13. Bird, P., and J. Baumgardner (1981) Steady propagation of delamination events, J. Geophys. Res., 86, 4891-4903.

Abstract. Delamination of the lithospheric thermal boundary from overlying continental crust propagates laterally from the line of initiation, accelerating as the sinking slab of detached lithosphere grows longer. This propagation has been numerically modeled with steady state equations in a moving reference frame by matching an interior finite element solution to flexible boundary conditions which represent the mechanical and thermal response of the surroundings. The form of the solution depends on the shear coupling of intruding asthenosphere to the top of the sinking slab across a thin layer of crustal material. Without coupling, the tip of the intrusion cools and stiffens to form a wedge dividing the crust (cold mode). With coupling, the intrusion is forced to convect and remains ductile (hot mode). The cold mode can propagate at all velocities; the hot mode has a lower limiting velocity of 1-2 cm/year but offers less resistance at higher speeds. Resistance to delamination includes a constant term from the buoyant crustal downwarp, plus a velocity-proportional term representing viscous deformation. However, the proportionality constant of the latter term is only weakly dependent on crust and lithosphere viscosities. Matching this resistance to loading lines of 100- to 800-km stabs sinking in a mantle of 1022 P, velocities of 0.3-8.0 cm/year are obtained. Changes in viscosity affect this rate, but cold mode delamination is unstoppable except at continental margins or by failure in the sinking slab. The surface expression of delamination is a leading "outer rise" followed by a submarine trough with a large negative free-air anomaly, which finally evolves into a 1-km plateau. If crustal viscosity and velocity are both low, however, there is a monontonic crustal uplift with no trough. Thus the present lack of linear supracontinental oceans does not preclude delamination at up to 4 cm/year driven by slabs up to 400 km in length.

P.S. Poise is not an SI unit. Convert 1022 P = 1021 Pa s. For a possible example of finite-amplitude delamination in progress underneath Morocco, see Fadil et al. [2006, Geology, 34(7)] P. Bird, 2008.08.21

Interesting quotation: "It is embarrassingly difficult to construct a model from these results in which delamination stops! If hot-mode delamination were to encounter local high viscosities which slowed it to less than 3 cm/year, it would cause cooling and stiffening of the intrusion. But delamination could probably continue in the cold mode. Apparently, there is always a cold mode solution with a finite velocity for any slab length over 200 km. However, in some solutions virtually all of the excess slab mass is hanging from the surface, and this could cause the slab to fail near the top, stopping the process. This instability cannot be predicted without a better knowledge of the rheology of the lithosphere. The only definite limit to delamination that is now apparent is that it could not cross oceanic regions of very thin crust with virtually infinite viscosity.