Rotation Of Inner Core Research Articles

Misinterpreted Seismic Evidence for Localized Rapid Changes of the Inner Core Boundary Surface

AbstractThe nature of the inner core (IC) temporal changes is of great importance in understanding the deep earth dynamics. The comment by Tian and Wen (2023, https://doi.org/10.1029/2023gl103173) on our previous paper (Yang & Song, 2022, https://doi.org/10.1029/2022gl098393) provided a new observation as evidence against the IC rotation and proposed that our observations are instead from localized rapid changes at the IC surface. Here we argue the opposite to its conclusions. The comment misinterpreted our logic and many of our observations and arguments. Its one new waveform does not contradict with the “rotation” model. The original evidence for the “surface” model is demonstrated to be an artifact from station clock errors and instrument changes. Additionally, the surface model lacks a solid physical and quantitative basis to explain existing seismic evidence. We conclude that the rotation model is currently the best interpretation and the surface model is not a viable alternative.

Author Correction: Multidecadal variation of the Earth’s inner-core rotation

Author Correction: Multidecadal variation of the Earth’s inner-core rotation

Instabilities of Steady Flow in a Rotating Spherical Cavity Excited by Inner Core Oscillation

We experimentally investigated a stability of steady flow caused by inner core oscillation in a rotating spherical cavity with fluid. The inner core oscillation relative to the cavity is caused by steady external field, directed transversally to the rotation axis; thus, the oscillation frequency is equal to the rotation frequency of the system. Differential rotation of the core is deactivated, for that one of the core poles is connected with the nearest cavity pole by a torsionally elastic fish-line. It is found that the quasi-two-dimensional steady azimuthal flow is excited by the core oscillation; the flow intensity is proportional to the core oscillation amplitude squared. With increase of amplitude, the axially symmetrical flow loose stability; the instability mode is similar to the one found before in the case of free core oscillation, which was executing the mean differential rotation (Kozlov et al.: Eur. J. Mech. B-Fluid. 63(3), 39–46, 2017). The comparative analysis shows that the differential rotation of inner core is not an essential condition for the appearance of instabilities. The mechanism for the appearance of instabilities is related with inflection points in azimuthal velocity profile of the fluid flow caused by the core oscillation relative to the cavity.

The spin–orbit resonant problem including core–mantle gravitational coupling

In this work, we numerically study an improved model of the spin–orbit resonances with applications in the exoplanetary dynamics. While in the classical model the planetary rotation is characterized by the motion of the whole planet around the axis with the largest moment of inertia, the model which we revisit here considers differential rotation and gravitational coupling between distinct internal layers of the planet. We have prepared a numerical code with the equations of motion of differential rotation of an inner core and an outer mantle. We apply the model to the exoplanet Kepler-10b. Supposing a terrestrial-like interior structure for the planet, numerical exploration of the rotational phase space shows that the effects of the gravitational forces of the external layers of the planet on the rotation of a solid inner core may be not negligible.

Electromagnetically driven westward drift and inner-core superrotation in Earth’s core

A 3D numerical model of the earth's core with a viscosity two orders of magnitude lower than the state of the art suggests a link between the observed westward drift of the magnetic field and superrotation of the inner core. In our model, the axial electromagnetic torque has a dominant influence only at the surface and in the deepest reaches of the core, where it respectively drives a broad westward flow rising to an axisymmetric equatorial jet and imparts an eastward-directed torque on the solid inner core. Subtle changes in the structure of the internal magnetic field may alter not just the magnitude but the direction of these torques. This not only suggests that the quasi-oscillatory nature of inner-core superrotation [Tkalčić H, Young M, Bodin T, Ngo S, Sambridge M (2013) The shuffling rotation of the earth's inner core revealed by earthquake doublets. Nat Geosci 6:497-502.] may be driven by decadal changes in the magnetic field, but further that historical periods in which the field exhibited eastward drift were contemporaneous with a westward inner-core rotation. The model further indicates a strong internal shear layer on the tangent cylinder that may be a source of torsional waves inside the core.

Global seismic body-wave observations of temporal variations in the Earth's inner core, and implications for its differential rotation

Differential rotation of the Earth′s inner core has been predicted in some geodynamo models, and seismic studies over the past 15 yr have resolved rotation rates up to 1°yr−1. Most previous seismic body-wave studies have focussed on South Sandwich Islands events recorded at station COL in Alaska. Here, we present a globally extended study into temporal variations in the inner core over some 25 yr, using PKPbc-PKPdf traveltime residuals. To test for differential rotation of the inner core, displacement of inner-core heterogeneities over time is sought. We introduce a new method of space-flattening to remove the effect of spatial variations on the time variations; this allows for the use of both polar, semi-equatorial and equatorial geometries. First, we reanalyse polar paths from South Sandwich Islands events to stations COL and INK in North America. These stations yield a differential rotation of the inner core at a rate of 0.12–0.38°yr−1 in an eastward direction, in agreement with previous studies. However, station DAWY, which has a very similar path through the inner core as COL, yields at best a westward differential rotation of the inner core. Thus DAWY results are incompatible with the COL/INK inferred rotation. Secondly, earthquakes in the Aleutian Islands region, observed at BOSA and LBTB in southern Africa, exhibit temporal variations that are incompatible with the South Sandwich Islands-COL/INK inferred rotation rate. Thirdly, Kuril Islands events, recorded in South America at station BDF, yield inconclusive results. Finally, our final piece of evidence for the irreconcilability of differential inner-core rotation with global data comes from using earthquakes in the Vanuatu region, recorded at BCAO/BGCA in Central Africa, an equatorial geometry. These residuals resolve a westward inner-core rotation at a rate of 0.14°yr−1, over the same time period that South Sandwich Islands events indicate an eastward rotation. As any rigid-body rotation should yield the same direction and rate independent of where the inner core is sampled, our results allow us to reject previously reported inner-core differential rotation rates of up to 0.1–0.5°yr−1. Instead, our results suggest that structure in either the inner or the outer core is varying with time, over relatively short timescales and in ways that cannot be explained by, and do not support, a differentially rotating inner core.

Topography of Earth's inner core boundary from high-quality waveform doublets

Precise determination of the topography of a major internal boundary of the Earth is difficult because of the trade-off with the unknown velocity structure above it. However, the discoveries of the inner core (IC) rotation and high-quality teleseismic waveform doublets make the precise mapping of the topography of the inner core boundary (ICB) possible. Here we examine IC refracted (PKP-DF) and reflected (PKP-CD) waves recorded at the Yellowknife Array and other global stations from 14 high-quality doublets, among a large collection of doublets in S. Sandwich Islands that are recently discovered. Our results show clear evidence for spatial and temporal variations of IC reflections in traveltimes and in waveforms. If the time separation (dT) between the two members of the doublet is less than 3 yr, the IC arrivals show little temporal change in traveltimes or waveforms. If dT is greater than about 6 yr, some doublets show large variations but some others do not. The ICB regions beneath Atlantic and Indian Oceans show little temporal change. The regions that show large variations are beneath Africa and the Central America, which coincide with large seismic anomalies at the core–mantle boundary (CMB). Inside these two ICB regions, there are fine-scale (km scale) variations. The largest temporal changes of IC reflections are about 0.10 to 0.14 s, corresponding to a topographic variation of up to about 3.7 to 5.2 km. The results suggest ICB topography of a few kilometres on fine to regional scales. The geographical coincidence of the ICB and CMB anomalies may suggest strong thermal coupling of the mantle and the core. Dynamic models include a bumpy ICB rotating with the IC itself or a transient slurry boundary containing a mixture of molten materials and solidified patches of iron crystals, which is rapidly modified by the turbulence at the base of the convecting outer core. If the former is the main cause of the observed temporal change of the topography, the IC rotation is required to be an oscillation, whose half period has an upper limit of a few hundred years.

Estimation of inner-core rotation rate by using the Earth’s free oscillation

We estimate a rate of inner-core differential rotation from time variations of splitting functions of seven core modes of the Earth’s free oscillations excited by eight large earthquakes in a period of 1994–2003. The splitting functions and moment tensor elements are simultaneously determined for each core mode by a spectral fitting technique. The estimated moment tensor well agrees with Harvard CMT solution. The splitting functions are corrected for the effect of mantle heterogeneity using a 3D mantle velocity model. Inner-core rotation angle about the Earth’s spin axis is determined for each core mode as a function of event year by comparison of the corrected and reference splitting functions. Mean rotation rate of six core modes is estimated at 0.03±0.18° per year westward, and this value is insignificantly different from zero. Therefore, the inner core is not rotating at a significant rate relatively to the crust and mantle.

Short wavelength topography on the inner-core boundary

Constraining the topography of the inner-core boundary is important for studies of core-mantle coupling and the generation of the geodynamo. We present evidence for significant temporal variability in the amplitude of the inner core reflected phase PKiKP for an exceptionally high-quality earthquake doublet, observed postcritically at the short-period Yellowknife seismic array (YK), which occurred in the South Sandwich Islands within a 10-year interval (1993/2003). This observation, complemented by data from several other doublets, indicates the presence of topography at the inner-core boundary, with a horizontal wavelength on the order of 10 km. Such topography could be sustained by small-scale convection at the top of the inner core and is compatible with a rate of super rotation of the inner core of approximately 0.1-0.15 degrees per year. In the absence of inner-core rotation, decadal scale temporal changes in the inner-core boundary topography would provide an upper bound on the viscosity at the top of the inner core.

Thermal fluid transport phenomena in concentric annulus with movement and rotation of inner core

Thermal fluid transport phenomena in concentric annulus with movement and rotation of inner core

Relative wobble of the Earth's inner core derived from polar motion and associated gravity variations

SUMMARY In this paper an explanation of the observed decadal variations of the polar motion of the Earth is presented. Recent investigations show that the contribution of surface processes is too small to excite the observed magnitudes of the decadal variations of polar motion. After removing the known effects of atmospheric variations from the observed polar motion, we obtain significant residuals that obviously can only be explained by processes in the core. In this paper, we investigate the effect of a relative inner-core rotation. In particular, we assume that the orientation of the figure axis of the inner core changes with respect to the outer core and mantle. Due to the flattening of the inner core and the density difference between the inner and outer core, these changes contribute to variations of the Earth's polar motion due to internal mass redistributions. The objective of this study is to determine those changes in the orientation of the figure axis of the inner core that produce mass redistributions necessary to excite the decadal variations of the observed polar motion minus the estimated atmospheric influence. Using polar motion data and the atmospheric excitation function, it is possible to determine the excitation function of the internal process superimposed on the free wobble of the Earth by linear approximation of the Liouville equation. On the other hand, provided that only the contribution of the mass redistributions is significant, we can express the time function obtained in terms of the orientation of the figure axis of the inner core. The final expression then contains the corresponding orientation angles as unknowns. Using this expression, we calculate the orientation angles from the numerically determined values of the excitation function. The calculation results in a mean tilt of 1°, and a mean eastward drift of 0.7° yr−1 of the figure axis of the inner core and quasi-periodic decadal variations of its orientation angles. The associated changes of the mass geometry in the core due to these variations of the figure axis of the inner core are then used to estimate their influence on the Earth's outer gravity field. Finally, we compare the magnitude of the resulting gravity field variations with the accuracy of recent and future gravity field models.

Influence of possible inner-core motions on the polar motion and the gravity field

Provided that the figure axis of the inner core coincides with the dipole axis of the geomagnetic field, the relative rotation of the oblate inner core with respect to the outer core and the mantle can be determined. Because of the density difference between the inner and outer core, the assumed precessional motion of the inner core relative to the mantle is accompanied by a mass redistribution causing variations of polar motion. Assuming standard density models, it is found that variations of polar motion caused by variations of relative inner-core rotation due to that of the real dipole axis are similar to the decadal variations derived from observed pole coordinates. Calculations of the gravity potential show that the assumed relative rotation of the inner core causes gravity changes which may be detectable by modern satellite methods during the next decade.

Limits on differential rotation of the inner core from an analysis of the Earth's free oscillations

Differential rotation of the Earth's inner core has been inferred by several seismic ‘body-wave’ studies1,2,3,4,5,6 which indicate that the inner core is rotating at a rate between 0.2° and 3° per year faster than the Earth's crust and mantle. The wide range in inferred rotation rate is thought to be caused by the sensitivity of body-wave studies to local complexities in inner-core structure3,7. Free-oscillation ‘splitting functions’, on the other hand, are insensitive to local structure and therefore have the potential to estimate differential rotation more accurately. A previous free-oscillation study8, however, was equivocal in its conclusions because of the relatively poor quality and coverage of the long-period digital data available 20 years ago. Here we use a method for analysing free oscillations9 which is insensitive to earthquake source, location and mechanism to constrain this differential rotation. We find that inner-core differential rotation is essentially zero over the past 20 years (to within ±0.2° per year), implying that the inner core is probably gravitationally locked to the Earth's mantle10.

Anomalous rotation of the inner core and the toroidal magnetic field

We use numerical calculations of magnetic induction by axisymmetric motions in a spherical shell of conducting fluid to investigate the relationship between the Earth's toroidal magnetic field and the time‐dependent anomalous rotation of the solid inner core. We compute the induced toroidal magnetic field and inner core rotation maintained by the interaction of time‐independent, axisymmetric outer core fluid flow with models of the poloidal magnetic field. Three possible models of the azimuthal flow in the outer core are investigated: two thermal wind flows inside the tangent cylinder (predicted by some numerical models of the geodynamo) and a columnar flow outside the inner core tangent cylinder inferred from the geomagnetic westward drift. Results indicate that electromagnetic torques tightly couple the inner core rotation to the fluid motion. Electromagnetic spin‐up of the inner core occurs through damped torsional oscillations with periodicity near 4 years depending on the strength of the poloidal magnetic field. In steady state the thermal winds inside the tangent cylinder generate a peak toroidal field of 25 mT accompanying a prograde inner core rotation rate of 1°/yr. In contrast, the columnar westward drift model generates toroidal field with peak intensity near 4 mT and a small, retrograde anomalous inner core rotation of −0.013°/yr. The weak retrograde motion of the inner core produced by electromagnetic coupling to the westward drift cannot explain the seismically inferred prograde anomalous rotation.

Mechanics of inner core super‐rotation

A mechanism is proposed to explain the seismologically‐inferred prograde rotation of the Earth's solid inner core in terms of the structure of convection in the fluid outer core. Numerical calculations of convection and dynamo action in the outer core exhibit excess temperatures inside the tangent cylinder surrounding the inner core. We show that this temperature difference generates a prograde thermal wind and a strong azimuthal magnetic field inside the tangent cylinder. Electromagnetic torques on the inner core derived from induced azimuthal magnetic fields and the ambient poloidal field equilibrate when the inner core angular velocity lags the nearby tangent cylinder fluid angular velocity by approximately 14%. The inferred prograde rotation of the inner core (1.1–3°/year relative to the mantle) can be produced by a very small (⋍ 0.001 K) temperature anomaly within the tangent cylinder and indicates strong toroidal magnetic fields with peak intensities of 24–66 mT in that region of the core.

Seismological evidence for differential rotation of the Earth's inner core

The travel times of seismic waves that traverse the Earth's inner core show a small but systematic variation over the past three decades. This variation is best explained by a rotation of the inner core that moves the symmetry axis of its known seismic anisotropy. The inferred rotation rate is on the order of 1° per year faster than the daily rotation of the mantle and crust.