ALBERT

Description: Models incorporating plate-like behavior, i.e., near uniform surface velocity and deformation concentrated at plate boundaries, into a convective system, heated by a mix of internal and basal heating and allowing for temperature dependent viscosity, were constructed and compared to similar models not possessing plate-like behavior. The simplified numerical models are used to explore how plate-like behavior in a convective system can effect the lower boundary layer from which thermal plumes form. A principal conclusion is that plate-like behavior can significantly increase the temperature drop across the lower thermal boundary layer. This temperature drop affects the morphology of plumes by determining the viscosity drop across the boundary layer. Model results suggest that plumes on planets possessing plate-like behavior, e.g., the Earth, may differ in morphologic type from plumes on planets not possessing plate-like behavior, e.g., Venus and Mars.

Description: The thermal state of the Earth at the time relevant to formation of a magma ocean was dominated by the great impact that created the Moon. As shown in computer experiments, the iron in the impacting bodies quickly sank to the core of the proto-Earth, while a significant fraction of silicates was pushed far enough out beyond the geosynchronous limit to constitute the main material of the Moon. Most of any atmosphere would have been pushed aside, rather than being expelled in the impact. However, the energy remaining in the material not going to the core or expelled was still sufficient to raise its temperature some 1000's of degrees, enough to vaporize silicates and to generate a strong 'planetary wind': a hydrodynamic expansion carrying with it virtually all volatiles plus appreciable silicates. This expansion was violent and uneven in its most energetic stage, but probably the resulting magma ocean was global. The duration, until cooling, was sufficient for silicates to condense to melt and the duration was probably short. Comparison of the Earth and Venus indicates that the great impact was extraordinarily effective in removing volatiles from the proto-Earth; in particular, the enormous differences in primordial inert gases between the planets demand a catastrophic difference in origin circumstances. On the other hand, the comparison limits the amount of silicates lost by the Earth to a rather minor fraction; most of that expelled in the wind must have condensed soon enough for the silicate to fall back to Earth or be swept up by the proto-Moon. So the Earth was left with a magma ocean. The question is whether sufficient water was retained to constitute a steam atmosphere. Probably not, but unknowns affecting this question are the efficiencies of outgassing in great impacts and in subsequent convective churnings deep in the mantle. During the stage when mantle convection is turbulent, an appreciable fraction of volatiles were also retained at depth, perhaps in some mineral phases not yet well-defined. We still have primordial helium being outgassed.

Description: The main interaction of the earth's interior with the lithosphere is as a material source and sink. An absolute reference frame defined by minimizing the translational motion of tectonic plate boundaries differs by 0.6 cm/year from a frame defined by hot spot traces and by 0.4 cm/year from the frame defined by the most plausible model of drag forces on the plates. The rms absolute translational velocities are about 2 cm/year for ocean-ocean plate boundaries and 1.5 cm/year for ocean-continent plate boundaries. The close agreement between the source and sink and the drag-dependent definitions suggests that the lithosphere, as a stress guide, to some extent controls the locations of its sources and sinks.

Description: The lunar laser-ranging system at McDonald Observatory, Texas, is currently attaining accuracies of plus or minus 15 cm, and plus or minus 3 cm appears feasible. Numerical error analyses containing 97 parameters (35 of them for error sources) indicate that the plus or minus 3 cm system would measure station motions to plus or minus 1 cm/year accuracy within a year for east-west motions and within about 3 years for north-south. Furthermore, the correlations of station motions with other parameters are low, so that it is unlikely that the estimate is too optimistic because of modeling inadequacies of the error analysis.

Description: The earth physics satellite systems error analysis program was applied to the problem of predicting the relative accuracy of station position determinations under varying orbital and observing geometries. The reference case consists of nine ground stations extending over 1500 km which lasers ranged to a LAGEOS satellite, with simultaneous Doppler tracking from a geosynchronous satellite for 16 days. Eleven variations from the reference case were tested. The results showed little sensitivity to whether the LAGEOS altitude is 3700 or 5690 km. More significant were the high inclination, and that LAGEOS was tracked by a geosynchronous satellite.

Description: Linking ocean tides to satellite orbits

Description: Space and astronomic methods applied to solid earth and ocean physics

Description: Effective numerical treatment of multicomponent viscous flow problems involving the advection of sharp interfaces between materials of differing physical properties requires correction techniques to prevent spurious diffusion and dispersion. We develop a particular algorithm, based on modern shock-capture techniques, employing a two-step nonlinear method. The first step involves the global application of a high-order upwind scheme to a hyperbolic advection equation used to model the distribution of distinct material components in a flow field. The second step is corrective and involves the application of a global filter designed to remove dispersion errors that result from the advection of discontinuities (e.g., material interfaces) by high-order, minimally dissipative schemes. The filter introduces no additional diffusion error. Nonuniform viscosity across a material interface is allowed for by the implementation of a compositionally weighted-inverse interface viscosity scheme. The combined method approaches the optimal accuracy of modern shock-capture techniques with a minimal increase in computational time and memory. A key advantage of this method is its simplicity to incorporate into preexisting codes be they finite difference, element, or volume of two or three dimensions.

Description: It is proposed that subducting tectonic plates can affect the nature of thermal mantle plumes by determining the temperature drop across a plume source layer. The temperature drop affects source layer stability and the morphology of plumes emitted from it. Numerical models are presented to demonstrate how introduction of platelike behavior in a convecting temperature dependent medium, driven by a combination of internal and basal heating, can increase the temperature drop across the lower boundary layer. The temperature drop increases dramatically following introduction of platelike behavior due to formation of a cold temperature inversion above the lower boundary layer. This thermal inversion, induced by deposition of upper boundary layer material to the system base, decays in time, but the temperature drop across the lower boundary layer always remains considerably higher than in models lacking platelike behavior. On the basis of model-inferred boundary layer temperature drops and previous studies of plume dynamics, we argue that generally accepted notions as to the nature of mantle plumes on Earth may hinge on the presence of plates. The implication for Mars and Venus, planets apparently lacking plate tectonics, is that mantle plumes of these planets may differ morphologically from those of Earth. A corollary model-based argument is that as a result of slab-induced thermal inversions above the core mantle boundary the lower most mantle may be subadiabatic, on average (in space and time), if major plate reorganization timescales are less than those acquired to diffuse newly deposited slab material.

Description: We present results from convection models allowing for self-lubrication of downflows. Models impose a line source of chemically light, low viscosity material at the top of a convecting layer of temperature-dependent viscosity material. Low viscosity surface material serves as an analog to hydrated sediment/crust and the high viscosity upper portion of the convecting layer as an analog to mantle lithosphere. Slow near surface motion in the convecting layer entrains low viscosity material into zones of downflow, which has a lubricating effect. Once entrained lubricant is deeper than the cold high viscosity portion of the convecting layer, rapid upper boundary layer overturn occurs and system properties change (e.g., heat flux doubles). This marks transition to a lubricated state. Before and after transition, transport properties are dominantly determined by, respectively, the viscosity of mantle lithosphere and that of interior mantle. Lubricated and nonlubricated states appear as distinct regions in system output space suggesting that exchange between them is akin to a phase transition. That such exchange depends on a near surface lubricant implies that the geodynamics of planets lacking such lubricants may fundamentally differ from that of planets possessing them.