A two-and-a-half-dimensional flexing-drip model of lithospheric instabilities and proto-subduction (with two-phase grain-damage)

Abstract

The emergence of plate tectonics on the early Earth likely first requires subduction to initiate motion and to harness the mantle's convective gravitational energy as a power source. Whether such proto-subduction initiated as lithospheric drips (Rayleigh-Taylor like instabilities), or was triggered by mantle plumes (or even bolide impacts) remains a mystery. To infer whether drip instabilities and intermittent downwellings are possible causes of subduction initiation, we have developed a relatively simple two-and-a-half-dimensional (2.5-D) model of lithospheric instabilities. We specifically use this model to examine whether such instabilities, coupled to shear-localizing mechanisms like two-phase grain damage, can lead to subduction-like features, as well as semi-permanent weak zones that can be reactivated later to make new plate boundaries. Our model couples the physics of drip instabilities of amplitude $h$ in a horizontal 2-D layer with 2-D viscous lithospheric flexure (bending and folding) of amplitude $w$. The flexure model is generalized from the Biot's classical 1-D thin-plate theory by accounting for all bending and twisting torques, as well as complex rheology. The drip and flexure models are coupled in that the drips act as a load on the bending lithosphere, while vertical flexure affects the heat transport and pressure gradients governing drip growth. The coupled model predicts least stable mode selection of drip and flexure instabilities, in some cases bimodal instabilities wherein one mode is oscillatory, thus predicting intermittent downwellings. With two-phase grain damage, drips localize into narrow features, often organizing into strings of drips, which induce lineated or arcuate weak zones suggestive of dormant and inheritable plate boundaries.