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Tidal tomography constrains Earth’s deep-mantle buoyancy

Abstract

Earth’s body tide—also known as the solid Earth tide, the displacement of the solid Earth’s surface caused by gravitational forces from the Moon and the Sun—is sensitive to the density of the two Large Low Shear Velocity Provinces (LLSVPs) beneath Africa and the Pacific. These massive regions extend approximately 1,000 kilometres upward from the base of the mantle and their buoyancy remains actively debated within the geophysical community. Here we use tidal tomography to constrain Earth’s deep-mantle buoyancy derived from Global Positioning System (GPS)-based measurements of semi-diurnal body tide deformation. Using a probabilistic approach, we show that across the bottom two-thirds of the two LLSVPs the mean density is about 0.5 per cent higher than the average mantle density across this depth range (that is, its mean buoyancy is minus 0.5 per cent), although this anomaly may be concentrated towards the very base of the mantle. We conclude that the buoyancy of these structures is dominated by the enrichment of high-density chemical components, probably related to subducted oceanic plates or primordial material associated with Earth’s formation. Because the dynamics of the mantle is driven by density variations, our result has important dynamical implications for the stability of the LLSVPs and the long-term evolution of the Earth system.

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Figure 1: GPS measurements of vertical M2 body tide deformation21 overlaying seismic tomographic model S40RTS2 at a depth of 2,800 km.
Figure 2: Sensitivity of body tide measurements to density perturbations in the deep mantle.
Figure 3: Histograms of processed GPS data and best-performing mantle models.
Figure 4: Histograms of excess densities of best-performing mantle models and the deep mantle excess density field of the mean of these models.

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Acknowledgements

H.C.P.L. and J.X.M. acknowledge support from NSF CSEDI grant EAR-1464024, NASA grant NNX17AE42G, and Harvard University. J.L.D. was supported in part by NASA grant NNX17AD97G. H.-Y.Y. was supported by the Chinese Academy of Sciences under grant number XDB18010304 and 2015TW1ZB0001. H.C.P.L. thanks J. Austermann for performing mantle convection simulations during the review process.

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Authors and Affiliations

Authors

Contributions

H.C.P.L. led the development of the body tide theory, the numerical/statistical analysis of GPS measurements of semi-diurnal body tides reported in the literature, and the writing of the manuscript. J.X.M. contributed to the statistical analysis and interpretation of the results while J.L.D. contributed algorithms to calculate tidal amplitudes and investigated potential impacts of GPS orbit errors. J.T., D.A.-A., H.-Y.Y. and J.X.M. contributed to the development of the body tide theory and numerical software. All these authors contributed text to the manuscript.

Corresponding author

Correspondence to Harriet C. P. Lau.

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The authors declare no competing financial interests.

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Reviewer Information Nature thanks L. Métivier, B. Romanowicz and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Sensitivity of the body tide response to wave speed and density perturbations throughout the mantle.

The sensitivity of the computed semi-diurnal body tide response to perturbations in shear wave speed vs (left column), density ρ (middle column), and bulk sound speed vb (right column) structure. Perturbations to structure are applied in five layers throughout the mantle (from top row to bottom row): lowermost lower mantle (2,891–2,211 km depth); mid lower mantle (2,211–1,201 km depth); uppermost lower mantle (1,201–670 km depth); transition zone (670–400 km depth); and uppermost upper mantle (400–24 km). The perturbations are expressed in terms of normalized power and decomposed into spherical harmonic coefficients up to degree and order 6. We define the normalized power as the total sum of the squared residual (3D minus 1D Earth model).

Extended Data Figure 2 Effects of crustal and CMB topography, and ocean tidal loading on GPS body tide measurements.

a, Crustal49 and CMB topography50 corrections to the body tide response (see Methods) shown as a percentage of the measurement uncertainty in the GPS data21. The magnitude of the corrections is indicated by both the size and colour intensity of the circles. b, The vertical axis refers to two quantities, denoted by crosses and black circles: (1) perturbations to u3D at each station when five different CMB topography models are imposed, all denoted by crosses. The symbol ε denotes the perturbation computed from the CMB excess ellipticity model adopted in the main text50 and the remaining results (yellow, light-blue and dark-blue crosses) are based on topography models estimated from seismic observations60,61,62; (2) the uncertainty in the GPS measurements (σ, denoted by black circles). All perturbations to u3D (crosses) are of much lower amplitude than σ (black circles). c, The standard deviation, σOTL, of a set of predictions of vertical crustal displacement associated with ocean loading, uOTL, computed using the seven ocean tide models described in the Methods section. The green circles mark the locations of the GPS sites use in our analysis.

Extended Data Figure 3 Depth-dependent vs-to-density scaling28 adopted in this study.

Radial dependence of the scaling factor Rρ, applied (within the shallowest three layers of our Earth models) to convert perturbations in shear wave speed vs to perturbations in density28 ρ. The scaling factors within the lowest three regions (shaded) are treated as free parameters in the analyses described in the text.

Extended Data Figure 4 Histograms of best-performing mantle models when adopting single tomographic models.

Statistical tests performed as in Fig. 3c of the main text, but considering only a single seismic model listed in turn: a, HMSL23, b, S362MANI24, c, S40RTS2, d, SAW24B1625 and e, all (as in Fig. 3c). In each column, the top, middle and bottom panels correspond to regions DL, ML and DO, respectively. The statistical significance of each of these tests is given in parentheses above each column. Values listed in the top right corner of each of these panels are the mean and the standard deviations of the distributions.

Extended Data Figure 5 Depth sensitivity of body tide response to long wavelength density perturbations.

Depth sensitivity of body tide response to density perturbations of spherical harmonic degree l and order m throughout the mantle. ‘Normalized sensitivity’ represents the sum of the squared residuals of the vertical amplitude of the body tide at the GPS sites used in this study, where the maximum is scaled to 1.

Extended Data Figure 6 Results from synthetic inversion to test correlations between the deep and mid LLSVP regions.

A synthetic inversion analogous to the calculations performed to produce Fig. 3c. Here, synthetic ‘observations’ of the body tide are produced by adopting the seismic model S40RTS2 and imposing a mantle structure where Rρ(DL) = -0.5; Rρ(ML) = 0.1; and Rρ(DO) = 0.05 (as shown by the black vertical line on each panel). The top, middle and bottom panels correspond to regions DL, ML and DO, respectively. The posterior estimate and standard deviation for each parameter is listed on the associated panel. The colours discretize the range of Rρ estimates in the top panel and these colours are used to group together subsets of 3D Earth models common to all three panels. In characterizing the synthetic data, we adopted the same uncertainty as reported in the original GPS dataset by ref. 21.

Extended Data Figure 7 Results from synthetic inversion to test the effect of a dense, thin layer at the base of the mantle.

A synthetic inversion analogous to the calculations performed to produce Fig. 3c. Histograms are shown for estimates of the parameter Rρ(DL) (a), and the associated mean excess density <lnρ>DL (b). The synthetic data are computed by adopting the seismic model S40RTS2, Rρ(ML) = +0.1 and Rρ(DO) = +0.15. The DL layer used in the synthetics is comprised of a 100-km-thick sub-layer (that is, at the base of the mantle) with an Rρ value of −0.8 (dashed black line in a) and a 250-km-thick top layer with Rρ = +0.1 (dotted black line in a). The mean excess densities associated with these two layers are <lnρ>SL = 0.7% and <lnρ>TL = −0.1% (dashed and dotted black lines in b), respectively. The solid black line indicates the mean excess density across the whole DL region, <lnρ>DL. c, The distribution of our estimated <lnρ>SL from b, after correcting for the weighted sensitivity (see text). The true <lnρ>SL (that is, the value used to compute the synthetic data, 0.7%) is marked by the solid vertical black line.

Extended Data Figure 8 Example of body tide deformation field and spectral characteristics of seismic tomographic models in the deep mantle.

a, Difference in the amplitude of the in-phase vertical displacement of the semi-diurnal body tide predicted using 3D and 1D Earth models. The underlying mantle structure is that of S40RTS2, scaled to perturbations in bulk sound speed vb (as discussed in the main text) and to perturbations in ρ by applying the scaling factors shown in Extended Data Fig. 3. b, A combined power spectrum of the density field of the deep layer, DL, across the entire suite of 3D models tested. Each bar represents the maximum power across all models at the associated spherical harmonic degree. The values on the histogram are normalized using the maximum power across all models and all degrees (which occurs at spherical harmonic degree 2).

Extended Data Figure 9 Repeat inversion using only GPS stations away from coastlines.

Statistical tests performed as in Fig. 3c except that only a subset of GPS sites are used. In this calculation we use only inland sites (defined as being at least 150 km away from the nearest coastline, as in ref. 21). This reduces the number of sites from 456 to 135. The top, middle and bottom panels correspond to regions DL, ML and DO, respectively. The values listed in the top right corner of each panel are the mean and standard deviations of the associated distributions.

Extended Data Figure 10 Example histograms resulting from rotation tests.

Testing the statistical significance level of two different 3D Earth models (i* = 1 or 2) for which C1(i*) > C0 (as defined in the text). Each panel corresponds to a different 3D Earth model (constructed with the Rρ values listed in the inset) and shows the histogram of C3DR(i*, j) (where j = 1, 2,.., 1,000) values produced by rotating the predicted field (see Methods). The dashed green line shows the 95% level of these histograms and the solid green line shows C3D(i*) for the given 3D Earth model. In a, C3D(i* = 1) exceeds the 95% confidence level and thus passes the statistical significance test; in contrast, in b C3D(i* = 2) fails this test.

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Lau, H., Mitrovica, J., Davis, J. et al. Tidal tomography constrains Earth’s deep-mantle buoyancy. Nature 551, 321–326 (2017). https://doi.org/10.1038/nature24452

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