Characteristic Size of Tectonic Plates: Insights from Boundary Layer Theory with Grain-damage

Abstract:

The dominant degree-2 pattern of mantle convection is a commonly inferred feature from seismological observations (Dziewonski et al., 2010). This pattern is likely associated with large-scale structures like hotspot super-swells and Pacific subduction-zones. The mechanism that dictates this long-wavelength structure is currently a subject of debate. Interestingly, mantle convection models featuring temperature- and depth-dependent viscosity and Earth-like convective vigor typically predict a shorter characteristic wavelength, reflected in the spatial distribution of upwelling plumes and downwellings (Zhong et al., 2000). Plate generating physics is an additional effect that possibly governs the long-wavelength convective pattern; i.e., tectonic plates constitute the top cold thermal boundary layer, subduction of which is the most efficient component of the mantles convective heat transport.

To address the effect of plate generation on convective wavelength, we combine a boundary-layer model of mantle convection (Turcotte & Oxburgh, 1967), with the grain-damage model of lithospheric shear-localization (Bercovici & Ricard, 2012). As shown by Solomatov (1995), the strongly temperature-dependent viscosity of Earth materials would render it in the stagnant lid regime of convection, much like what is observed on Venus. Grain-damage allows for self-weakening that remobilizes the lithosphere, making plate like flow possible. Such self-weakening necessarily has an effect on the length of the lithospheric boundary layer and hence convective wavelength. Our simple model thus infers a characteristic size of tectonic plates for a given convective vigor. Superposition of the long convective length-scale, dictated by the cold, stiff, yet damaged and deformable thermal boundary layer, onto the length-scale dictated by convective instability yields a range of material parameters for which the convective pattern is consistent with observations.