Influence of composite rheology on planetary dynamics

Rock-deformation laboratory experiments have shown that upper mantle flows with a combination of different creep mechanisms making its rheology composite (Karato & Wu, 1993; Hirth & Kohlstedt, 2003). At low stress levels in the cold and deep upper mantle, deformation occurs by diffusion creep where diffusive mass transport happens between grain boundaries. Whereas at relatively high stress levels in the hot regions of the uppermost mantle, deformation occurs by dislocation creep where crystalline dislocations move between grains. Although composite rheology has been considered in some recent global-scale geodynamical studies of rocky planets (e.g., Dannberg et al., 2017; Schierjott et al., 2020; Tian et al., 2023; Arnould et al., 2023), its influence on the thermo-compositional evolution and tectonic regime of early Earth remains unexplored.

In this study, the code StagYY (Tackley, 2008) is used to model the thermochemical evolution of solid Earth with three different rheological setups. In the first rheological setup, viscous deformation includes only diffusion creep. In the second setup, deformation is accommodated by a combination of diffusion creep and stress-dependent dislocation creep. In the third setup, a proxy for dislocation creep viscosity is used, which resembles temperature- and pressure-dependent Newtonian flow viscosity, where activation energy and activation volume relate to laboratory-estimated dislocation activation parameters divided by the stress exponent, representing dislocation creep with a constant strain rate. Such an approximation has been demonstrated to be a reasonable proxy of power-law viscosity in the classical modelling work by U. Christensen (1983, 1984).

These models self-consistently generate oceanic and continental crust, consider both plutonic and volcanic magmatism and incorporate pressure-, temperature-, and composition-dependent water solubility maps. Irrespective of the rheology considered, models exhibit mobile-lid regime with high mobility (ratio of rms surface velocity to rms velocity of mantle) with plume-induced lithospheric subduction for the initial 200-300 Myr. Afterwards, they transition to episodic-lid or ridge-only regime and are characterised by global resurfacing events. When compared to models with only diffusion creep rheology, models with composite rheology (either as stress dependent dislocation creep or dislocation creep proxy) have higher surface mobilities, experience resurfacings more frequently, produce more continental crust, and are more efficient at planetary cooling. These trends stay similar even in models that do not consider melting. In terms of code performance, computations with composite rheology take longer than just with diffusion creep. However, dislocation creep proxy models are faster than stress-dependent dislocation creep models by a factor of ~1.6x. In summary, a combination of diffusion and dislocation creep proxy is a viable formulation to realistically model long-term thermochemical planetary evolution with relatively low additional computational expense.