Viscosity undulations in the lower mantle: The dynamical role of iron spin transition
Introduction
Lower mantle viscosity has been the subject of great debate over the last decades (Sammis et al., 1977, Ricard and Wuming, 1991, Forte and Mitrovica, 2001), and its determination would be fundamental to address a number of questions on the mantle, such as its composition, heterogeneity, and geodynamics. Interpretation of data, coming from geoid inversion and postglacial rebound studies, indicated undulations in the viscosity profile, with peaks around 1300 and 2000 km deep and a valley around 1600 km (Mitrovica and Forte, 2004). If viscosity is considered as controlled by thermally activated microscopic mechanisms (Sammis et al., 1977, Ellsworth et al., 1985), this viscosity profile could not be easily reconciled with a single diffusion creep mechanism taking place in the lower mantle. Those variations in the lower mantle viscosity suggest that several microscopic competing diffusion mechanisms could be taking place in the mantle. On the other hand, the recent discovery of the iron spin transition in major mantle minerals (Badro et al., 2003, Badro et al., 2004, Lin et al., 2005, Lin et al., 2007, Speziale et al., 2005, Tsuchiya et al., 2006, Fei et al., 2007), and the corresponding anomalies in their elasticity (Crowhurst et al., 2008, Wentzcovitch et al., 2009, Marquardt et al., 2009, Wu et al., 2009, Antonangeli et al., 2011, Wu and Wentzcovitch, 2014), could reconcile the description of viscosity with a single thermally activated mechanism by using the available information from simultaneous inversion of geoid and post-glacial rebound data (Mitrovica and Forte, 2004).
Van Keken et al. (1992) found that some radial viscosity profile would produce a pulsating diapiric rise. This work has simulated numerous investigations of the effects of non-monotonous viscosity profile in the lower mantle. Tomographic models of slabs that penetrated in the lower mantle show strong signals of large body lying between 1500 and 2000 km depth (Grand, 1994), such as the Farallon slab (Sigloch et al., 2008). This result has been confirmed by the analysis of a variety of global tomographic models, e.g. Tx2007 (Simmons et al., 2006), Rmsl-s06 (Li et al., 2007), Saw642an (Panning and Romanowicz, 2006), all finding a clear transition from fast to slow shear seismic velocities for degree up to ∼16 at a less than 1500 km depth (Boschi et al., 2008). Morra et al. (2010) showed that a sinking plate might penetrate, reorganize or even stall when crossing a 200 to 500 km high viscosity region in the middle of the lower mantle. Shahnas et al. (2011) used global mantle convection models to demonstrate that the only effects on the density of the iron spin transition enhances the vigor of rising plumes below 2000 km depth and slightly increases the temperature of the lowermost region of the mantle. Peltier and Drummond (2010) used glacial isostatic adjustment observations to infer a modest increase of the viscosity at mid mantle depths. Overall, those investigations have shown that a non-monotonic lower mantle viscosity profile would create substantial complications to the dynamics of sinking slabs and rising plumes. Here, we employ a standard scaling for plume head size evolution (e.g., Griffiths and Campbell, 1990, Ribe et al., 2007) integrating it along a one-dimensional vertical profile to calculate a broad range of solutions for the dynamics of a plume rise through a variety of physically based lower mantle viscosity profiles, obtained by first principles calculations of mineral elasticity.
We used the elastic properties of ferropericlase (Fp), Mg1 − xFexO with , computed by a combination of first principles calculations and quasiharmonic approximation (Carrier et al., 2008, Wentzcovitch et al., 2009, Wu et al., 2013), to determine its viscosity under lower mantle conditions. Fp was treated as a solid solution in a mixed spin state, with the concentration of material with iron in high and low spin determined by the respective free energies. Although Fp is only the second most abundant lower mantle mineral, it is likely controlling deformation in the lower mantle (Zerr and Boehler, 1994, Yamazaki and Karato, 2001). This is justified by the fact that Fp is softer than the more abundant ferrosilicate perovskite under the same thermodynamic conditions. The viscosity of Fp was described within the elastic strain model (Sammis et al., 1977, Ellsworth et al., 1985), in which the activation energy parameters were computed along adiabatic (0.3 K/km) (Boehler, 2000) and superadiabatic (1.2 K/km) (da Silva et al., 2000) geotherms. The manuscript explores the role of dilatation and shear microscopic mechanisms (Ellsworth et al., 1985), variations in activation energies at the top of the lower mantle, and the Newtonian character of the mantle. The results show that the variations in Fp elasticity due to the iron spin transition can explain the undulations in the mantle viscosity, such as the viscosity hill about 800 km above the core–mantle boundary (Mitrovica and Forte, 2004).
Section snippets
Theoretical models
The viscosity (η) of Fp was described as a thermally activated process, as a result of diffusion of atomic species (Saha et al., 2013), where is the Gibbs free energy of activation and is a function of stress. For a Newtonian fluid, is a constant and , where is the activation energy of the appropriate dynamical mechanism (Ellsworth et al., 1985). On the other hand, the effective viscosity of a power law fluid of order n is equivalent to the viscosity of a
Viscosity of ferropericlase
Fig. 1 shows the adiabatic bulk and shear moduli and the respective sound wave velocities of Fp along two geotherms. The spin transition causes strong softening in the bulk modulus, but minor effect in the shear modulus. These results are consistent with recent experimental data on the elasticity of ferropericlase (Marquardt et al., 2009). The figure shows that the softening is more noticeable in the adiabatic geotherm than in the superadiabatic one. This is because the depth regions in which
Implications for mantle dynamics
Implications of the undulated lower mantle viscosity profile exist for both, down- and up-wellings in the mantle. Three dimensional models show that a viscosity “hill” of one order of magnitude through 500–1000 km of lower mantle is sufficient to slow down the sinking speed of a slab, and that a viscosity peak of two orders of magnitude can completely stop the sinking (Morra et al., 2010). Analytical calculations demonstrate that the sinking velocity of a slab is only weakly dependent on its
Summary
In summary, we have demonstrated that changes in the elastic parameters due to iron spin transition of Fp can produce dramatic variations in the rheological properties of the material, as to cause a non-monotonic behavior with depth. Our results indicate that, at lower mantle conditions, the effect of the spin transition in Fp is to create viscosity undulations respect to the radial profile and also horizontal variations. High viscosity regions would trap sinking slabs favoring chemical mixing,
Acknowledgments
This research was partially supported by grants NSF/EAR 0635990, NSF/ITR 0428774, and NSF/DMR 0325218 (ITAMIT) and the geochemistry and geophysics programs of the National Science Foundation. Computations were performed at the Minnesota Supercomputing Institute and on the Big Red Cluster at Indiana University. JFJ acknowledges partial support from Brazilian agencies FAPESP (grant number 2009/14082-3) and CNPq (grant number 473307/2013-8). GM acknowledges Louisiana Board of Regents – Research
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