A new approach to computing accurate gravity time variations for a realistic earth model with lateral heterogeneities

International audienceWe have developed a new elasto-gravitational earth model able to take into account lateral variations, deviatoric pre-stresses and topographies. As a first application, we assume an el-lipsoidal earth with hydrostatic pre-stresses, and validate and discuss our numerical model by comparison with previous studies on the M 2 body tide. We then study the response of the ellipsoidal earth to zonal atmospheric loads, and find that global lateral variations within the Earth, such as ellipticity, have a weak impact (about 1 per cent) on the elasto-gravitational deformations induced by atmospheric loading. At low frequencies, the Earth is deformed mainly by luni-solar tides and by surface loads, including ocean, atmosphere, ice volumes and post-glacial rebound. In this work, we focus our attention on the Earth's body tides and atmospheric loadings. The most accepted Earth body-tide models presently deal with an ellipsoidal, rotating earth, containing a liquid core and an anelastic mantle with hydrostatic pre-stresses (Wahr 1981; Wahr & Bergen 1986). The Earth, however, is not an exact ellipsoid, but presents lateral variations and deviatoric pre-stresses: there are long-wavelength density anomalies within the mantle, as shown by geoid anomalies and tomography studies (e.g. Romanowicz & Gung 2002). Wang (1994) and Dehant et al. (1999) studied the influence of lateral heterogeneities on Earth tides and showed that this effect is small but not necessarily negligible. They did not, however, take into account possible deviatoric pre-stresses: these effects on the Earth's body tides are totally unknown. In addition to tidal forces, mass changes in the atmosphere also cause deformation and mass redistribution inside the planet, involving both local and global surface motions and variations in the gravity field, which may be observed in geodetic experiments. For several decades, satellite geodesy has provided information on the temporal variation of the Earth's geopotential, and especially on the low-degree zonal harmonics (J 2 , J 3. . .) (Gegout & Cazenave 1993), which are essentially controlled by surface loads. These hydrological , atmospheric or oceanic effects on the Earth's gravity field are usually modelled assuming a spherical earth with hydro-static pre-stress (e.g. Farrell 1972; Wahr et al. 1998). With the advent of the new generation of gravity measurements, one of the challenges of the coming decade will be to provide more realistic earth models that show the variation of gravity with time. In particular, global studies based on gravity data from satellites such as GRACE, GOCE, and future GRACE/GOCE follow-on ones require accurate body-tide deformation models. More realistic gravity variation models are also needed for local and ground measurements, particularly for the very accurate superconducting gravimeters and the associated gravimetric observatory network such as the Global Geodynamic Project (Crossley et al. 1999). The formalism developed to compute this elasto-gravitational model is usually based on spherical harmonic analysis. The addition of lateral variations leads to couplings between spherical harmonics , i.e. to a more complex formalism that requires a large numerical effort (e.g. Wang 1994; Plag et al. 1996). We develop here a new approach for a non-radially symmetrical earth model using a finite-element method known as the spectral element method. The efficiency of this method is less dependent on the shape of the lateral heterogeneities than the spherical harmonic method. Our method is therefore well adapted to studying the impact of global and local lateral variations on the Earth deformation. We solve the elasto-gravitational equations taking into consideration the lateral variations within the Earth by using a first-order perturbation theory (Smith 1974; Dahlen & Tromp 1998). This new model allows us to take into account lateral variations of density and rheological parameters, deviatoric pre-stresses and interface topography. In order to validate our calculations, we tackle a well-known problem: the impact of the hydrostatic ellipticity on the Earth body tides. An analytical solution for this problem can be derived for a simple model in which the earth is assumed to be homogeneous and incompressible. The gravitational potential and the vertical displacement on the surface of the deformed ellipsoid were first derived by Love (1911) and then corrected by Wang (1994). We have recently extended these analytical results to the tangential surface displacement (Greff-Lefftz et al. 2005). We first validate our model with our analytical solutions, and then compare our results wit

Mantle lateral variations and elastogravitational deformations – I. Numerical modelling

International audienceThe Earth response (deformation and gravity) to tides or to surface loads is traditionally computed assuming radial symmetry in stratified earth models, at the hydrostatic equilibrium. The present study aims at providing a new earth elastogravitational deformation model which accounts for the whole complexity of a more realistic earth. The model is based on a dynamically consistent equilibrium state which includes lateral variations in density and elastic parameters, and interface topographies. The deviation from the hydrostatic equilibrium has been taken into account as a first-order perturbation. We use a finite element method (spectral element method) and solve numerically the gravitoelasticity equations. As a validation application, we investigate the deformation of the Earth to surface loads. We first evaluate the classical loading Love numbers with a relative precision of about 0.3 per cent for PREM earth model. Then we assume an ellipsoidal homogeneous incom-pressible earth with hydrostatic pre-stresses. We investigate the impact of ellipticity on loading Love numbers analytically and numerically. We validate and discuss our numerical model. At periods greater than 1 hr, the solid earth is mainly deformed by luni-solar tides and by surface loads induced by different external fluid layers (ocean, atmosphere, continental hydrology, ice volumes). This work is devoted to the analytical and numerical development to compute the response of the Earth to such forcing. The body tides have been investigated since the 19th century. In 1862, Lord Kelvin (Sir William Thomson) made the first calculation of the elastic deformation of a homogeneous incompressible earth under the action of the tidal gravitational potential (Thomson 1862). Some years later, Love (1911) studied a compressible homogeneous earth model and showed that the tidal effects could be represented by a set of dimensionless numbers, the so-called Love numbers. Takeuchi (1950) obtained a first estimation of the Love numbers by a numerical integration of the equations using a reference earth model deduced from seismology. These results have been later extended (Smith 1974; Wahr 1981) to an ellipsoidal, rotating Earth with hydrostatic pre-stresses and a liquid core, and finally the effects of mantle anelasticity have been included (Wahr & Bergen 1986; Dehant 1987). In addition to tidal forces, mass changes in the atmosphere cause deformation and mass redistribution inside the planet. The Earth's response to such forcing involves both local and global surface motions and variations in the gravity field, which may be observed in geodetic experiments. These hydrological, atmospheric or oceanic effects on the Earth's gravity field are usually modelled for a spherical Earth with hydrostatic pre-stress (e.g. Farrell 1972; Wahr et al. 1998), generally identified to the preliminary reference earth model (PREM) developed by Dziewonski & Anderson (1981). However, the internal structure of the Earth is more complex than in a spherical non-rotating elastic isotropic (SNREI) earth model like PREM. Seismology and fluid dynamic studies show that the mantle presents heterogeneous structure induced by a thermochemical convection (Davaille 1999; Gu et al. 2001; Forte & Mitrovica 2001) and a bias from hydrostatic state. Large lateral heterogeneities have taken place on a million year timescale (Courtillot et al. 2003), like the two supposed superplumes under the Pacific and South Africa superswells, or like descending slabs. These aspects of the mantle structure are classically not taken into account in the deformation models. The elastogravitational deformations are presently observed with very high accuracy. The accuracy of superconducting gravimeter and of positioning techniques (GPS, VLBI) has seen a large improvement in the last decade. Moreover, the global gravity field will be of interest in the next 10 yr with the launch of the missions GRACE (in 2002) and GOCE (in 2007), which are dedicated to gravimetry and gradiometry 106

Dissipation at the core-mantle boundary on a small-scale topography

International audienceThe parameters of the nutations are now known with a good accuracy, and the theory accounts for most of their values. Dissipative friction at the core-mantle boundary (CMB) and at the inner core boundary is an important ingredient of the theory. Up to now, viscous coupling at a smooth interface and electromagnetic coupling have been considered. In some cases they appear hardly strong enough to account for the observations. We advocate here that the CMB has a small-scale roughness and estimate the dissipation resulting from the interaction of the fluid core motion with this topography. We conclude that it might be significant

Constraining Ceres' interior from its Rotational Motion

Context. Ceres is the most massive body of the asteroid belt and contains about 25 wt.% (weight percent) of water. Understanding its thermal evolution and assessing its current state are major goals of the Dawn Mission. Constraints on internal structure can be inferred from various observations. Especially, detailed knowledge of the rotational motion can help constrain the mass distribution inside the body, which in turn can lead to information on its geophysical history. Aims. We investigate the signature of the interior on the rotational motion of Ceres and discuss possible future measurements performed by the spacecraft Dawn that will help to constrain Ceres' internal structure. Methods. We compute the polar motion, precession-nutation, and length-of-day variations. We estimate the amplitudes of the rigid and non-rigid response for these various motions for models of Ceres interior constrained by recent shape data and surface properties. Results. As a general result, the amplitudes of oscillations in the rotation appear to be small, and their determination from spaceborne techniques will be challenging. For example, the amplitudes of the semi-annual and annual nutations are around ~364 and ~140 milli-arcseconds, and they show little variation within the parametric space of interior models envisioned for Ceres. This, combined with the very long-period of the precession motion, requires very precise measurements. We also estimate the timescale for Ceres' orientation to relax to a generalized Cassini State, and we find that the tidal dissipation within that object was probably too small to drive any significant damping of its obliquity since formation. However, combining the shape and gravity observations by Dawn offers the prospect to identify departures of non-hydrostaticity at the global and regional scale, which will be instrumental in constraining Ceres' past and current thermal state. We also discuss the existence of a possible Chandler mode in the rotational motion of Ceres, whose potential excitation by endogenic and/or exogenic processes may help detect the presence of liquid reservoirs within the asteroid.Comment: submitted to Astronomy and Astrophysic

Assessing the importance and expression of the 6-year geomagnetic oscillation

The first time derivative of residual length-of-day observations is known to contain a distinctive 6 year periodic oscillation. Here we theorize that through the flow accelerations at the top of the core the same periodicity should arise in the geomagnetic secular acceleration. We use the secular acceleration of the CHAOS-3 and CM4 geomagnetic field models to recover frequency spectra through both a traditional Fourier analysis and an empirical mode decomposition. We identify the 6 year periodic signal in the geomagnetic secular acceleration and characterize its spatial behavior. This signal seems to be closely related to recent geomagnetic jerks. We also identify a 2.5 year periodic signal in CHAOS-3 with unknown origin. This signal is strictly axially dipolar and is absent from other magnetic or geodetic time series

Upwelling plumes, superswells and true polar wander

International audienceThe geological evolution of the rotational axis of the Earth is most likely controlled by internal mass redistribution within the mantle. Palaeomagnetic observations suggest that it is episodic in nature, with periods of quasi-standstill alternating with periods of faster wander. Here, we investigate two models for the influence of mantle plumes that vary at different spatial wavelengths on the time variations of the rotational axis (true polar wander; TPW). In the first model, we represent an upwelling plume as a sphere whose radius varies as a function of the flux of material in the conduit and that traverses the mantle at the Stokes velocity. Such a plume produces very little wander of the rotational axis. We then study the effects of two superswells that mimic the ones observed with seismic tomography and conclude that a doming regime within the mantle involves significant polar wander. Some of the features of this TPW that are directly linked to the periodicity of doming are reminiscent of observed phases of slow and fast TPW, with similar peak velocities

Length of day variations due to mantle dynamics at geological timescale

International audienceThe geological evolution of length of day (LOD) variations is mainly controlled by the frictional tidal torque responsible for the secular slowdown of the Earth's rotation and for the receding of the Moon. Superimposed on this variation, which has existed since the early history of the planet, there are, at shorter timescales (less than 1 Myr), LOD perturbations induced by the glaciation-deglaciation cycles. In this paper, we investigate the influence of mantle dynamics on LOD at the geological timescale. We use the complete non-linear equations to compute the influence of mantle density heterogeneities on the angular velocity of the rotation, that is to say on the LOD. We discuss the degree zero coefficient of the spherical harmonic expansion of the mantle mass anomaly, which is strongly dependent on the conservation of mass of the Earth. We first compute the effects induced by upwelling domes and subducted plates sinking into the mantle, which are known to induce geological variations in the orientation of the rotation axis with respect to a fixed terrestrial frame (the so-called True Polar Wander). We find that the time-variable mantle density heterogeneities associated with the large-scale pattern of plate tectonic motions since 120 Ma and with the upwelling domes can perturb LOD by about ? per year, that is, with an order of magnitude smaller than the effects induced by the last deglaciation. Superimposed on this linear trend, we show that there are fluctuations around 0.1-0.2 s Myr-1 on a timescale of a few tens of millions of years. We then combine a spherical model of mantle circulation with solutions for the equations governing the rotation of a viscous planet, to improve the constraint of mantle mass conservation. Finally, we compare our results with other effects

Sensitivity experiments on True Polar Wander

International audienceUsing 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 Earth's 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 Earth's rotation axis. We present two examples. We speculate that the distribution of continents with respect to the equator on the Earth's 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