Apparent polar wander of the mean-lithosphere reference frame

Apparent polar wander in the mean-lithosphere (= no-net-rotation = no-net-torque uniform drag) reference frame is compared with apparent polar wander in the hotspot reference frame over the past 100 Myr. Palaeo-magnetic poles and plate rotations previously used to determine an apparent polar wander path for the hotspot reference frame are here used to determine an apparent polar wander path in the mean-lithosphere reference frame. We find that the two paths are similar, especially for Late Cretaceous time, when a 10°–20° shift of the pole occurred. To first-order the hotspots and lithosphere (as a whole) moved in unison relative to the palaeomagnetic axis during Late Cretaceous time. A non-dipole field explanation for the apparent shift can probably be excluded. However, either motion of the time-averaged geomagnetic axis relative to the spin axis or polar wandering could have caused this shift, the latter being the more likely explanation.     

Implications of a non-adiabatic density gradient for the Earth's viscoelastic response to surface loading

The response of a viscoelastic Earth to the melting of the Late Pleistocene ice sheets has been the subject of a number of investigations employing PREM. In PREM, a non-adiabatic density gradient (NADG) exists in the upper mantle, and to understand the implications of this model it is thus important to examine the effects of this NADG on the Earth's response to surface loads. This paper is based on the assumption that the contribution to the depth dependence of the density that is not due to self-compression is due to compositional change. This contribution is referred to as 'non-adiabatic'. We evaluate the effects of a non-adiabatic density jump (NADJ) for the 670  km discontinuity and the NADG in the upper mantle by adopting a compressible earth model with both a compositional density gradient and a density jump. Numerical calculations based on these models indicate that the magnitude of the Earth's response associated with the NADG is much smaller than that associated with the NADJ at 670  km depth. It is also confirmed that the higher modes associated with the NADJ and the NADG are much more sensitive to the existence of an elastic lithosphere than the fundamental modes associated with the density jumps at the surface and core–mantle boundary.     

A new class of stratified viscoelastic models by analytical techniques

Multilayer, spherically stratified, self-gravitating relaxation models with a large number of layers (more than 100) can be dealt with analytically. Relaxation processes are studied for both Heaviside surface loads and tidal forcings. Simulations of the relaxation process of a realistic earth model with an incompressible Maxwell rheology show that models containing about 30 to 40 layers have reached continuum limits on all timescales and for all harmonic degrees up to at least 150 whenever an elastic lithosphere is present, irrespective of the viscosity profile in the mantle. In particular, fine-graded stratification of the shallow layers proves to be important for high harmonic degrees in these models. The models produce correct long-time (fluid) limits. It is shown that differences in the transient behaviour of the various models are due to the applied volume-averaging procedure of the rheological parameters. Our earlier proposed hypothesis that purported shortcomings in the fundamental physics of (discrete) normal-mode theory are artificial consequences of numerical inaccuracies, theoretical misinterpretations and the use of incomplete sets of normal modes is reinforced by the results presented. We show explicitly that the models produce both continuous behaviour resulting from continuous rheological stratifications and discrete behaviour resulting from sharp density contrasts, as at the outer surface and the core-mantle boundary. The differences between volume-averaged models and fixed-boundary contrast models are outlined. Reducing many-layer models with a volume-averaging procedure before employing a normal mode analysis is both economical and highly accurate on all timescales and for all spherical harmonic degrees. The procedure minimizes the chances of missing contributing modes, while using models with more layers will not result in any substantial increase of accuracy.     

A weighted least-squares fit of the Australian apparent polar wander path for the last 100 Myr

Summary. Recent versions of the Australian apparent polar wander path (APWP) for the late Mesozoic and Tertiary show considerable variation. Re-examination of the Australian igneous data suggests that they are more reliable than assumed by some recent authors. The trajectory of the Australian APWP is defined by fitting the position of a set of poles including both igneous and laterite/overprint data. This allows the dated igneous poles to be used to determine age as a function of distance along the trajectory. Both the trajectory and the age are fitted by means of weighted least-squares regression, and are given approximate confidence limits.
Age is best fitted in the Australian case as a linear function of distance along the APWP. This result contrasts with that of Idnurm, who suggested a variable rate of polar wander during the Tertiary. The new APWP is in better agreement with hot-spot data. Dating of New Caledonian laterites by the new APWP gives a result consistent with geological evidence, while dating by reference to Idnurm's path does not. Large non-dipole components or significant true polar wander are not needed to explain the Australian Tertiary APWP.     

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.     

Effect of 3-D viscoelastic structure on post-seismic relaxation from the 2004 M= 9.2 Sumatra earthquake

The 2004 M = 9.2 Sumatra–Andaman earthquake profoundly altered the state of stress in a large volume surrounding the ∼1400 km long rupture. Induced mantle flow fields and coupled surface deformation are sensitive to the 3-D rheology structure. To predict the post-seismic motions from this earthquake, relaxation of a 3-D spherical viscoelastic earth model is simulated using the theory of coupled normal modes. The quasi-static deformation basis set and solution on the 3-D model is constructed using: a spherically stratified viscoelastic earth model with a linear stress–strain relation; an aspherical perturbation in viscoelastic structure; a 'static' mode basis set consisting of Earth's spheroidal and toroidal free oscillations; a "viscoelastic" mode basis set; and interaction kernels that describe the coupling among viscoelastic and static modes. Application to the 2004 Sumatra–Andaman earthquake illustrates the profound modification of the post-seismic flow field at depth by a slab structure and similarly large effects on the near-field post-seismic deformation field at Earth's surface. Comparison with post-seismic GPS observations illustrates the extent to which viscoelastic relaxation contributes to the regional post-seismic deformation.     

Iceocean mass balance during the Late Pleistocene glacial cycles in view of CHAMP and GRACE satellite missions

During the last glacial cycles, global sea level dropped several times by about 120 m and large ice sheets covered North America, northern Europe and Antarctica during the glacial stages. The changes in the iceocean mass balance have displaced mantle material mainly via viscous flow, and the perturbation of the equilibrium figure of the Earth by glacial isostatic adjustment is still observable today in timedependent changes of gravitational and rotational observations. Contemporary iceocean mass balance from volume changes of polar ice caps also contributes to secular variations of the Earth's gravitational field.
In the near future, several satellite gravity missions will significantly improve the accuracy of the observed timedependent gravitational field. In view of the expected improvements in the observations, we predict glacially induced perturbations of the gravitational field, induced by Late Pleistocene and contemporary ice volume changes, for a variety of radial mantle viscosity profiles. We assess the degree of uncertainty for the glacially induced contributions to gravitational and rotational parameters, both in the spectral and the spatial domain.
Predictions of power spectra for the glacially induced freeair gravity and geoid anomalies are about one order of magnitude lower than the observed values, and uncertainties arising from different plausible viscosity profiles are around 0.150.4 mGal and 0.21.5 m, respectively. Uncertainties from different ice models are of secondary importance for the predicted power spectra. Predicted secular changes in geoid anomalies in formerly glaciated areas are mainly controlled by the viscosity profile and contemporary ice volume changes. We also show that the simple threelayer viscosity profiles currently employed for the majority of postglacial rebound studies represent a limited subset for model predictions of the timedependent gravitational field.