RAYLEIGH-TAYLOR INSTABILITY AND CONVECTIVE THINNING OF MECHANICALLY THICKENED LITHOSPHERE - EFFECTS OF NONLINEAR VISCOSITY DECREASING EXPONENTIALLY WITH DEPTH AND OF HORIZONTAL SHORTENING OF THE LAYER

Localized mechanical thickening of cold, dense lithosphere should enha nce its gravitational instability. Numerical experiments carried out w ith a layer in which viscosity decreases exponentially with depth, ove rlying either an inviscid or a viscous half-space, reveal exponential growth, as predicted by linear theory. As shown earlier for a layer wi th non-linear viscosity and with a constant theological parameter (Hou seman & Molnar 1997), a perturbation to the thickness of the layer gro ws super-exponentially; for exponential variation of the theological p arameter, the time dependence of growth obeys an equation of the form (Z/L)((1 - n) )= (n - 1)(C beta gL(2)/nB(0))(n )(T-b - t),( ) where Z is the magnitude of the perturbation to the thickness of the layer; L is the characteristic e-folding distance through the layer for the the ological parameter B, which is proportional to viscosity and reaches a minimum of B, at the base of the layer; n is the power relating stres s to strain rate; C (similar to 0.4, for the experiments considered he re) is an empirical constant that depends on wavelength; beta is the v ertical gradient in density (assumed to decrease linearly with depth i n the layer); g is the gravitational acceleration; t is the time; and t(b) is the time at which a blob of material drawn from the basal part of the layer drops away from the layer. A simple application of this scaling relationship to the Earth, ignoring the retarding effect of di ffusion of heat, suggests that somewhat more than half of the lithosph ere should be removed in a period of similar to 20 Myr after the thick ness of the layer has doubled. The imposition of horizontal shortening of the layer accelerates this process. In the presence of a constant background strain rate, growth will initially be exponential as the no n-Newtonian viscosity is governed by the background strain rate. Only after the perturbation has grown to several tens of per cent of the th ickness of the layer does growth become super-exponential and yet more rapid. An application of this scaling and its calibration by numerica l experiments presented here suggests that super-exponential growth is likely to begin when the perturbation approaches similar to 100 per c ent of the thickness of the layer, or roughly 100 km, when applied to the lithosphere. Thus, where the crust has doubled in thickness in a p eriod of 10-30 Myr, we anticipate that roughly half, or more, of the t hickened mantle lithosphere will be removed in a period of 10-20 Myr f ollowing the initiation of shortening.