No abstract

We quantify the effects of post-seismic deformation on the radial and horizontal components of the displacement, in the near- and far-field of strike- and dip-slip point dislocations; these sources are embedded in the elastic top layer of a spherical, self-gravitating, stratified viscoelastic earth. Within the scheme of the normal mode technique, we derive the explicit analytical expression of the fundamental matrix for the toroidal component of the field equations; this component is propagated, together with its spheroidal counterpart, from the core-mantle boundary to the earth's surface. Viscosity stratification at 670km depth influences the radial and horizontal deformation accompanying viscoelastic relaxation in the mantle over time-scales of 103-104 yr, both in the near-field, ranging from 100 to 500 km and in the far-field, from 103 to 5 X 103 km. If the upper mantle is differentiated into a low-viscosity zone beneath the lithosphere and a normal upper mantle, faster relaxation is obtained. For an asthenospheric viscosity of 1020 Pa s we obtain, for a strike-slip dislocation and a seismic moment of 1022 N m characteristic of an average large earthquake, horizontal rates of 1-4 mm yr-1 in the near-field and 0.05-0.4 mm yr-1 in the far-field; these values are maintained over time-scales of 10-103 yr. Larger rates, with shorter duration, are obtained if the viscosity is reduced in the low-viscosity channel. As expected, strike-slip dislocations are the most effective in driving horizontal deformation in the far-field in comparison with dip-slip ones. It is noteworthy that horizontal velocities are maintained longer in the far-field in comparison with radial ones, which is not surprising since momentum is propagated in far regions essentially in the horizontal direction; radial deformation is generally lower in the far-field. VLBI techniques, with a precision of a few parts per billion over distances of 103 km, can detect global post-seismic deformation induced by large earthquakes. Our results affect the interpretation of the transfer of stress and seismic activity among different plate boundaries

Changes in the earth's rotation produced by the waxing and waning of large mobile ice sheets can be used to infer the viscosity of the mantle from a comparison with the recent secular polar drift as revealed in the International Latitude Service data and also in the estimates of the nontidal acceleration of the length of the day. We have developed by using an analytical approach a physical model of a rotating earth consisting of an elastic lithosphere, a viscoelastic mantle, and an inviscid core. Forcings from the two major ice sheets, Laurentide and Fennoscandia, have been considered. Sensitivity analysis of the parameters governing the external forcings, such as the length and the time of termination of the deglaciation phase, show in general that there exist two families of mean mantle viscosities, 0(1022 P) and 0(1023 P), which can match the data satisfactorily. However, we find it an improvement to incorporate some amount of shrinkage from the Antarctic ice sheet, obtaining simultaneously a better fit with the two rotational data sets to the lower viscosity solutions. Hence forcings from the southern hemisphere may be able to remove the ambiguity associated with the extraction of mantle viscosity from rotational data. We have also solved the initial value problem of the components of instantaneous angular velocity by means of the Laplace transform for applied loads characterizing the continental ice sheets, which since the mid‐Pliocene have periodically expanded and contracted over the northern hemisphere. In consequence of this continual forcing, polar wander of around 5–10 degrees can take place for a mean mantle viscosity 0 (1022 P). Recent reanalysis of paleomagnetic data in conjunction with hot spot tracks have revealed that several degrees of true polar wander could have occurred in the last 5 m.y. These calculations thus provide a physical explanation for the observed movement of the rotation axis. Membrane stresses of 0 (10) bars can develop from this secular polar motion.

The description of plate motions in the so‐called hotspot reference frame introduces a global rotation of the lithosphere with respect to the mantle. This rotation, called toroidal field of degree 1, is roughly westward. It reaches an amplitude of about 2 cm/yr and has been consistently found in the different generation of plate tectonic models. Various authors have tried to relate this observation to the deceleration of the Earth's rotation, to polar wander, or to tidal drag. However, these different physical mechanisms cannot explain the requested amplitude. In this paper, we compare the values of this rotation vector using different relative plate motion models expressed in the hotspot reference frame. In a model Earth with lateral viscosity variations, a differential rotation is predicted. The observed net lithospheric rotation is consistent with the dynamics of a model Earth where the asthenospheric viscosity below the oceans is at least one order of magnitude lower than underneath the continents. This relative westward drift of the lithosphere may account for the significant structural differences between east or west dipping subduction zones.

S U M M A R YThe rotational behaviour of a stratified visco-elastic planet submitted to changes in its inertia tensor is studied in a viscous quasi-fluid approximation. This approximation allows for large displacements of the Earth rotation axis with respect to the entire mantle but is only valid for mass redistribution within the planet occurring on the time scale of a few million years. Such a motion, called true polar wander (TPW), is detected by palaeomagneticiens assuming that the Earth's magnetic field remains on average aligned with the spin axis. Our model shows that a downgoing cold slab induces a TPW which quickly brings this slab to the pole for a mantle of uniform viscosity. The same slab is slowly moved toward the equator when a large viscosity increase with depth takes place in the mantle. Our model is also suitable to investigate the effects of a non-steady-state convection on the Earth's rotation. We discuss these effects using a simple mass redistribution model inspired by the pioneering paper of Goldreich & Toomre (1969). It consists of studying the TPW induced by a random distribution of slabs sinking into the mantle. For such a mass redistribution, only a strongly stratified mantle can reduce the Earth's pole velocity below l"Ma-', which is the upper bound value observed by palaeomagnetic investigations for the last 200 Ma. Our model also shows that when corrected for the hydrostatic flattening, the Earth's polar inertia generally corresponds to the maximum inertia, as it is presently observed. However, this may not be the case during some short time periods. We also discuss The amount of excess polar flattening that can be related to tidal deceleration. This frozen component is found to be negligible. The equation of motion of a rotating body in a rotating frame is the well known Euler dynamic equation. When no external torque is applied, it reads d -( J -w ) + w A J . w = O . dt where J is the second-order symmetric inertia tensor and o is the angular velocity. Both are expressed in a rotating Earth-tixed coordinate system. This equation also holds when J is a time-dependent function (Munk & MacDonald 1960). In this case, it takes the name of Liouville equation.The inertia tensor J is traditionally divided into three contributions of decreasing amplitudes. The first is the tensor of a spherical non-rotating Earth. We write it as IS, where 6 , is the Kronecker symbol. This term is close to 284 0.33Ma2 where M and a are the mass and the radius of Earth. A second term is due to the centrifugal potential that deforms the Earth. It can be shown that this potential is proportional to wiwi -$02Sii where wi are the components of o in the geographical frame (e.g. Lambeck 1980). Any change in rotation is therefore equivalent to a new potential applied to the Earth's surface. Under such a boundary condition, the planet evolves toward a new configuration corresponding to an inertia tensor equal to the convolution of k T ( t ) , the tidal Love number of harmonic degree 2, with the time history of the cha...