A mechanism is proposed to explain epeirogenic motions of craton interiors in terms of the response of the lithosphere to subduction. The effects of changes in sea level are distinguished from subsidence of the basement by analyzing the tilt of chronostratigraphic sequences in which the bounding horizons were deposited at approximately the same elevation with respect to sea level. As an example, the Late Cretaceous subsidence and Tertiary uplift of the western interior of North America is examined, and a maximum tilt amplitude of 3 km, with a horizontal deflection scale of approximately 1400 km, is inferred. The link between platform sedimentation and subduction is tested by using numerical models of mantle convection which mimic the subduction and by examining the horizontal scale of the deflections to the overlying lithosphere. It is found that this scale is relatively insensitive to the temperature contrast between the slab and the surrounding mantle, the flexural rigidity of the lithosphere, and even the physical process assumed to govern the subduction. The most important factor affecting the scale is the dip of the subduction zone, and shallower subduction angles (less than 45 ø) can produce horizontal deflections of the •,,aer of 1000 km or more. In contrast, the vertical scale of the deflection is sensitive to all the above parameters. Using these results, two subduction models are introduced which predict both the time and length scales of the North American tilt, and it is conjectured that the process may be responsible for other regions of platform subsidence where subducted

No abstract

We have carried out a comparison study for a set of benchmark problems which are relevant for convection in the Earth's mantle. The cases comprise steady isoviscous convection, variable viscosity convection and time-dependent convection with internal heating. We compare Nusselt numbers, velocity, temperature, heat-flow , topography and geoid data. Among the applied codes are finite-difference, finite-element and spectral methods. In a synthesis we give best estimates of the 'true' solutions and ranges of uncertainty. We recommend these data for the validation of convection codes in the future.

An approximate set of equations is derived for a compressible liquid of infinite Prandtl number. These are referred to as the anelastic-liquid equations. The approximation requires the product of absolute temperature and volume coefficient of thermal expansion to be small compared to one. A single parameter defined as the ratio of the depth of the convecting layer,d, to the temperature scale height of the liquid,HT, governs the importance of the non-Boussinesq effects of compressibility, viscous dissipation, variable adiabatic temperature gradients and non-hydrostatic pressure gradients. Whend/HT[Lt ] 1 the Boussinesq equations result, but whend/HTisO(1) the non-Boussinesq terms become important. Using a time-dependent numerical model, the anelastic-liquid equations are solved in two dimensions and a systematic investigation of compressible convection is presented in whichd/HTis varied from 0·1 to 1·5. Both marginal stability and finite-amplitude convection are studied. Ford/HT[les ] 1·0 the effect of density variations is primarily geometric; descending parcels of liquid contract and ascending parcels expand, resulting in an increase in vorticity with depth. Whend/HT> 1·0 the density stratification significantly stabilizes the lower regions of the marginal state solutions. At all values ofd/HT[ges ] 0·25, an adiabatic temperature gradient proportional to temperature has a noticeable stabilizing effect on the lower regions. Ford/HT[ges ] 0·5, marginal solutions are completely stabilized at the bottom of the layer and penetrative convection occurs for a finite range of supercritical Rayleigh numbers. In the finite-amplitude solutions adiabatic heating and cooling produces an isentropic central region. Viscous dissipation acts to redistribute buoyancy sources and intense frictional heating influences flow solutions locally in a time-dependent manner. The ratio of the total viscous heating in the convecting system, ϕ, to the heat flux across the upper surface,Fu, has an upper limit equal tod/HT. This limit is achieved at high Rayleigh numbers, when heating is entirely from below, and, for sufficiently large values ofd/HT, Φ/Fuis greater than 1·00.