Marianne Greff-Lefftz

ON ATMOSPHERIC PRESSURE PERTURBATIONS ON PRECESSION AND NUTATIONS

Abstract The atmospheric pressure effects on the nutations are evaluated using the analytical expression of the rotational motion of the Earth in inertial space as a function of the external surface pressure torque. The most efficient term in perturbing the nutations is the S1 solar barometric tide of thermal origin; this wave induces a contribution to the prograde annual nutation but seasonal modulations of S1 may also cause perturbations to other nutations. Two extreme cases of oceanic response to pressure fluctuations are considered (inverted barometer ocean or non-inverted barometer ocean) and various kinds of figures (ellipsoid, geoid, topography) are introduced in the pressure torque computation. According to the forcing amplitude of the pressure field and to various assumptions in the torque computation, we obtain contributions to the nutation values ranging from a few tenths of a milliarcsecond up to several milliarcseconds for the semi-annual and annual terms. This shows the importance of atmospheric pressure corrections which have been ignored until now in the theoretical expressions of nutations as well as in the set of corrections applied to the observed nutations.

Core-mantle coupling and polar motion

Abstract We present the general expression for the topographic and electromagnetic torques acting at the core-mantle boundary (CMB) as a function of the outer core flow. Invoking angular momentum conservation of the Earth and of the core, we compute the perturbations in the rotation of the Earth, at the decade time-scale, resulting from this fluid motion, since 1900. Electromagnetic coupling is too weak to excite polar motion by two or three orders of magnitude. Although the pressure torque on a CMB topography computed by the authors involves some correlations between the temporal variation of the computed ω2-component of the polar motion and that observed, its amplitude is too weak by a factor of 10 and we have to conclude that it does not seem to be responsible for the decade variations of the polar motion.

Atmospheric and oceanic excitation of the rotation of a three-layer Earth

In this paper, we evaluate the nutational Earth response to the excitation exerted by a surface fluid (atmosphere, ocean, and hydrology) for a simple Earth model, constituted of three homogeneous layers: a solid deformable inner-core, a liquid outer core, and an elastic mantle. Our formula, valid in the quasi-diurnal frequency band, includes two resonances, at the Free Core Nutation (FCN) and the Free Inner-Core Nutation (FICN). Additionally, we have evaluated the amplitudes of those wobbles in response to a random noise excitation. We show that, compared with the FCN signal, the resonance at the FICN frequency induced by a surface fluid layer only induces a very small signal in the Earth rotation, and that, with an excitation comparable to the one available at the FCN, the FICN would generate a signal at the Earth surface at the sub-micrometer level.

Effects of inner core viscosity on gravity changes and spatial nutations induced by luni-solar tides

Abstract In this paper, we investigate the perturbations induced by the nearly-diurnal luni-solar tidal potential on the surface gravity changes and on the spatial nutations. The effects of the magnetic friction at the inner core boundary (ICB) and on the inner core viscosity at this time scale are studied. We show that very precise very long baseline interferometry (VLBI) observations of the in-phase and out-of-phase components of some nutations can give information on the Earth’s deep interior, especially on the effective viscosity of the inner core and on the amplitude of the radial component of the magnetic field at the ICB.

MAGNETIC FIELD AND ROTATIONAL EIGENFREQUENCIES

Abstract The theory of the rotation of the fluid core is modified in order to take into account the magnetic field within the core. Because of the conductivity of the lower mantle, there is a frictional magnetic torque which appears at the core–mantle boundary (CMB); the magnitude of this torque depends on the conductivity profile within the mantle and on the magnetic energy at the CMB. It perturbs the rotational eigenmodes involving a damping in the free core nutation (FCN) and in the Chandler wobble. The geostrophic pressure at the CMB acts on the bumps of this interface involving a topographic torque. Because of the geostrophic rigidification, this surface pressure field is advected by the core velocity, and consequently, the topography being fixed in a frame related to the mantle, it appears a restoring torque acting on the core. Such a torque perturbs the FCN and creates a slow new rotational eigenmode.

Sensitivity experiments on True Polar Wander

Using sensitivity experiments based on the position of subductions and of superplumes, we derive models for the temporal evolution of 3-D mass anomalies in the mantle and compute the associated inertia perturbations and polar wander. We show that although the large length-scale mantle dynamics during the Earths history may have been dominated by coupled supercontinent-superplume cycles, subductions alone are sufficient to trigger major True Polar Wander (TPW) episodes, or rotation of the whole lithosphere and mantle with respect to the Earths rotation axis. We present two examples. We speculate that the distribution of continents with respect to the equator on the Earths surface is driven by episodic subductions during the Wilson cycle: alternating fast subduction girdles around continents and upwellings during the divergence phases, with both reduced or stopped subductions activity around continents and moderate inter-continental subductions during the convergence phases, lead to successive equatorial or polar distributions of continents, both configurations being separated by strong episodes of TPW. Finally, using plate reconstructions and geologic maps, over the period 1100–720 Ma, the period of amalgamation and destruction of the Rodinia supercontinent, we explain with our model the observed large eastward/westward and poleward/equatorward motions of the rotation axis.

Core-mantle coupling and viscoelastic deformations

Abstract Writing the angular momentum theorem for the Earth and for its fluid core, we show that there are couplings between the core and the mantle induced by viscomagnetic torque, by external active torque, by topographic torque acting at the core-mantle boundary (CMB) but also by viscoelastic deformations of the CMB which may perturb the axial rotations of the Earth and of the core. We compute these deformations at the CMB induced by the Pleistocenic deglaciation. The time-dependence of inertia tensor perturbations, i.e. the rheology of the mantle, is very important in the calculation of the coupling. Taking into account the passive viscomagnetic torque of tangential traction acting at the CMB, we investigate, for different values and various temporal evolutions of the topographic torque, the perturbations in the rotations of the Earth and of the core induced by the deglaciation, by the constant torque of tidal friction and by the 18.6 year tidal potential. We show that, for these excitation sources, the existence of a constant topographic torque involves the core oscillating with respect to the mantle and thus forbids any large drift of the core with respect to the mantle. However, it seems theoretically possible to have an excitation source with enough energy which involves a shift of the core with respect to the mantle. If the pressure within the fluid core varies with time, the motion of the core with respect to the mantle could be drastically different.

Dynamic topography and lithospheric stresses since 400 Ma

We present a global model of dynamic topography and lithospheric stresses for the last 400 Ma. Our starting point is a simple geodynamic model combining both contributions of subducted lithosphere and long wavelength upwellings in a reference frame linked to the fixed african plate. A dominant feature of plate tectonics is the quasi permanence of a girdle of subductions around the Pacific ocean (or its ancestor), which creates large-wavelength positive topography anomaly within the ring they form. The superimposition of the resultant extension with the one induced by the dome leads to a permanent extensional regime over Africa and the future Indian ocean which creates faults with azimuth directions depending on the direction of the most active part of the ring of subductions. We thus obtain fractures with NW-SE azimuth during the period 275-165 Ma parallel to the strike of the subduction zone of the West South American active margin, which appears to be very active during this period. Between 155-95 Ma, subduction became more active along the Eastern Australian coast involving a change in the direction of the faults toward an E-W direction, in agreement with the observed fault systems between Africa and India, Antartica and Australia. During the Mesozoic and the Cenozoic, we correlate the permanent extensional regime over Africa and Indian ocean with the observed rift systems. Finally we emphasize the role of three primary hotspots as local additional contributors to the stress field imposed by our proposed subduction-doming system, which help in the opening of Indian and South Atlantic oceans.

Degree-one deformations of the Earth

The degree one deformations of the Earth, in a reference frame related to the center of mass of the planet, are computed using a theoretical approach (Love numbers formalism) at short time-scale (from the month up to the century), where the Earth has an elastic behavior. The translations at each interface of the layers of the Earth’s model (especially at the surface, at the Core-Mantle boundary (CMB) and at the Inner Core boundary (ICB)) are computed when the excitation source is the atmospheric pressure or a magnetic pressure acting at the CMB and at the ICB. The effects of external and internal tangential tractions axe also investigated. The total force, resulting from the excitation sources, in a geographic frame (centered at the center of mass) has to be equal to zero, in order to conserve the center of mass of the Earth. This involves a relation between the different forcing mechar nisms; we obtain a Consistency Relation, i.e., a special condition that the degree-one valid solutions have to obey (Faxrell, 1972). As geophysical application, we have computed the degreeone static deformations induced by atmospheric loading. To end, at secular and geological timescales, where the Earth has a viscoelastic behaviour, we have computed the secular and geological variations of the geocenter induced by postglacial rebound and by mantle density heterogeneities