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Earth's Upper Mantle Rheology

Projet financé par l'ANR MANTLE RHEOLOGY

O. Castelnau (PIMM), P. Cordier (UMET), R.A. Lebensohn (LANL), S. Merkel (UMET), P. Raterron (UMET), W. Crichton (ESRF)

Earth's plate tectonics generates major haz(~30%)ards for human societies (earthquakes, volcanic eruptions, tsunamis, etc.). It is largely constrained by the rheology of the Earth upper mantle (Figure 1, top 410 km) composed of polycrystalline aggregates comprising olivine (~60 vol.%) mixed with pyroxenes  (~30%) and other minor phases such as garnets, and possibly melt. 

Figure 1: Earth cut (image by Colin Rose)

The complex behavior of this material comes from the extreme viscoplastic anisotropy at the crystal scale, so that the simultaneous activation of several deformation mechanisms (dislocation glide, dislocation climb, grain boundary diffusion ...) is probably necessary. Despite decades of experimental work, rheology of Earth mantle minerals is not well understood for several reasons:
  1. until recently, deformation experiments could not reach the pressure (~14 GPa) and temperature (~1500K) of the mantle;
  2. the pressure has a strong influence on dislocation mobility;
  3. data extrapolation to the extremely small in situ strain-rates (~10-15 s-1) requires a multiscale approach coupling several techniques and modeling;
  4. the extreme local anisotropy of all mineral phases requires the use of accurate homogenization models, which have almost never been applied in the context of deep Earth minerals.
The aim of this project is to achieve an accurate modeling of upper-mantle plasticity, which accounts for high-pressure experimental data on olivine and olivine-pyroxenes-garnet-melt aggregates obtained in state-of-the art high pressure equipments set at synchrotron facilities on mono- and poly-crystals, ab initio calculations for the dislocation properties at the nanometer scale, and polycrystal plasticity inferred from micromechanical modeling approaches. The resulting multiscale model (from nanometer to kilometer scales) will be a first-of-a-kind and, while applied in specific geodynamical context, will provide crucial information for the interpretation of upper-mantle seismic data and the modeling of mantle convection  (Figure 2). 

Figure 2:  in earth's mantle

The used polycrystal model will be based on mean-field homogenization methods (self-consistent scheme associated with the "Second-Order" linearization procedure of Ponte Castañeda). This second-order self-consistent approach is very efficient for minearl materials. The effective behavior predicted by this approach are compared with ensemble averages of the the fast Fourier transform FFT-based full-field solutions. This comparison show that the predictions obtayned by means of the second-order approach are in better agreement with the FFT-based full-field solutions (Figure 3).

Figure 3 Right: Stress field compute by FFT in olivine polycrystal
Left: Comparison between FFT-based full-field solutions (FFT) and several mean-field approaches (SO: second-order linearization; AFF: affine linearization; TGT: tangent lenarization) for different values of plastic anisotropic parameters M.