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Inferring nonlinear mantle rheology from the shape of the Hawaiian swell


The convective circulation generated within the Earth’s mantle by buoyancy forces of thermal and compositional origin is intimately controlled by the rheology of the rocks that compose it. These can deform either by the diffusion of point defects (diffusion creep, with a linear relationship between strain rate and stress) or by the movement of intracrystalline dislocations (nonlinear dislocation creep)1,2. However, there is still no reliable map showing where in the mantle each of these mechanisms is dominant, and so it is important to identify regions where the operative mechanism can be inferred directly from surface geophysical observations. Here we identify a new observable quantity—the rate of downstream decay of the anomalous seafloor topography (swell) produced by a mantle plume—which depends only on the value of the exponent in the strain rate versus stress relationship that defines the difference between diffusion and dislocation creep. Comparison of the Hawaiian swell topography with the predictions of a simple fluid mechanical model shows that the swell shape is poorly explained by diffusion creep, and requires a dislocation creep rheology. The rheology predicted by the model is reasonably consistent with laboratory deformation data for both olivine3 and clinopyroxene4, suggesting that the source of Hawaiian lavas could contain either or both of these components.

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Figure 1: Residual topography of the Hawaiian swell.
Figure 2: Lubrication-theory model for the Hawaiian swell.
Figure 3: Comparison of the lubrication model predictions with the residual topography of the Hawaiian swell.


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We thank A. Davaille, C. Herzberg, S.-I. Karato and D. Kohlstedt for discussions and advice. This work was supported by the French embassy in Tehran and by the SEDIT programme of INSU and the ANR (grant PTECTO) in France.

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Authors and Affiliations



N.A. derived the lubrication equation, determined the similarity solution and the full numerical solutions of that equation, and analysed the topography data. N.M.R. proposed the idea for the study, determined the three-dimensional numerical solutions with temperature-dependent rheology, and wrote the manuscript. F.S. co-directed the parts of the work done in Zanjan. All authors discussed the results and commented on the manuscript.

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Correspondence to N. Asaadi or N. M. Ribe.

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The authors declare no competing financial interests.

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Supplementary Figures

This file contains Supplementary Figures 1-3 with legends. Supplementary Figure 1 shows the validation of the lubrication-theory model against a three-dimensional convection model with temperature-and pressure-dependent viscosity (Newtonian rheology). Supplementary Figure 2 shows the validation of the lubrication-theory model against a three-dimensional convection model with temperature-pressure-, and strain-rate dependent viscosity (non-Newtonian rheology, power-law exponent 3.5). Supplementary Figure 3 shows the comparison of the lubrication model predictions with power-law index 4.7 (appropriate for clinopyroxene) with the residual topography of the Hawaiian swell. (PDF 539 kb)

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Asaadi, N., Ribe, N. & Sobouti, F. Inferring nonlinear mantle rheology from the shape of the Hawaiian swell. Nature 473, 501–504 (2011).

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