The influence of a density stratification and of an incompressibility modulus on the spectrum of core modes

The concept of a deformation of a simple, non-rotating, spherically symmetric earth model with a fluid outer core, although it is a highly artificial physical situation, provides a useful computational algorithm that allows one lo determine analytically modes of vibration without any Love-number theory. In particular, on these analytically determined modes, we impose regularity conditions at the centre and boundary conditions at the surface, as well as conditions of continuity at the inner-core-outer-core boundary and at the core-mantle boundary. They lead to an eigenvalue equation for the frequency of oscillation. The range of frequencies obtained in this way for different earth models gives an indication of the influence of compressibility and non-homogeneity on the spectrum of eigenfrequencies.     

Effect of the viscoelastic lithosphere on polar wander speed caused by the Late Pleistocene glacial cycles

Previous studies of the wander of the rotation pole associated with the Late Pleistocene glacial cycles indicate that the predicted polar wander speed is sensitive to the density jump at the 670 km discontinuity, the thickness of the elastic lithosphere, and the lower mantle viscosity. In particular, the M1 mode related to the density jump at 670 km depth has been shown to contribute a dominant portion of predicted polar wander speed for sufficiently small lower mantle viscosities. In this study, we examine the sensitivity of polar wander to variations in the viscosity of the viscoelastic lithosphere using simplified compressible Maxwell viscoelastic earth models. Model calculations for earth models with a viscoelastic lithosphere of finite viscosity indicate that the contribution of the M1 mode is similar to those associated with the density discontinuity at the core–mantle boundary (C0 mode) and the lithosphere (L0 mode). We speculate that this is due to the interaction between the M1 mode and the transient mode associated with the viscoelastic lithosphere, which reduces the magnitude of polar wander rates. Therefore, the M1 mode does not contribute a dominant portion of the predicted polar wander speed for earth models with a viscoelastic lithosphere of finite viscosity. In this case, predictions of polar wander speed as a function of lower mantle viscosity exhibit the qualitative form of an 'inverted parabola', as predicted for the J ˙₂ curve. We caution, however, that these results are obtained for simplified earth models, and the results for seismological earth models such as PREM may be complicated by the interaction between the M1 mode and the large set of transient modes.     

Electromagnetic core–mantle coupling—I. Explaining decadal changes in the length of day

Measured changes in the Earth's length of day on a decadal timescale are usually attributed to the exchange of angular momentum between the solid mantle and fluid core. One of several possible mechanisms for this exchange is electromagnetic coupling between the core and a weakly conducting mantle. This mechanism is included in recent numerical models of the geodynamo. The 'advective torque', associated with the mantle toroidal field produced by flux rearrangement at the core–mantle boundary (CMB), is likely to be an important part of the torque for matching variations in length of day. This can be calculated from a model of the fluid flow at the top of the outer core; however, results have generally shown little correspondence between the observed and calculated torques. There is a formal non-uniqueness in the determination of the flow from measurements of magnetic secular variation, and unfortunately the part of the flow contributing to the torque is precisely that which is not constrained by the data. Thus, the forward modelling approach is unlikely to be useful. Instead, we solve an inverse problem: assuming that mantle conductivity is concentrated in a thin layer at the CMB (perhaps D"), we seek flows that both explain the observed secular variation and generate the observed changes in length of day. We obtain flows that satisfy both constraints and are also almost steady and almost geostrophic, and therefore assert that electromagnetic coupling is capable of explaining the observed changes in length of day.     

Mantle convection with a brittle lithosphere: thoughts on the global tectonic styles of the Earth and Venus

Plates are an integral part of the convection system in the fluid mantle, but plate boundaries are the product of brittle faulting and plate motions are strongly influenced by the existence of such faults. The conditions for plate tectonics are studied by considering brittle behaviour, using Byerlee's law to limit the maximum stress in the lithosphere, in a mantle convection model with temperature-dependent viscosity.
When the yield stress is high, convection is confined below a thick, stagnant lithosphere. At low yield stress, brittle deformation mobilizes the lithosphere which becomes a part of the overall circulation; surface deformation occurs in localized regions close to upwellings and downwellings in the system. At intermediate levels of the yield stress, there is a cycling between these two states: thick lithosphere episodically mobilizes and collapses into the interior before reforming.
The mobile-lid regime resembles convection of a fluid with temperature-dependent viscosity and the boundary-layer scalings are found to be analogous. This regime has a well defined Nusselt number–Rayleigh number relationship which is in good agreement with scaling theory. The surface velocity is nearly independent of the yield stress, indicating that the 'plate' motion is resisted by viscous stresses in the mantle.
Analysis suggests that mobilization of the Earth's lithosphere can occur if the friction coefficient in the lithosphere is less than 0.03–0.13—lower than laboratory values but consistent with seismic field studies. On Venus, the friction coefficient may be high as a result of the dry conditions, and brittle mobilization of the lithosphere would then be episodic and catastrophic.     

Mantle convection under simulated plates: effects of heating modes and ridge and trench migration, and implications for the core—mantle boundary, bathymetry, the geoid and Benioff zones

Summary. Numerical convection models are presented in which plates are simulated by imposing piecewise constant horizontal velocities on the upper boundary. A 4 × 1 box of constant viscosity fluid and two-dimensional (2-D) flow is assumed. Four heating modes are compared: the four combinations of internal or bottom heating and prescribed bottom temperature or heat flux. The case with internal heating and an isothermal base is relevant to lower mantle or whole mantle convection, and it yields a lower thermal boundary layer which is laterally variable and can be locally reversed, corresponding to heat flowing back into the core locally. When scaled to the whole mantle, the surface deflections and gravity and geoid perturbations calculated from the models are comparable to those observed at the Earth's surface. For models with migrating ridges and trenches, the flow structure lags well behind the changing surface 'plate'configurations. This may help to explain the poor correlation between the main geoid features and plate boundaries. Trench migration substantially affects the dip of the cool descending fluid because of induced horizontal shear in the vicinity of the trench. Such shear is small for whole mantle convection, but is large for upper mantle convection, and would probably result in the Tonga Benioff zone dipping to the SE, opposite to the observed dip, for the case of upper mantle convection.