038/s41586-024-07536-4. https://doi.org/10.1038/s41586-024-07536-4
  2. John E. Vidale, Wei Wang, Ruoyan Wang, Guanning Pang, Keith Koper (2025). Annual-scale variability in both the rotation rate and near surface of Earth's inner core. Nature Geoscience 18, 267–272. DOI: 10.1038/s41561-025-01642-2. https://doi.org/10.1038/s41561-025-01642-2
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  6. Xiaodong Song, Paul G. Richards (1996). Seismological evidence for differential rotation of the Earth's inner core. Nature 382, 221–224. DOI: 10.1038/382221a0. https://doi.org/10.1038/382221a0
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