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Dynamic history of the inner core constrained by seismic anisotropy


Progressive crystallization of Earth’s inner core drives convection in the outer core and magnetic field generation. Determining the rate and pattern of inner-core growth is thus crucial to understanding the evolution of the geodynamo. The growth history of the inner core is probably recorded in the distribution and strength of its seismic anisotropy, which arises from deformation texturing constrained by conditions at the inner-core solid–fluid boundary. Here we show from analysis of seismic body wave travel times that the strength of seismic anisotropy increases with depth within the inner core, and the strongest anisotropy is offset from Earth’s rotation axis. Then, using geodynamic growth models and mineral physics calculations, we simulate the development of inner-core anisotropy in a self-consistent manner. From this we find that an inner core composed of hexagonally close-packed iron–nickel alloy, deformed by a combination of preferential equatorial growth and slow translation, can match the seismic observations without requiring hemispheres with sharp boundaries. Our model of inner-core growth history is compatible with external constraints from outer-core dynamics, and supports arguments for a relatively young inner core (~0.5–1.5 Ga) and a viscosity >1018 Pa s.

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Fig. 1: Sampling of the inner core with polar PKP rays.
Fig. 2: Effective velocity anomaly in the inner core from PKPab–df and PKPbc–df travel time observations as a function of ξ and epicentral distance.
Fig. 3: Inner-core growth, strain and anisotropy.
Fig. 4: Predicted versus observed PKP velocity anomalies for hcp Fe93.75Ni6.25 at 5,500 K and 360 GPa and trade-offs between IC age, S2 and translation rate.

Data availability

The seismic travel-time measurements that support the findings of this study (Figs. 1, 2 and 4 and Extended Data Figs. 3, 5, 7 and 9) are available in Supplementary Data 1 and at Raw seismic waveform data and metadata are accessible through the facilities of IRIS Data Services, and specifically the IRIS Data Management Center. The EHB Online Bulletins are available from the ISC; for access to the EHB see

Code availability

VPSC7 code is available on request from R. A. Lebensohn and information about accessing the code can be found at GrowYourIC code is available at and this work uses version 0.6 (ref. 76). Plots were produced using Generic Mapping Tools77.


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The authors acknowledge the following funding sources: National Science Foundation grants EAR-1135452 and EAR-1829283 to D.A.F. and B.R.; the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 795289 to M.L.; and National Science Foundation grant EAR 1343908 and US Department of Energy grant DE-FG02-05ER15637 to B.C.

Author information




All authors contributed to project design, methodology development, model conceptualization and manuscript preparation. D.A.F. was responsible for seismic data curation and formal analysis and wrote the first draft of the paper. M.L. contributed to the geodynamic modelling and B.C. provided the mineral physics input. D.A.F. and B.R. coordinated the project.

Corresponding author

Correspondence to Daniel A. Frost.

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The authors declare no competing interests.

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Peer review information Nature Geoscience thanks the anonymous reviewers for their contribution to the peer review of this work. Primary Handling Editor: Stefan Lachowycz.

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Extended data

Extended Data Fig. 1 Distribution of sources of receivers.

Locations of sources (circles) and receivers (triangles) used in this study. Stations with newly acquired data are shown in cyan.

Extended Data Fig. 2 Measuring PKP differential travel times.

Example waveforms of (left) PKPdf and (right) PKPab for a M6.0 event in Baffin Bay on 2009/07/07 observed at station P124 in Antarctica. Waveforms are aligned on the predicted arrival time of the respective phases. Waveforms are shown as (ac) broadly filtered at 0.03–2 Hz, (bd) narrowly filtered at 0.4–2.0 Hz. In (c) and (d) waveforms have been Hilbert transformed. Measured arrival times are shown as red lines. Predicted arrivals (in model ak135 with ellipticity corrections) are shown by black solid and dashed lines for direct and depth phases, respectively.

Extended Data Fig. 3 Differential travel times as a function of angle to the rotation axis, ξ, and depth.

PKPbc-df and PKPab-df travel time anomalies and effective velocity anomalies (excluding the data recorded at stations in Alaska) as a function of angle ξ with respect to the rotation axis, separated by ray turning depth for (a, b, and c) ICB to 5600 km, (d, e, and f) 5600 km to 6000 km, and (g, h, and i) 6000 km to Earth’s centre. (a, d, g): All travel time anomalies. (b, e, h) Travel time anomalies split into data turning in the western (red) and eastern (blue) hemispheres. (c, f, i) Effective velocity anomalies in the IC split by hemisphere. The WH western boundary is set at 159° W, and the WH eastern boundary is set at 40° E, as explained in Extended Data Figure 4.

Extended Data Fig. 4 Locating the western boundary of the western hemisphere.

Best fit of WH western boundary locations calculated using polar data (ξ < 15°) and excluding data from stations in Alaska. Black solid line marks the R2 fit and red region describes the region of highest R2, most likely containing the location of the boundary, which runs between 166° W and 159° W. R2 drops sharply at < 166° W and >153° W. Black dashed line and grey shading show the mean and standard deviation of R2 values for 200 bootstrap resamples. The eastern boundary is fixed at 40°E, following the result of Irving (2016). Western boundary locations from previous studies are marked in blue: Tanaka & Hamaguchi 19976; Creager 19997; Waszek et al. 201178; Irving & Deuss 20118; while that of Lythgoe et al. 20149 plots outside of the region shown.

Extended Data Fig. 5 Pattern of effective velocity anomaly with depth.

Effective velocity anomaly in the IC as a function of epicentral distance for ξ in the range (a and c) 0 to 30°, and (b and d) 0 to 15°. Left panels show data coloured by ξ, and right panels show data split into those turning in the eastern (blue) and western (red) hemispheres. The western hemisphere is defined as between 159° W and 40° E, as explained in Extended Data Figure 4. The linear trend with distance, solid line, is particularly clear for the most polar data (c and f), indicating increasing anisotropy with depth.

Extended Data Fig. 6 Distribution of slow axes of anisotropy.

Slow directions of anisotropy in our final model (Fig. 3), measured relative to the rotation (N-S) axis in the (a) plane perpendicular to the direction of translation (blue arrow coming out of plane), and (b) plane parallel to the direction of translation (blue arrow) from the left (east) to right (west) of the figure, respectively.

Extended Data Fig.7 Predicted versus observed PKP velocity anomalies for pure hcp Fe.

Predicted (dark blue and red dots and with mean as grey squares) and observed (light blue and orange dots and with mean as black diamonds) effective velocity anomalies as a function of (a) epicentral distance for data with ξ ≤ 15°, marked by dashed line in b and c, and as a function of ξ in the (b) western and (c) eastern hemispheres. Error bars for the data show the mean and one standard deviation at 2.5° and 5° increments for panels a, and b and c, respectively. We use the elastic tensor for pure HCP Fe at 5500 K and 360 GPa67, an age of 0.5 Ga, and a translation rate of 0.3 radii over the age of the IC. Variance reduction for the data with ξ < 15° is 73% compared to 93% for our model with Fe93.25Ni6.75.

Extended Data Fig. 8 The effect of pressure on anisotropy.

(a) Elastic constants for hcp iron as a function of pressure calculated from the reference position at 360 GPa and 5500 K, extrapolated using results from several calculations67,61 at 5500 K and 316 GPa, and 5500 K and 360 GPa. (b) Resultant anisotropy across the pressure range of the inner core. Direction of minimum velocity anomaly is marked by black circles. The orientation of the minimum anisotropy moves towards higher ξ values (more equatorial) with increasing pressure.

Extended Data Fig. 9 Differential travel time anomalies for western hemisphere data turning within 450 km of the ICB with respect to model ak135, as a function of angle to the rotation axis, ξ.

Travel time anomalies of (a) PKPbc-df and (b) PKPac-df phase pairs showing that observations at stations in Alaska (green) do not fit the global pattern, while observations from sources in Alaska (purple) do. Anisotropy curves are calculated using equation. S1, assuming constant cylindrical anisotropy through the inner core, for all data (green curve) and all data except that recorded in Alaska (blue curve).

Supplementary information

Supplementary Information

Supplementary Figs. 1 and 2.

Supplementary Data 1

Travel-time picks measured in this study.

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Frost, D.A., Lasbleis, M., Chandler, B. et al. Dynamic history of the inner core constrained by seismic anisotropy. Nat. Geosci. (2021).

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