Can We Approximate Non-Newtonian Rheology to Model Mantle Convection?

Abstract:

The rheology is a key influencing factor in mantle convection as it is directly responsible for the convective vigor, therefore altering heat transport and the distribution of stresses. Deformation in terrestrial mantles is mainly accommodated by two mechanisms: diffusion and dislocation creep. While the former probably plays a dominant role at high pressures, the latter is thought to be important at relatively low pressures, as inferred by seismic anisotropy in the Earth’s upper mantle [1].

Dislocation creep is more challenging to handle than diffusion creep as the viscosity becomes strain-rate dependent, introducing a non-linearity that requires more computational resources. Thus, to avoid this additional complexity, a Newtonian rheology (i.e. diffusion creep) with reduced activation parameters is often used to mimic non-Newtonian behavior [2], causing misleading results if applied to certain scenarios.

We run thermal evolution models in 2D cylindrical geometry using the mantle convection code Gaia [3] for Mercury, the Moon and Mars. It has been argued that their mantles deform by pure dislocation creep but our simulations show that, when using a mixed rheology that accounts for both diffusion and dislocation creep, deformation in the mantles of Mercury, Moon and Mars is dominated by diffusion creep, while dislocation creep only occurs in small confined regions. Further, our results show a transition from a diffusion creep to a dislocation creep dominated mantle as the Rayleigh number increases and indicate that systems even with relatively high effective Rayleigh numbers (up to 5 x 10⁷) are dominated by diffusion creep. Terrestrial bodies like Mercury, the Moon or Mars can thus be correctly modeled using a Newtonian rheology. This may change for bodies like the Earth or Venus since the effective Rayleigh numbers are higher and thus either a mixture of both diffusion and dislocation or purely dislocation creep would define the deformation mechanism. Moreover, dislocation creep-dominated regions are significant at the beginning of the thermal evolution when the mantle is hot and thus the system characterized by vigorous convection. As the mantle cools with time, diffusion creep tends to take over.

[1] J. van Hunen et al., EPSL, 2005; [2] U. Christensen, Geophys. J. R. astr. Soc., 1984; [3] C. Hüttig et al., PEPI, 2013.