Mantle convection and the state of the Earth's interior

During 1983 to 1986 emphasis in the study of mantle convection shifted away from fluid mechanical analysis of simple systems with uniform material properties and simple geometries, toward analysis of the effects of more complicated, presumably more realistic models. The important processes related to mantle convection are considered. The developments in seismology are discussed

Dynamic interpretation of geoid anomalies

The NASA Geodynamics program has as two of its missions precise determination of spatial variations in earth's geopotential (or geoid) and highly accurate monitoring of polar motion, including changes in the length of day (LOD). For the past several years, data sets provided by NASA, along with data and models from other areas of geophysic were used to place fundamental contraints on the large scale dynamics of earth and her sister planet Venus. The main approach was using fluid mechanical models of mantle flow to predict the long-wavelength variations in the geoid

Intraplate deformation, stress in the lithosphere and the driving mechanism for plate motions

During this period work was carried out on three fronts relevant to the understanding of intraplate deformation, stress in the lithosphere, and the driving mechanisms for plate motions: (1) observational constraints, using GPS geodesy on the deformation in the region of the boundry between the Pacific and North American plates in central and southern California; (2) numerical modeling of the effects of temperature dependent lithospheric viscosity on the stress and strain history of extensional regimes; and (3) improvement of estimates of mantle viscosity variation, the long-wave-length density variations in the mantle, and the topography of the core-mantel boundary from modeling of geoid anomalies, nutation, and changes in length of day. These projects are described in more detail, followed by a discussion of meetings attended and a list of abstracts and papers submitted and/or published

Driving forces: Slab subduction and mantle convection

Mantle convection is the mechanism ultimately responsible for most geological activity at Earth's surface. To zeroth order, the lithosphere is the cold outer thermal boundary layer of the convecting mantle. Subduction of cold dense lithosphere provides tha major source of negative buoyancy driving mantle convection and, hence, surface tectonics. There are, however, importnat differences between plate tectonics and the more familiar convecting systems observed in the laboratory. Most important, the temperature dependence of the effective viscosity of mantle rocks makes the thermal boundary layer mechanically strong, leading to nearly rigid plates. This strength stabilizes the cold boundary layer against small amplitude perturbations and allows it to store substantial gravitational potential energy. Paradoxically, through going faults at subduction zones make the lithosphere there locally weak, allowing rapid convergence, unlike what is observed in laboratory experiments using fluids with temperature dependent viscosities. This bimodal strength distribution of the lithosphere distinguishes plate tectonics from simple convection experiments. In addition, Earth has a buoyant, relatively weak layer (the crust) occupying the upper part of the thermal boundary layer. Phase changes lead to extra sources of heat and bouyancy. These phenomena lead to observed richness of behavior of the plate tectonic style of mantle convection

Geoid, topography, and convection-driven crustal deformation on Venus

High-resolution Magellan images and altimetry of Venus reveal a wide range of styles and scales of surface deformation that cannot readily be explained within the classical terrestrial plate tectonic paradigm. The high correlation of long-wavelength topography and gravity and the large apparent depths of compensation suggest that Venus lacks an upper-mantle low-viscosity zone. A key difference between Earth and Venus may be the degree of coupling between the convecting mantle and the overlying lithosphere. Mantle flow should then have recognizable signatures in the relationships between surface topography, crustal deformation, and the observed gravity field

Earth rotation and core topography

The NASA Geodynamics program has as one of its missions highly accurate monitoring of polar motion, including changes in length of day (LOD). These observations place fundamental constraints on processes occurring in the atmosphere, in the mantle, and in the core of the planet. Short-timescale (t less than or approx 1 yr) variations in LOD are mainly the result of interaction between the atmosphere and the solid earth, while variations in LOD on decade timescales result from the exchange of angular momentum between the mantle and the fluid core. One mechanism for this exchange of angular momentum is through topographic coupling between pressure variations associated with flow in the core interacting with topography at the core-mantel boundary (CMB). Work done under another NASA grant addressing the origin of long-wavelength geoid anomalies as well as evidence from seismology, resulted in several models of CMB topography. The purpose of work supported by NAG5-819 was to study further the problem of CMB topography, using geodesy, fluid mechanics, geomagnetics, and seismology. This is a final report

Mantle convection with strong subduction zones

Because mantle viscosity is temperature‐dependent, cold subducting lithosphere should be strong, which implies that the rapid, localized deformation associated with subduction should strongly resist plate motions. Due to computational constraints, the deformation of a subducting plate cannot be accurately resolved in mantle‐scale convection models, so its effect on convection is difficult to investigate. We have developed a new method for implementing subduction that parametrizes the deformation of the oceanic lithosphere within a small region of a finite element grid. By imposing velocity boundary conditions in the vicinity of the subduction zone, we enforce a geometry for subduction, producing a slab with a realistic thermal structure. To make the model dynamically consistent, we specify a rate for subduction that balances the energy budget for convection, which includes an expression for the energy needed to deform the oceanic lithosphere as it subducts. This expression is determined here from a local model of bending for a strong viscous lithosphere. By implementing subduction in this way, we have demonstrated convection with plates and slabs that resemble those observed on Earth, but in which up to 40 per cent of the mantle's total convective resistance is associated with deformation occurring within the subduction zone. This additional resistance slows plate velocities by nearly a factor of two compared to models with a weak slab. For sufficiently strong lithosphere, the bending deformation slows surface plates sufficiently that they no longer actively participate in global‐scale convection, which occurs instead beneath a ‘sluggish lid’. By introducing a low‐viscosity asthenosphere beneath the oceanic plate, we demonstrate that small‐scale convection at the base of oceanic lithosphere may limit plate thickness, and thus the resistance to bending, and cause plate velocities to depend on the strength of the bending lithosphere rather than on the viscosity of the underlying mantle. For a cooling Earth, the effective lithosphere viscosity should be nearly constant, but the mantle viscosity should increase with time. Thus, subduction‐resisted convection should produce nearly constant plate velocities and heat flow over time, which has implications for the Earth's thermal evolution. We estimate that this style of convection should apply if the effective viscosity of the bending lithosphere is greater than about 10^(23) Pa s, but only if some mechanism, such as small‐scale convection, prevents the bending resistance from stopping plates altogether. Such a mechanism could be fundamental to plate tectonics and Earth's thermal history

The Singularity Mystery Associated with a Radially Continuous Maxwell Viscoelastic Structure

The singularity problem associated with a radially continuous Maxwell viscoclastic structure is investigated. A special tool called the isolation function is developed. Results calculated using the isolation function show that the discrete model assumption is no longer valid when the viscoelastic parameter becomes a continuous function of radius. Continuous variations in the upper mantle viscoelastic parameter are especially powerful in destroying the mode-like structures. The contribution to the load Love numbers of the singularities is sensitive to the convexity of the viscoelastic parameter models. The difference between the vertical response and the horizontal response found in layered viscoelastic parameter models remains with continuous models

Degree one loading by pressure variations at the CMB

Hemispherical asymmetry in core dynamics induces degree-1 pressure variations at the core mantle boundary (CMB), which in turn deforms the overlaying elastic mantle, at the same time keeps center of mass of the whole Earth stationary in space. We develop a systematic procedure to deal with the degree-1 CMB pressure loading. We find by direct calculation a surprisingly negative load Love number h[subscript 1]=−1.425 for vertical displacement. Further analysis indicates that the negative h[subscript 1] corresponds to thickening above the positive load that defies intuition that pressure inflation pushes overlaying material up and thins the enveloping shell. We also redefine the pressure load Love numbers in general to enable comparison between the surface mass load and the CMB pressure load for the whole spectrum of harmonic degrees. We find that the gravitational perturbations from the two kinds of loads at degrees n>1 are very similar in amplitude but opposite in sign. In particular, if the CMB pressure variation at degree 2 is at the level of ∼1 hpa/yr (1 cm water height per year), it would perturb the variation of Earth’s oblateness, known as the J[subscript 2], at the observed level.United States. National Aeronautics and Space Administration (No. NNX09AK 70G

The Elastic Response of the Earth to Interannual Variations in Antarctic Precipitation

Measurements of elastic displacements of the bedrock surrounding large ice sheets have been proposed as a means to detect mass changes in these ice sheets. However, accumulation of glacial mass on the ice sheets is a noisy process, subject to large spatial and temporal variations in precipitation. We simulated the response of the Antarctic continent to a stochastic model of interannual precipitation variations and found that interannual variations in the elastic response of the earth are large when compared to the long-term mean of displacements produced by an assumed average ice mass imbalance of 10%. If, as some scientists predict, Antarctic ice mass changes in the future become dramatic, the long-term signal should be large enough to be detected by a few years of geodetic measurements, despite climatic noise