Surface effects of Rayleigh-Taylor instability: Feedback between drip dynamics and crustal deformation

For many continental plates, significant vertical motion of Earth's surface has occurred within the plate interior which can not be clearly linked to plate tectonic processes. For example, several craton areas exhibit anomalous basins, e.g., the Williston basin, Illinois basin and Michigan basin in North America. In orogenic belts, there are examples of local areas (~100 km wide) where the surface has undergone subsidence and then uplift of >1 km, such as the Arizaro basin (central Andes) and Wallowa Mountains (northeast Oregon). Given the near-circular shape of the surface deflection, it has been suggested that they may be related to gravitational foundering of dense lower lithosphere, i.e., Rayleigh-Taylor instability (or 'RT drip'). In order to investigate the surface effects of an RT drip, we use two methods: (1) 2D thermal-mechanical numerical models to study links between drip dynamics and crustal deformation and (2) a theoretical analysis of the crustal deformation induced by stresses from the RT drip. The numerical models consist of a continental lithosphere overlying a sublithospheric mantle. A high-density material is placed in the mantle lithosphere or lower crust to initiate a drip event, and a stress-free boundary condition allows the development of surface topography during model evolution. A reasonable range of crustal viscosity and thickness is tested to study the RT drip in different tectonic settings, from a cold craton to a hot orogen with thick crust. Four types of surface deflection are observed: (1) subsidence; (2) subsidence followed by uplift; (3) uplift; and (4) little deflection. When the crust is relatively strong or thin, the surface has a negative elevation, forming a basin. For a weak or thick crust, the RT drip induces crustal flow, leading to crustal thickening that can uplift the surface; an extremely weak crust decouples the surface and RT drip and the surface is unperturbed. Our theoretical analysis considers the surface deflection as a superposition of the RT drip dynamics and crustal channel flow induced by both shearing by the drip (Couette flow) and the lateral pressure gradient due to the high-density body (Poiseuille flow). We compute the crustal flux associated with these processes and show that the type of surface expression depends on the crustal flux rate, whereas magnitude of surface deflection depend on the density of the foundering body. For a Newtonian crust, the crustal flux scales linearly with crustal viscosity and by the cube of the thickness of the crustal channel. Thus, induced crustal flow is largest for regions with a hot, thick crust. Our results indicate that the presence and/or gravitational removal of a dense lithospheric body can produce a range of surface expressions. Basins may be prevalent in craton areas, and surface uplift or little deflection may be more common along orogenic belts.