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Tilted transverse isotropy in Earth’s inner core

Nature Geoscience (2024)Cite this article

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Abstract

Seismic waves traversing the inner core in a direction parallel to Earth’s rotation axis arrive faster than waves travelling in the equatorial plane. These observations have been explained in terms of a transversely isotropic inner-core model with a fast symmetry axis parallel to the rotation axis. In recent years, more complex models of the inner core have been developed containing strong regional variations such as hemispheres, isotropic layers and an innermost inner core, most of which assume spatially variable transverse isotropy with a fixed symmetry axis. Here we instead explain the travel times of inner-core-sensitive seismic waves in terms of tilted transverse isotropy, in which the magnitude of transverse isotropy is fixed, but the orientation of the symmetry axis is allowed to vary spatially. This model, derived from seismic tomography, fits travel time data and spatially variable fixed-axis models, yet requires fewer parameters. It features a central inner core with a strong alignment of the fast symmetry axis in the direction of Earth’s spin axis and two shallow caps beneath the Mid-Atlantic and the Indian Ocean/Indonesia regions with symmetry axes tilted towards the equatorial plane. This model indicates the potential for varying crystal orientations within the inner core, which would constrain inner-core dynamics.

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Fig. 1: Observed and predicted travel time data.
Fig. 2: Posterior probability distributions of the three Love parameters.
Fig. 3: Symmetry axis orientations.
Fig. 4: The symmetry axis orientation plotted as 3D streamlines.

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Data availability

Travel time data are available via Figshare at https://doi.org/10.6084/m9.figshare.26535394.v1 (ref. 48). Model parameters and ParaView movies are available as an electronic supplement.

Code availability

The code used to generate TTI inner core models is available upon request from the corresponding author.

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Acknowledgements

This research was accomplished with financial support from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 681535–ATUNE) and a Vici award number 016.160.310/526 from the Netherlands Organization for Scientific Research (NWO).

Author information

Authors and Affiliations

  1. Department of Geosciences, Utrecht University, Utrecht, The Netherlands

    Hen Brett & Arwen Deuss

  2. Department of Geosciences and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, USA

    Jeroen Tromp

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  1. Hen Brett
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Contributions

H.B. wrote the computer programmes and made the TTI model; J.T. proposed the project and helped with the theory; A.D. supervised the project and performed the interpretation. All three authors contributed equally to writing the paper.

Corresponding authors

Correspondence to Hen Brett or Arwen Deuss.

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The authors declare no competing interests.

Peer review

Peer review information

Nature Geoscience thanks Daniel Frost, Satoru Tanaka and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editors: Alireza Bahadori and Stefan Lachowycz, in collaboration with the Nature Geoscience team.

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Extended data

Extended Data Fig. 1 PKP raypaths and travel time curves.

(a) Raypaths for the compressional PKP waves used in this study to image inner-core anisotropy, showing PKIKP (also called PKPdf), PKPab, PKPbc, and PKiKP (also called PKPcd) and (b) traveltime curves for the same waves.

Extended Data Fig. 2 Schematic diagram showing the effect of rotations.

Schematic diagram showing the effect of rotations about the z-axis by an angle η1 and y-axis by an angle η2 and a combined rotation of the two.

Extended Data Fig. 3 Summary of the Transdimensional Markov Chain Monte Carlo ensemble.

Summary of the Transdimensional Markov Chain Monte Carlo ensemble chains; we ran 20 chains for 4,000,000 iterations with an acceptance rate (the percentage of accepted perturbations) of 30.5%. The misfit drops rapidly in the first 200,000 iterations before reaching a misfit minimum; the transdimensional algorithm then samples models around this minimum value. Misfit is calculated using an L2 norm and then shown relative to the misfit of PREM (where misfit = 1.0 means the misfit of a chain is the same as PREM, misfit > 1.0 means the misfit of a chain is greater than PREM and misfit < 1.0 means the misfit of a chain is the lower than the prediction of PREM) (a) Variation of misfit with iteration in all 20 chains for our transdimensional model. (b) Variation of the number of volumes with iteration in all 20 chains for our transdimensional model. (c) Distribution of models as a function of the number of volumes.

Extended Data Fig. 4 Colatitude Maps.

Similar to Fig. 3, but showing only the symmetry axis colatitude and its standard deviation. Maps created with Cartopy49 with continent outlines from Natural Earth (https://www.naturalearthdata.com). Maps showing the symmetry axis colatitude at a, the inner-core boundary (1221.5 km radius), b, 800 km, and c, 400 km radius. Corresponding standard deviations (SD) are shown in panels d–f.

Extended Data Fig. 5 Observed and predicted travel time data from a fixed axis model.

Similar to Fig. 1, but comparing our traveltime data set (blue dots) with traveltime predictions (orange dots) based on our previous model17 with a fixed symmetry axis. a, PKPcd–PKPdf travel times. b, PKPbc–PKPdf travel times. c, PKPab–PKPdf travel times. d, Absolute (Abs.) PKPdf travel times. Travel times are plotted as a function of the angle of the inner-core segment of the PKPdf ray relative to Earth’s spin axis, ζ. e–h, Fractional travel times δt/t as a function of turning-point longitude in the inner core. Observed travel times (blue dots) are compared to predictions based on our TTI inner-core model (orange dots).

Extended Data Fig. 6 Symmetry axis orientation maps without SSI data.

Similar to Fig. 3, but for a Tilted Transverse Isotropy inner core model excluding the anomalous South Sandwhich Island events. Maps in a–c created with Cartopy49 with continent outlines from Natural Earth (https://www.naturalearthdata.com). a–c, Maps showing the orientation of the symmetry axis at the inner-core boundary (a), 800 km (b) and 400 km (c) radius. d, Cross-sections in the equatorial plane. e, Cross-sections in the meridional plane.

Extended Data Fig. 7 Mineral physics travel time predictions for three iron crystal types.

Mineral physics predictions for three different phases of iron using elastic parameters from ab initio calculations.

Supplementary information

Supplementary Data

This contains the values of the model, discretized in a fine grid in 3D, with a header describing each model parameter and tab separated values.

Supplementary Video 1

This is an animation spinning around our model, showing streamlines of the axis orientation, with the colour of the streamline segments indicating the axis colatitude, with blue segments being polar.

Supplementary Video 2

This is an animation spinning around our model, showing streamlines of the axis orientation, with the colour of the streamline segments indicating the axis colatitude, with blue segments closer to a colatitude of 0.0 and red segments being closer to a colatitude of 90. This animation has been restricted to only showing streamline segments with a colatitude of 35° or less.

Supplementary Video 3

This is an animation spinning around our model, showing streamlines of the axis orientation, with the colour of the streamline segments indicating the axis colatitude, with blue segments closer to a colatitude of 0.0 and red segments being closer to a colatitude of 90. This animation has been restricted to only showing streamline segments within 690 km of the centre of Earth, showing a potential innermost inner core.

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Brett, H., Tromp, J. & Deuss, A. Tilted transverse isotropy in Earth’s inner core. Nat. Geosci. (2024). https://doi.org/10.1038/s41561-024-01539-6

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