Rayleigh-Taylor instability of the upper mantle and its role in intraplate orogeny

Abstract

We explore the possibility that intraplate orogeny is the result of gravitational instability of the mantle lithosphere beneath the orogenic zone. We use a two‐layered system overlying a half‐space to represent a low‐density crust overlying a high‐density lithospheric mantle overlying a reference density asthenosphere. A small harmonic perturbation is then imposed on the base of the high‐density layer and the system is allowed to flow under the gravitational instability described by the Rayleigh–Taylor instability. Viscosity and density are uniform within the layers and Newtonian rheology is assumed. We investigate the ability of the downwelling, high‐density, lithospheric layer to thicken the low‐density crustal layer above the downwelling. We solve the system using two methods: a numerical solution to the full set of 2‐D viscous flow equations and a linearized approximation of the early growth of the instability, valid for small deflections. For typical physical parameters, our results show that the ratio of downward displacement at the Moho to that at the base of the lithosphere is ∼6 per cent provided that the crust is weaker than the lithosphere. Our results show that a buoyant crustal layer overlying the higher‐density lithospheric layer may be thickened and uplifted over a lithospheric downwelling, achieving a maximum crustal thickening factor of ∼1.4 (for typical lithospheric parameters). This is enough to thicken a 35 km crust to 50 km and produce a significant intraplate mountain range. We find that thick, buoyant continental crust causes the instability to occur at a lateral wavelength of order 300 km regardless of whether a stress‐free or rigid condition is used on the upper boundary. Thin, less buoyant crust, however, allows the instability to occur at much longer wavelengths. For a stress‐free upper boundary the surface deflection over the downwelling is upwards due to crustal convergence, unless the crust is very rigid (crustal viscosity >13 times mantle viscosity), in which case the surface deflection over the downwelling is down, creating a topographic depression. For detachment of the downwelling blob to occur within 30 Myr, without any external tectonic activity, an average lithospheric viscosity of ∼1021 Pa s is required. Once detachment of the downwelling mass has occurred the system responds to flow driven by a thickened crust. This causes the crust to flow back to its equilibrium position and a period of extension thus follows the period of compression. Such a cycle could conceivably be repeated if the thinned lithosphere is able to thermally equilibrate, cool and thicken again after extension.

Crustal deformation induced by mantle dynamics: insights from models of gravitational lithosphere removal

“…4d, cf. Neil & Houseman 1999). The initial isostatic subsidence and negative dynamic topography created by the downwelling mantle are counteracted by the crustal thickening.…”

“…Kusznir & Park 1984;Mazzotti & Hyndman 2002); and (2) stresses transmitted upwards from the dynamic mantle (e.g. McKenzie 1977;Neil & Houseman 1999). Mechanism (2) includes stresses originating from either the sublithospheric mantle or the mantle lithosphere.…”

“…In either case, the mantle-based stresses may result in deformation of the overlying crust and/or deflection of the Earth's surface (e.g. Morgan 1965;Neil & Houseman 1999;Buiter et al 2002;Pysklywec & Shahnas 2003;Burov & Guillou-Frottier 2005;Burov & Cloetingh 2009;Duretz et al 2012;Flament et al 2013). Within the sublithospheric mantle, downwelling (e.g.…”

“…A number of studies have used linear stability analysis to assess crustal deformation during gravitational removal, assuming either a single-layer viscous crust (e.g. Neil & Houseman 1999;Molnar & Houseman 2013) or one with an exponential decrease in viscosity with depth (Molnar & Houseman 2015). These studies demonstrate if the crust is relatively strong (>13-30 times more viscous than mantle), lithosphere removal is accompanied by surface subsidence.…”

“…Other studies have considered the time-dependent evolution of lithosphere removal below a single-layer crust with either a constant viscosity (e.g. Neil & Houseman 1999;Pysklywec & Shahnas 2003;Hoogenboom & Houseman 2006) or variable viscosity (e.g. Elkins-Tanton 2007;Gemmer & Houseman 2007;Gögüş & Pysklywec 2008), or a two-layer crust with a variable viscosity (e.g.…”