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Lithospheric Behaviour in Global Mantle Convection Models and its Influence on Mantle Structure and Evolution in Terrestrial Planets
P. J. Tackley, H. van Heck, F. Crameri, T. Nakagawa, M. Armann, T. Keller, T. V. Gerya, B. J. P. Kaus Institute of Geophysics, Department of Earth Sciences, ETH Zürich, Switzerland
Understanding plate tectonics remains one of the major challenges in solid Earth geoscience. Mantle convection models with strongly temperature‐dependent viscosity develop a stagnant lid, which is realistic for Venus and Mars but not for Earth. In such models, plate motion has often been imposed by hand. However, it has been found that including plastic failure using constant or depth‐dependent yield stress self‐consistently breaks the stagnant lid, giving a first‐order approximation of plate tectonics at low yield stress, episodic plate tectonics at intermediate yield stress, and a stagnant lid at high yield stress (e.g., [Tackley, 2000; van Heck and Tackley, 2008]). In this approach, the yield stress is a gross parameterisation of small‐scale processes that are not resolved, and this leads to some unrealistic features such as double‐sided subduction and a value of the effective yield strength of ~100 MPa that is much lower than laboratory experiments would suggest. Nevertheless this has proven to be an useful approach, and we here present a systematic numerical study of convection with strongly temperature‐dependent, visco‐plastic rheology and mixed heating (internal + basal), from which are derived systematic scaling laws that allow prediction of tectonic mode as a function of governing parameters Ra, yield stress and internal heating rate, which can be used in modelling the evolution of planets.
All such models to date use a free‐slip top boundary condition, in which the shear stress is zero but the surface is forced to be flat, which is unrealistic for subduction zones. Recent models with a free surface display dramatically different and more Earth‐like behaviour, with single‐sided rather than double‐sided subduction, and more time‐dependent behaviour. Another dynamically important feature is a weak crustal layer, which can decouple the subducting slab from the overlying plate [Gerya et al., 2008]. We present numerical experiments that characterise the tectonic behaviour of the system as a function of various governing parameters.
Figure 1. Comparison of convection with self‐consistent plate tectonics with (left) a free slip upper boundary, with which double‐sided subduction develops, and (right) a free surface, with single‐sided subduction.
This approach to lithospheric deformation is being used in global mantle convection models of the evolution of Earth, Venus and Mars. These models include melting that leads to crustal production, the major phase transitions in the olivine and pyroxene‐
garnet systems, and a core that cools time according to a parameterised model. Our Earth models (with plate tectonics) show the importance of crustal recycling in generating mantle heterogeneity, including dynamically‐induced layering around 660 km depth and above the CMB, which strongly influences the evolution of the core [Nakagawa et al., 2009; Nakagawa and Tackley, 2005]. Our Mars models (with a stagnant lid) develop a crustal dichotomy in a few 100 million years due to a long wavelength ‘one ridge’ upwelling, demonstrating that internal processes could account for this first‐order feature [Keller and Tackley, 2009]. Our Venus models with a stagnant lid indicate magmatism as the dominant heat transport mechanism, which unfortunately does not match observations of a uniform ~500 Ma surface age on Venus, while similar models with episodic plate tectonics can match this observation. Matching the geoid constrains the value of mantle viscosity. Hence, lithospheric tectonics plays a dominant role in determining the evolution of a planet’s interior.
Figure 2. Thermo‐chemical evolution models for Mercury (temperature isosurface and cross‐section), Venus (top:composition and bottom:temperature), Earth (top:temperature isosurfaces with cold slabs in blue and hot plumes in red; bottom:the location of subducted crust) and Mars (top: temperature, showing one ridge convection and bottom: crustal thickness).
References
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van Heck, H. and P. J. Tackley (2008) Planforms of self‐consistently generated plate tectonics in 3‐D spherical geometry, Geophys. Res. Lett. 35, L19312, doi:10.1029/2008GL035190
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