Inner core static tilt inferred from intradecadal oscillation in the Earth’s rotation

The geodynamic state of the Earth's inner core, particularly the relationship between its rotation and that of the mantle, is a subject of ongoing debate. A key aspect of this debate centers on the existence of a static tilt between the inner core and the mantle. The classical model of Earth's rotation assumes alignment of the inner core's figure axis and rotation axis with the mantle's axes, maintaining equilibrium. However, random torques can induce a dynamic tilt, leading to the inner core wobble (ICW). The ICW period is highly sensitive to the density jump at the inner core boundary (ICB), with theoretical predictions ranging from 6.6 to 7.8 years based on the Preliminary Reference Earth Model (PREM). The heterogeneity of the mantle, however, introduces the possibility of a static tilt, where the inner core's rotation axis deviates from alignment with the mantle's axis. Some previous research has suggested a significant static tilt of 10°, but this has lacked observational confirmation. The lack of clear detection in core-sensitive normal modes of Earth's free oscillation has increased uncertainties about the magnitude or even existence of a static tilt. Nevertheless, a statically tilted inner core would have significant implications for various aspects of Earth's geodynamics, including inner core differential rotation, surface gravity changes, seismic tomography, and geodynamo theory. This study aims to investigate the existence and magnitude of a static tilt by analyzing the ICW's manifestation in both polar motion (PM) and length-of-day (LOD) variations. The detection of a similar periodic signal in both datasets, correlated with the ICW, would provide compelling evidence for a statically tilted inner core, allowing for the determination of the tilt angle by comparing the amplitudes of the signals.

Previous studies have explored the inner core wobble (ICW) using various approaches, but with inconclusive results. Some studies have suggested the presence of an ICW signal in polar motion data, often with periods slightly deviating from theoretical predictions. However, the identification of the ICW has remained controversial due to the presence of other signals in similar frequency bands, such as those originating from atmospheric and oceanic effects. The influence of external sources like atmospheric and oceanic angular momentum on PM and LOD variations has been extensively studied, requiring careful separation of these effects from potential ICW signals. The theoretical framework for understanding the ICW and its relationship to a static tilt involves the dynamics of angular momentum exchange between the inner core and the mantle. Models incorporating the gravitational interaction between the inner core and mantle predict the ICW's period and amplitude based on various Earth parameters, including the density jump at the ICB. Existing inconsistencies between theoretical predictions and observational data regarding ICW periods and amplitudes highlight the need for more refined models and more precise observations. Studies analyzing seismic data have also offered insights into the inner core's structure and heterogeneity, with some findings hinting at density variations that could support a statically tilted inner core. Previous studies have primarily focused on polar motion data alone for ICW detection, missing the potentially crucial information from LOD changes which could be caused by a static tilt.

This study utilized long-term time series of polar motion (PM) and length-of-day (LOD) variations to search for evidence of an inner core wobble. The PM data used were from the EOPC01 dataset, spanning from 1900 to 2020 with a one-year sampling interval. The LOD data were a combination of long-term datasets (1623-2008 and 1962-2019). Atmospheric and oceanic angular momentum (AAM and OAM) effects were considered and removed from the datasets through preprocessing steps detailed in the Methods section. Preprocessing included downsampling all records to 1 year to standardize the sampling intervals and applying a low-pass filter to reduce aliasing effects. The stabilized AR-z spectral analysis method was employed to identify periodic signals within the PM and LOD records with high frequency resolution. This method allows for the detection of harmonic signals even in the presence of noise. The authors focused on prograde signals, as the ICW is expected to be a prograde motion. After removing the influence of external excitations, an 8.5-year signal was identified in both PM and LOD data. This signal was deemed the most probable candidate for the ICW due to the absence of a corresponding signal at the negative frequency, a characteristic of prograde motion and consistency in both PM and LOD datasets. The signal was extracted using cosine least-squares fitting. The study also employed the conservation of angular momentum principle to estimate the inner core's static tilt. Equations describing the equatorial and axial torques exerted on the mantle were derived, based on the theory of Earth's rotation. By analyzing the phase relationship between the ICW signals in the y-component of PM and the time derivative of ALOD, the orientation and magnitude of the static tilt were inferred. Finally, the density jump (ΔρICB) at the ICB was constrained based on the observed ICW period, using an existing formula relating the ICW period to various Earth parameters and adjusting the density profile of the outer core while maintaining the Earth's total mass and angular momentum.

The key findings of this study are: 1. Confirmation of an 8.5-year signal in Earth’s polar motion and length-of-day variations as the inner core wobble (ICW). The identification relies on the use of the AR-z spectral method to improve signal resolution and distinguish the ICW from external excitation sources such as atmospheric and oceanic angular momentum. The authors demonstrate the presence of a clear 8.5-year signal in both datasets after removing the effects of these external factors. The presence of the signal in both datasets is interpreted as strong evidence for a static tilt between the inner core and mantle. 2. Inference of a static tilt angle (θ) between the inner core and mantle of 0.17 ± 0.03°. This tilt is significantly smaller than previously assumed in geodynamic research, with an orientation likely towards -90°W relative to the mantle. This estimate was obtained by comparing the amplitudes of the ICW signal in both polar motion and length-of-day data using models based on conservation of angular momentum. The close phase synchronization between the ICW signal in the y-component of PM and the time derivative of ALOD is a critical observation that supports the existence of a westwards tilt. 3. Estimation of the density jump at the inner core boundary (ICB) as 0.52 ± 0.05 g/cm³. This value was determined by inverting the observed 8.5-year ICW period, using a formula relating the period to the density jump. The slightly larger observed ICW period than theoretical predictions is discussed and is considered acceptable considering similar discrepancies in the observed periods of other Earth rotation modes and uncertainties in the ICB density. The inferred westwards tilt is consistent with the seismological observation of a denser northwestern hemisphere in the inner core. The findings are schematically illustrated in figures within the paper, showing the orientation of the inner core tilt and the phase relationship of the ICW signal in different datasets.

The findings of this study significantly refine our understanding of the Earth's inner core dynamics. The significantly smaller static tilt angle (0.17 ± 0.03°) compared to previous assumptions (around 10°) challenges existing geodynamic models and necessitates a reassessment of the forces acting on the inner core. The consistency between the observed ICW period, the inferred tilt angle, and the seismologically suggested density variations in the inner core provides strong support for the existence of a westwards tilt. This suggests a non-uniform density distribution within the inner core with a denser northwestern region, potentially linked to crystallization and melting processes at the inner core boundary. The relatively low tilt magnitude implies that the previously proposed influence on other geophysical phenomena due to larger tilt might be less significant than expected. The revised value of the density jump at the ICB (0.52 ± 0.05 g/cm³) also refines our knowledge about inner core composition and structure. The study's methods, including the use of stabilized AR-z spectra and the comprehensive consideration of atmospheric and oceanic effects, enhance the robustness of the findings. This work suggests new avenues for future research to refine the models of Earth’s rotation and inner core dynamics. More detailed seismic studies to investigate the density structure of the inner core, as well as improved theoretical models incorporating the observed small tilt angle are essential for complete understanding. The implications of the study extend beyond geophysics, potentially impacting our understanding of planetary interiors and core-mantle interactions in other celestial bodies.

This study provides compelling evidence for a static tilt between the Earth's inner core and mantle, significantly smaller than previously hypothesized. The observed 8.5-year inner core wobble (ICW) signal in both polar motion and length-of-day variations, along with the derived tilt angle of 0.17 ± 0.03° and a density jump of 0.52 ± 0.05 g/cm³ at the inner core boundary, offer new constraints for geophysical models of the Earth's deep interior. Future research should focus on refining the model of Earth's rotation to incorporate this small tilt and further investigate the detailed density structure of the inner core using high-resolution seismic tomography.

The study's findings are based on the analysis of relatively long-term time series data, with an inherent limitation in resolving high-frequency variations within the inner core. Further, the model employed to estimate the density jump at the inner core boundary relies on several assumptions about the Earth's structure and composition, introducing some uncertainty into the result. While the study comprehensively accounts for the influence of atmospheric and oceanic angular momentum, other subtle external effects may still exist and could affect the detected ICW signal. The assumption of a simple, homogeneous inner core in parts of the analysis simplifies a complex system, and this simplification may introduce some bias in the results.