Effects of Thermodynamic Properties on Slab Evolution

We perform a series of numerical experiments to investigate the effects of thermodynamic properties on the geometrical evolution of subducting slabs. We calculate density (ρ), thermal expansivity (α), and heat capacity (c_p) of mantle mineral assemblages of a harzburgite composition over a range of pressure and temperature conditions applicable to the Earth's mantle, using the thermodynamic database of Stixrude and Lithgow-Bertelloni [2011] and the thermodynamic calculation code Perple_X [Connolly, 2009]. Following Nakagawa et al. [2009], we assume that thermal diffusivity (κ) follows a power-law relationship with density (κ=κ₀(ρ/ρ₀)³, where κ₀ and ρ₀ are reference diffusivity and density, respectively). The calculations show that ρ, α, and κ change significantly along mantle geotherms; the ranges of their values are 3300-5100 km/m³, 1.5-3.5 10^-5/K, and 3-17 W/m K, respectively. The change in c_p is small (< 5%). We incorporate the pressure and temperature (PT) dependence of these thermodynamic properties into a 2-D finite element code with compressible convection formulations under the truncated anelastic liquid approximation [Lee and King, 2009] and develop a dynamic subduction model with kinematic boundary conditions. In the model, we use a composite mantle rheology that accounts for both diffusion and dislocation creep with flow law parameterization of wet olivine [Hirth and Kohlstedt, 2003]. Following Billen and Hirth [2007] and Lee and King [2011], we adjust the flow law parameter values for the lower mantle to test the effects of viscosity contrast between the upper and lower mantle on slab evolution. We use a reference model with a constant ρ, κ α, and c_p, which is equivalent to using the incompressible extended Bousisnesq approximation. Preliminary results show that incorporating PT-dependent ρ enhances the vigor of the buoyancy driven flow compared to the reference model. Further, lithostatic pressure at a given depth is higher than in the reference model, affecting mantle viscosity. These effects alter the mantle convection pattern but do not alter the overall behavior of subducting slabs significantly. In contrast, incorporating PT-dependent α can have a strong effect on slab behavior; for example, for a given model parameterization, it leads to buckling of the slab in the lower mantle while the reference model shows no such buckling. Changing viscosity contrast at the transition zone can also cause a similar change in slab behavior. Incorporation of PT-dependent κ leads to a hotter lower mantle than that in the reference model on the time scale of billions of years due to greater conductive heat transfer in the lower mantle. The effect of PT-dependent c_p is small compared to that of ρ, κ and α. These preliminary results indicate that ρ, κ and α have a strong influence on the thermal structure of the mantle, and their combined effect on slab evolution appears as strong as the effect of rheology. We plan to further analyze and quantify the effects of ρ, κ and α on the slab behavior.