Material versus isobaric internal boundaries in the Earth and their influence on postglacial rebound

Most previous earth models used to calculate viscoelastic relaxation after the removal of the Late Pleistocene ice loads implicitly assume that there is no exchange of mass across the mantle density discontinuities on periods of tens of thousands of years (the material boundary formulation). In the present study, simple incompressible models are used to determine the Earth's behaviour in the case where the density discontinuity remains at a constant pressure rather than deforming with the material (the isobaric boundary formulation). The calculation of the movement of the boundary is more rigorous than in earlier studies and uses the local incremental pressure calculated at the depth of the boundary and allows for the vertical deformation caused by the change in volume as material changes phase. It is shown that the buoyancy modes associated with the density discontinuities decrease in strength and increase in relaxation time analogous to what results when the density contrast is reduced. Also, two viscoelastic modes arise from an isobaric boundary, which is also predicted when there is a contrast in rigidity or viscosity across a material boundary. The difference in predicted radial deformation between the isobaric boundary model and the material boundary model is largest for long-wavelength loads for which the material incremental pressure at depth is largest. If the isobaric boundary model is appropriate for the treatment of the mineral phase changes in the mantle on glacial rebound timescales, then previous inferences of the deep-mantle to shallow-mantle viscosity ratio based on large-scale deformation (spherical harmonic degree < 10) of the Earth and including data from the early part of the glacio-isostatic uplift are too small.     

Rheology of the Earth and a thermoconvective mechanism for sedimentary basin formation

A power-law non-Newtonian fluid is usually assumed to model slow flows in the mantle and, in particular, convective flows. However, the power-law fluid has no memory, in contrast to a real material. A new non-linear integral (having a memory) model is proposed to describe the rheology of rocks. The model is consistent with the theory of simple fluids with fading memory and with laboratory studies of rock creep. The proposed model reduces to the power-law fluid model for stationary flows and to the Andrade model for flows associated with small strains. Stationary convection beneath continents has been studied by Fleitout & Yuen (1984 ), who used the power-law fluid model and obtained the cold immobile boundary layer (continental lithosphere). In a stability analysis of this layer, the Andrade model must be used. The analysis shows that the lithosphere is overstable (the period of oscillation is about 200  Ma). In the present study, it is suggested that these thermoconvective oscillations of the lithosphere are a mechanism for sedimentary basin formation. The vertical crustal movement in sedimentary basins can be considered as a slow subsidence on which small-amplitude oscillations are superimposed. The longest period of oscillatory crustal movement is of the same order of magnitude as the period of convective oscillation of the lithosphere found in the stability analysis. Taking into account the difference between depositional and erosional transport rates we can explain the permanent subsidence as well as the oscillations.     

Geophysical model of the dynamical flattening of the Earth in agreement with the precession constant

The dynamical flattening of the Earth, as observed by geodetic techniques, is different by about 1 per cent from the value associated with the PREM density profile with hydrostatic equilibrium. In this paper, we compute a new dynamical flattening H induced by PREM mean density with hydrostatic equilibrium, to which we add lateral heterogeneities associated with (1) seismic velocity variations observed by tomography and (2) internal boundary topographies. First, we compute mantle circulation associated with the density anomalies derived from a tomography model. The flow-induced boundary deformations are then converted into additional mass anomalies which are added to the tomography model for computing the associated perturbation to the Earth's inertia tensor. Finally, we show that it is possible to obtain a dynamical flattening from the total inertia tensor (i.e. the sum of the PREM inertia tensor and of the perturbation) in agreement with that observed.     

Excitation of thermoconvective waves in the continental lithosphere

For flows associated with small strains, the rheology of rocks is described by the linear integral (having a memory) law, which reduces to the Andrade law in the case of constant stress. A continental lithosphere with such a rheology is overstable. Thermoconvective waves that propagate through the lithosphere with minimal attenuation have a period of about 200  Myr and a wavelength of the order of 400  km. An initial temperature point-concentrated perturbation in the lithosphere excites amplitude-modulated thermoconvective waves (wave packets). When the initial perturbation occurs in a finite area, thermoconvective waves propagate outwards from this area, and thermoconvective oscillations (standing waves) are established inside the area. Thermoconvective waves induce oscillations of the Earth' surface, accompanied by sedimentation and erosion, and can be considered as a mechanism for the distribution of sediments on continental cratons.