Global isostatic geoid anomalies for plate and boundary layer models of the lithosphere

Commonly used one dimensional geoid models predict that the isostatic geoid anomaly over old ocean basins for the boundary layer thermal model of the lithosphere is a factor of two greater than that for the plate model. Calculations presented, using the spherical analogues of the plate and boundary layer thermal models, show that for the actual global distribution of plate ages, one dimensional models are not accurate and a spherical, fully three dimensional treatment is necessary. The maximum difference in geoid heights predicted for the two models is only about two meters. The thermal structure of old lithosphere is unlikely to be resolvable using global geoid anomalies. Stripping the effects of plate aging and a hypothetical uniform, 35 km, isostatically-compensated continental crust from the observed geoid emphasizes that the largest-amplitude geoid anomaly is the geoid low of almost 120 m over West Antarctica, a factor of two greater than the low of 60 m over Ceylon

Interseismic strain accumulation: Spin-up, cycle invariance, and irregular rupture sequences

Using models of infinite length strike-slip faults in an elastic layer above linear viscoelastic regions, we investigate interseismic deformation. In the models we investigate, interseismic strain accumulation on mature faults is the result of the cumulative effects of all previous ruptures and is independent of the fault loading conditions. The time for a fault to spin-up to a mature state depends on the rheologies and the fault loading conditions. After the model has spun-up, the temporal variation of shear stresses is determined by the fault slip rate and model rheologies. The change in stress during spin-up depends on the slip rate, rheologies, and fault loading conditions but is independent of the magnitude of the initial stress. Over enough cycles such that the cumulative deformation is block-like, the average mature interseismic velocities are equal to the interseismic velocities of an elastic model with the same geometry and distribution of shear moduli. In a model that has spun-up with the fault rupturing periodically, the cumulative deformation is block-like at the end of each seismic cycle, and the interseismic deformation is cycle-invariant (i.e., the same in all cycles). When the fault ruptures nonperiodically, the fault spins up to a mature state that is the same as if the fault had ruptured periodically with the mean slip rate. When the fault slip rate within each cycle varies, the interseismic deformation evolves toward the cycle-invariant deformation determined by the most recent fault slip rate. Around a fault whose slip rate has been faster (slower) than average, interseismic velocities are larger (smaller) than the cycle-invariant velocities and increase (decrease) from cycle to cycle

The effects of rheological layering on post-seismic deformation

We examine the effects of rheological layering on post-seismic deformation using models of an elastic layer over a viscoelastic layer and a viscoelastic half-space. We extend a general linear viscoelastic theory we have previously proposed to models with two layers over a half-space, although we only consider univiscous Maxwell and biviscous Burgers rheologies. In layered viscoelastic models, there are multiple mechanical timescales of post-seismic deformation; however, not all of these timescales arise as distinct phases of post-seismic relaxation observed at the surface. The surface displacements in layered models with only univiscous, Maxwell viscoelastic rheologies always exhibit one exponential-like phase of relaxation. Layered models containing biviscous rheologies may produce multiple phases of relaxation, where the distinctness of the phases depends on the geometry and the contrast in strengths between the layers. Post-seismic displacements in models with biviscous rheologies can often be described by logarithmic functions

Small-scale convection beneath the transverse ranges, California: Implications for interpretation of gravity anomalies

Tomographic inversion of upper mantle P wave velocity heterogeneities beneath southern California shows two prominent features: an east-west trending curtain of high velocity material (up to 3% fast) in the upper 250 km beneath the Transverse Ranges and a region of low velocity material (up to 4% slow) in the 100 km beneath the Salton Trough. These seismic velocity anomalies were interpreted as due to small scale convection in the mantle. Using this hypothesis and assuming that temperature and density anomalies are linearly related to seismic velocity anomalies through standard coefficients of proportionality, leads to inferred variations of approx. + or - 300 C and approx. + or - 0.03 g/cc

Fundamental studies in geodynamics

Research in fundamental studies in geodynamics continued in a number of fields including seismic observations and analysis, synthesis of geochemical data, theoretical investigation of geoid anomalies, extensive numerical experiments in a number of geodynamical contexts, and a new field seismic volcanology. Summaries of work in progress or completed during this report period are given. Abstracts of publications submitted from work in progress during this report period are attached as an appendix

A critical assessment of viscous models of trench topography and corner flow

Stresses for Newtonian viscous flow in a simple geometry (e.g., corner flow, bending flow) are obtained in order to study the effect of imposed velocity boundary conditions. Stress for a delta function velocity boundary condition decays as 1/R(2); for a step function velocity, stress goes as 1/R; for a discontinuity in curvature, the stress singularity is logarithmic. For corner flow, which has a discontinuity of velocity at a certain point, the corresponding stress has a 1/R singularity. However, for a more realistic circular-slab model, the stress singularity becomes logarithmic. Thus the stress distribution is very sensitive to the boundary conditions, and in evaluating the applicability of viscous models of trench topography it is essential to use realistic geometries. Topography and seismicity data from northern Hoshu, Japan, were used to construct a finite element model, with flow assumed tangent to the top of the grid, for both Newtonian and non-Newtonian flow (power law 3 rheology). Normal stresses at the top of the grid are compared to the observed trench topography and gravity anomalies. There is poor agreement. Purely viscous models of subducting slables with specified velocity boundary conditions do not predict normal stress patterns compatible with observed topography and gravity. Elasticity and plasticity appear to be important for the subduction process

A dynamic model of Venus's gravity field

Unlike Earth, long wavelength gravity anomalies and topography correlate well on Venus. Venus's admittance curve from spherical harmonic degree 2 to 18 is inconsistent with either Airy or Pratt isostasy, but is consistent with dynamic support from mantle convection. A model using whole mantle flow and a high viscosity near surface layer overlying a constant viscosity mantle reproduces this admittance curve. On Earth, the effective viscosity deduced from geoid modeling increases by a factor of 300 from the asthenosphere to the lower mantle. These viscosity estimates may be biased by the neglect of lateral variations in mantle viscosity associated with hot plumes and cold subducted slabs. The different effective viscosity profiles for Earth and Venus may reflect their convective styles, with tectonism and mantle heat transport dominated by hot plumes on Venus and by subducted slabs on Earth. Convection at degree 2 appears much stronger on Earth than on Venus. A degree 2 convective structure may be unstable on Venus, but may have been stabilized on Earth by the insulating effects of the Pangean supercontinental assemblage

Thermal perturbations caused by large impacts and consequences for mantle convection

We examine the effects of thermal perturbations on a convecting layer of incompressible fluid with uniform viscosity in the limit of infinite Prandtl number, for two upper boundary conditions (free- and no-slip) and heat sources (100% volumetric heating and 100% bottom heating) in 2-D Cartesian finite element simulations. Small, low-temperature perturbations are swept into nearby downflows and have almost no effect on the ambient flow field. Large, high-temperature perturbations are rapidly buoyed and flattened, and spread along the layer\u27s upper boundary as a viscous gravity current. The spreading flow severs and displaces downwellings in its path, and also thins and stabilizes the upper thermal boundary layer (TBL), preventing new instabilities from growing until the spreading motion stops. A return flow driven by the spreading current displaces the roots of plumes toward the center of the spreading region and inhibits nascent plumes in the basal TBL. When spreading halts, the flow field is reorganized as convection reinitiates. We obtain an expression for the spreading time scale, ts, in terms of the Rayleigh number and a dimensionless perturbation temperature (Θ), as well as a size (Λ), and a condition that indicates when convection is slowed at a system-wide scale. We also describe a method for calculating the heat deposited by shock waves at the increased temperatures and pressures of terrestrial mantles, and supply estimates for projectile radii in the range 200 to 900 km and vertical incident velocities in the range 7 to 20 km s−1. We also consider potential applications of this work for understanding the history of early Mars

Relaxation of Surface Profiles by Evaporation Dynamics

We present simulations of the relaxation towards equilibrium of one dimensional steps and sinusoidal grooves imprinted on a surface below its roughening transition. We use a generalization of the hypercube stacking model of Forrest and Tang, that allows for temperature dependent next-nearest-neighbor interactions. For the step geometry the results at T=0 agree well with the t^(1/4) prediction of continuum theory for the spreading of the step. In the case of periodic profiles we modify the mobility for the tips of the profile and find the approximate solution of the resulting free boundary problem to be in reasonable agreement with the T=0 simulations.Comment: 6 pages, Revtex, 5 Postscript figures, to appear in PRB 15, October 199

Quantum lattice dynamical effects on the single-particle excitations in 1D Mott and Peierls insulators

As a generic model describing quasi-one-dimensional Mott and Peierls insulators, we investigate the Holstein-Hubbard model for half-filled bands using numerical techniques. Combining Lanczos diagonalization with Chebyshev moment expansion we calculate exactly the photoemission and inverse photoemission spectra and use these to establish the phase diagram of the model. While polaronic features emerge only at strong electron-phonon couplings, pronounced phonon signatures, such as multi-quanta band states, can be found in the Mott insulating regime as well. In order to corroborate the Mott to Peierls transition scenario, we determine the spin and charge excitation gaps by a finite-size scaling analysis based on density-matrix renormalization group calculations.Comment: 5 pages, 5 figure