Stagnant-lid convection with diffusion and dislocation creep rheology: Influence of a non-evolving grain size

Abstract

SUMMARY Heat transfer in one-plate planets is governed by mantle convection beneath the stagnant lid. Newtonian diffusion creep and non-Newtonian dislocation creep are the main mechanisms controlling large-scale mantle deformation. Diffusion creep strongly depends on the grain size (d), which in turn controls the relative importance of the two mechanisms. However, dislocation creep is usually neglected in numerical models of convection in planetary mantles. These mostly assume linear diffusion creep rheologies, often based on reduced activation parameters (compared to experimental values) that are thought to mimic the effects of dislocation creep and, as a side benefit, also ease the convergence of linear solvers. Assuming Mars-like parameters, we investigated the influence of a non-evolving grain size on Rayleigh–Bénard convection in the stagnant lid regime. In contrast to previous studies based on the Frank–Kamentskii approximation, we used Arrhenius laws for diffusion and dislocation creep—including temperature as well as pressure dependence—based on experimental measurements of olivine deformation. For d ≲ 2.5 mm, convection is dominated by diffusion creep. We observed an approximately equal partitioning between the two mechanisms for d ≈ 5 mm, while dislocation creep dominates for d ≳ 8 mm. Independent estimates of an average grain size of few mm up to 1 cm or more for present-day Mars suggest thus that dislocation creep plays an important role and possibly dominates the deformation. Mimicking dislocation creep convection using an effective linear rheology with reduced activation parameters, as often done in simulations of convection and thermal evolution of Mars, has significant limitations. Although it is possible to mimic mean temperature, mean lid thickness and Nusselt number, there are important differences in the flow pattern, root mean square velocity, and lid shape. The latter in particular affects the amount and distribution of partial melt, suggesting that care should be taken upon predicting the evolution of crust production when using simplified rheologies. The heat transport efficiency expressed in terms of the Nusselt number as a function of the Rayleigh number is thought to depend on the deformation mechanisms at play. We show that the relative volume in which dislocation creep dominates has nearly no influence on the Nusselt–Rayleigh scaling relation when a mixed rheology is used. In contrast, the flow pattern influences the Nusselt number more strongly. We derived a scaling law for the Nusselt number based on the mean lid thickness (〈L〉) and on the effective Rayleigh number (Raeff) obtained by suitably averaging the viscosity beneath the stagnant lid. We found that the Nusselt number follows the scaling $\mathrm{Nu} = 0.37 \langle L \rangle ^{-0.666} \mathrm{Ra}_{\mathrm{eff}}^{0.071}$ regardless of the deformation mechanism.

The Thermo‐Chemical Evolution of Mars With a Strongly Stratified Mantle

“…The viscosity of the Martian mantle plays an important role, and is assumed to depend on temperature, T , hydrostatic pressure, P , and melt fraction ϕ following an Arrhenius relationship (Karato & Wu, 1993): where E * and V * are the effective activation energy and activation volume, R is the gas constant, and T ref and P ref are the reference temperature and pressure at which viscosity equals the reference viscosity, η 0 (in the absence of melt). The effective activation volume and energy can either directly account for viscous deformation in the diffusion creep regime, or mimic deformation in the dislocation creep regime (Kiefer & Li, 2016; Plesa et al., 2015; Samuel et al., 2019; Schulz et al., 2020; Thiriet, Michaut, et al., 2018). In the first case, E * and V * correspond to the intrinsic values.…”

Effects of Composite Rheology on Plate‐Like Behavior in Global‐Scale Mantle Convection

“…In some stagnant‐lid models, we increased the static grain‐size, which produced an increase in mantle average viscosity, stress, and proportion of dislocation creep in the uppermost mantle (Figure S6 in Supporting Information ), associated with lithospheric thickening, as already described in Schulz et al. (2020). This test, applied to models without dynamic grain‐growth and reduction, reveals the competing effects of large grain‐size (which tends to increase mantle viscosity) and large amounts of dislocation creep (which tend to decrease it) on lithosphere thickness, at least up to a doubling of static grain‐size with our setup (Figure S6 in Supporting Information ).…”

“…Although the convective regime remains unchanged in these models, changing the amount of dislocation creep can strongly decrease the viscosity in the asthenosphere and decrease lithospheric thickness by up to 60%. These effects could have a large impact on the distribution of partial melting and the rates of magmatism on stagnant‐lid planets (e.g., Schulz et al., 2020; Tosi & Padovan, 2021). However, these models also suggest that once a stagnant‐lid is established with a pure diffusion creep rheology, adding composite rheology in the upper‐mantle does not promote the generation of more plate‐like behavior.…”

Small‐Scale Overturn of High‐Ti Cumulates Promoted by the Long Lifetime of the Lunar Magma Ocean

“…We thus keep them constant, and focus on the role of the rheology. As in Yu et al (2019), we vary the value of the activation energy (E*) using either 335 kJ/mol (the value for diffusion creep previously adopted), or 150 kJ/mol, a decreased value aimed at mimicking the effect of dislocation creep (see e.g., Schulz et al (2020)).…”