Buffett, Bruce A.
Ziegler, Leah
Constable, Cathy G.
Regeneration of the Earth's magnetic field by convection in the liquid core produces a broad spectrum of time variation. Relative palaeointensity measurements in marine sediments provide a detailed record over the past 2 Myr, but an explicit reconstruction of the underlying dynamics is not feasible. A more practical alternative is to construct a stochastic model from estimates of the virtual axial dipole moment. The deterministic part of the model (drift term) describes time-averaged behaviour, whereas the random part (diffusion term) characterizes complex interactions over convective timescales. We recover estimates of the drift and diffusion terms from the SINT2000 model of Valet et al. and the PADM2M model of Ziegler et al. The results are used in numerical solutions of the Fokker-Planck equation to predict statistical properties of the palaeomagnetic field, including the average rates of magnetic reversals and excursions. A physical interpretation of the stochastic model suggests that the timescale for adjustments in the axial dipole moment is set by the dipole decay time tau(d). We obtain tau(d) = 29 kyr from the stochastic models, which falls within the expected range for the Earth's core. We also predict the amplitude of convective fluctuations in the core, and establish a physical connection to the rates of magnetic reversals and excursions. Chrons lasting longer than 10 Myr are unlikely under present-day conditions. However, long chrons become more likely if the diffusion term is reduced by a factor of 2. Such a change is accomplished by reducing the velocity fluctuations in the core by a factor of root 2, which could be attributed to a shift in the spatial pattern of heat flux from the core or a reduction in the total core heat flow.
Upward fluid flow is often invoked to explain the occurrence of methane hydrate in ocean sediments, whereas one-dimensional compaction models predict downward flow relative to the seafloor. Explaining the presence of upward flow requires a more complete compaction model. We develop a two-dimensional model of compaction-driven flow to quantify the focusing of pore fluids by topography and fractures when sediments have anisotropic permeability. We use a bulk anisotropic permeability to capture the effects of lithologic layering when the grid spacing is too coarse to resolve individual layers. Even small slopes (10 degrees) in bedding planes produce upward fluid velocity, with focusing becoming more effective as slopes increase. Additionally, focusing causes high excess pore pressure to develop below topographic highs, promoting high-angle fracturing near the crest. Magnitudes of upward pore fluid velocity are much larger in fractured zones, particularly when the surrounding sediment matrix is anisotropic in permeability. Enhanced flow of methane-bearing fluids from depth provides a simple explanation for preferential accumulation of hydrate under topographic highs. Citation: Frederick, J. M., and B. A. Buffett (2011), Topography-and fracture-driven fluid focusing in layered ocean sediments, Geophys. Res. Lett., 38, L08614, doi:10.1029/2010GL046027.
Magnetic fields at the Earth's surface represent only a fraction of the field inside the core(1). The strength and structure of the internal field are poorly known(2-5), yet the details are important for our understanding of the geodynamo. Here I obtain an indirect estimate for the field strength from measurements of tidal dissipation. Tidally driven flow in the Earth's liquid core develops internal shear layers, which distort the internal magnetic field and generate electric currents. Ohmic losses damp the tidal motions and produce detectable signatures in the Earth's nutations. Previously reported evidence of anomalous dissipation in nutations(3,6) can be explained with a core-averaged field of 2.5 mT, eliminating the need for high fluid viscosity(6) or a stronger magnetic field at the inner-core boundary(3). Estimates for the internal field constrain the power required for the geodynamo(7,8).
Several recent studies have used palaeomagnetic estimates of the virtual axial dipole moment to construct a quantitative stochastic model for fluctuations and reversals in the Earth's dipole field. We investigate the physical significance of the terms in a standard stochastic (Langevin) model using output from a numerical geodynamo model. The first term, known as the drift term, characterizes the slow adjustment of the dipole field toward a time-averaged state. We find that the timescale for this slow adjustment is set by the magnetic decay time of dipole fluctuations. These fluctuations are typically be represented by the first few decay modes. The second term is often called the noise term because it characterizes the influence of short-period convective fluctuations in the core. We establish a connection between the noise term and the rms variation in magnetic induction. Applying these results to the palaeomagnetic field suggests that the rms variation in dipole generation exceeds the mean rate of generation. Such large fluctuations may be necessary to permit magnetic reversals. Palaeomagnetic estimates of the drift term favour a high electrical conductivity in the core. A lower bound on electrical conductivity is 0.6 x 10(6) Sm-1. Similarly, we establish an upper bound on turbulent magnetic diffusivity (0.8 m(2) s(-1)), although realistic estimates may be much less.
Dynamo simulations require sub-grid scale (SGS) models for the momentum and heat flux, the Lorentz force, and the magnetic induction. Previous large eddy simulations (LES) using the scale similarity model have represented many aspects of the SGS motion. However, discrepancies are observed due to interchanging the order of filtering operation and spatial differentiation. In this study, we implement a correction term for this commutation error specifically for the scale-similarity model. Furthermore, we implement a dynamic scheme to evaluate time-dependent coefficients for the SGS models. We perform dynamo simulations in a rotating plane layer with different spatial resolutions, and compare results for the time dependence of the large-scale magnetic field. Simulations are performed at two different Rayleigh numbers, using constant values for the other dimensionless numbers (Ekman, Prandtl, and magnetic Prandtl numbers). Both cases show that the dynamic LES can accurately represent the large-scale magnetic field, whereas the dynamo failed in the direct simulations without the SGS terms at the same spatial resolutions. We conclude that the dynamic versions of the SGS and commutation error correction are essential for successful dynamos on coarser grids.
Bending of the lithosphere at subduction zones generates stresses that contribute to the force balance on plates. We determine the net horizontal force on subducting plates by imposing a simple kinematic description of strain in the equations that govern the mechanical equilibrium of a thin viscous sheet. The magnitude of the force depends on the velocity, thickness, and curvature of the subducting plate. Using representative values for old oceanic lithosphere, we obtain an effective horizontal force that is nearly 40% of the buoyancy force due to slabs in the upper mantle.
Chemical interactions between the core and the mantle have been proposed as a mechanism to transfer O and Si to the core. Adding light elements to the top of the core creates a stratified layer, which grows by chemical diffusion into the underlying convecting region. We develop a physical model to describe the evolution of the layer and estimate physical properties to aid in its detection. The interface between the stratified layer and the convecting interior is defined by the onset of double diffusive instabilities. Oscillatory instabilities arise from the interplay of a stable compositional stratification and an unstable thermal stratification due to a superadiabatic heat flow at the core-mantle boundary. Double diffusive convection in the region of neutral stratification establishes the base of the layer and sets the rate of entrainment of excess light element into the interior of the core. Growth of the layer by diffusion is interrupted by nucleation of the inner core, which segregates light elements into the convecting part of the core. For calculations using O as the sole light element, we find that the base of the stratified layer retreats toward the core-mantle boundary as the radius of the inner core increases. Representative ( but uncertain) model parameters yield a present-day layer thickness of 60 to 70 km. We also calculate the anomaly in P wave velocity relative to the value for a well-mixed core. The velocity anomaly decreases almost linearly across the layer with a peak value of 2% at the core-mantle boundary. This anomaly should be large enough to detect in seismic observations, although the sign of the anomaly is opposite to estimates obtained in previous seismic studies. We suggest possible explanations for this discrepancy and speculate about the implications for the structure of the Earth's interior.
We consider a stochastic differential equation model for Earth's axial magnetic dipole field. Our goal is to estimate the model's parameters using diverse and independent data sources that had previously been treated separately, so that the model is a valid representation of an expanded paleomagnetic record on kyr to Myr timescales. We formulate the estimation problem within the Bayesian framework and define a feature-based posterior distribution that describes probabilities of model parameters given a set of features derived from the data. Numerically, we use Markov chain Monte Carlo (MCMC) to obtain a sample-based representation of the posterior distribution. The Bayesian problem formulation and its MCMC solution allow us to study the model's limitations and remaining posterior uncertainties. Another important aspect of our overall approach is that it reveals inconsistencies between model and data or within the various data sets. Identifying these shortcomings is a first and necessary step towards building more sophisticated models or towards resolving inconsistencies within the data. The stochastic model we derive represents selected aspects of the long-term behavior of the geomagnetic dipole field with limitations and errors that are well defined. We believe that such a model is useful (besides its limitations) for hypothesis testing and give a few examples of how the model can be used in this context.
Bending of lithospheric plates at subduction zones is thought to be an important source of dissipation for convection in the Earth's mantle. However, the influence of bending on plate motion is uncertain. Here we use a variational description of mantle convection to show that bending strongly affects the direction of plate motion. Subduction of slabs and subsidence of oceanic lithosphere with age provide the primary driving forces. Dissipation is partitioned between plate bending and various sources of friction at plate boundaries and in the interior of the mantle due to viscous flow. We determine the poles of rotation for the Pacific and Nazca plates by requiring the net work to be stationary with respect to small changes in the direction of motion. The best fit to the observed rotation poles is obtained with an effective lithospheric viscosity of 6 x 10(22) Pa s. Bending of the Pacific plate dissipates roughly 40% of the energy released by subduction through the upper mantle. (c) 2006 Elsevier B.V. All rights reserved.
Dissipation due to tidally driven flow in the Earth's liquid core is detected in observations of nutations. One source of dissipation is due to electromagnetic core-mantle coupling, but this mechanism requires a high electrical conductivity on the mantle side of the boundary and a strong radial magnetic field. An alternative mechanism is viable in the presence of fluid stratification at the top of the core. Stratification causes the fluid close to the core-mantle boundary to be trapped by the effects of topography. Further from the boundary the stratified fluid is swept past the mantle with the underlying tidal flow. Shear in the flow induces electric currents where the fluid is permeated with a radial magnetic field. The resulting dissipation is only weakly dependent on the electrical conductivity of the mantle and the required strength of the radial magnetic field can be lowered. For a representative calculation we explain the observed dissipation with a radial field of 0.5 mT and a mantle conductivity of 1000 S/m, provided the buoyancy frequency in the stratified layer is 0.09 s(-1). Such a strong stratification has recently been proposed on the basis of chemical interactions between the core and the mantle. Nutation observations support the presence of stratification to the extent that the resulting dissipation mechanism is more compatible with conventional estimates for the radial magnetic field and the mantle conductivity. (C) 2010 Elsevier B.V. All rights reserved.
The effects of gravitational coupling between the inner core and the mantle are incorporated into numerical simulations of the geodynamo. Differential rotation between the inner core and the mantle is permitted by allowing the inner core to viscously deform. Calculations with a deformation time scale of 1 yr, corresponding to an average viscosity of 5times10 16 Pa s, predict eastward rotation of the inner core with a mean rate of 0.02 deg/yr relative to the mantle. Fluctuations about this mean rate of rotation occur with a typical period of 75 yr and have sufficient amplitude to explain observed changes in length of day at decadal periods. When gravitational coupling is removed, or viscous coupling is added by imposing no-slip boundary conditions the mean inner core rotation rate is almost an order of magnitude greater
Seismological observations suggest the inner core has been rotating faster than the mantle during the past 30-50 years. Differential rotation can produce large gravitational torques on the mantle which, if not balanced by other torques, would be detectable as changes in the rotation;rate of the mantle (Length of Day or LOD). We compare seismological estimates of inner core rotation with estimates derived by inverting LOD observations using models of gravitational coupling. Model predictions depend on several parameters, but for the expected range of parameter values, the seismological estimates of relative rotation are at least an order of magnitude larger than those predicted by the LOD data. Furthermore, the LOD data predict oscillation in the angular alignment of the inner core and mantle during the past 30-50 years, while the seismological data seem to require a component of steady rotation. We show that steady rotation of the inner core implies a steady torque on the mantle. This torque is not accelerating the rotation rate of the mantle, so it must be opposed by another torque. The required torque is consistent with a frictional electromagnetic stress on the base of the mantle due to a westward flow at the top of the core.
Marine occurrences of gas hydrate are normally confined to the top few hundred meters of sediments along deep continental margins. The zone of stability for gas hydrate is limited in depth by increases in temperature below the seafloor. We use thermodynamic calculations to show that gas hydrate can exist in a metastable state below the usual base of the stability zone. We estimate that gas hydrate can be overheated by several degrees and that it may persist in this metastable state in the seafloor for as long as 10(6) years. Sudden decomposition of metastable hydrate should produce substantial pore pressure in the sediments, contributing to slope failure in locations where gas hydrate is found. Such a mechanism might help to explain why slumping appears to be more frequent than average during the interval around the last glacial maximum.