Véronique Dehant

Tides for a convective Earth

In this paper we give values of the tidal gravimetric factor as well as of the Love numbers for the tidal surface displacement and for the tidal mass redistribution potential that are consistent with the presently adopted definitions. We present analytical expressions for these quantities and compute numerical values for two rotating, nonspherical Earth models. In the first model the Earth is everywhere in hydrostatic equilibrium, and the inner core and mantle are both elastic. In the second model the Earth is ellipsoidal with an inelastic mantle and with a nonhydrostatic initial state for which the effects of mantle convection and its associated boundary deformations are considered. This latter model is constrained to reproduce the observed free core nutation period and global Earth dynamical flattening.

Analytical approach to the computation of the Earth, the outer core and the inner core rotational motions

Abstract We have investigated the rotational motions of a simple Earth model composed of three homogeneous layers: an elastic inner core, a liquid outer core and an elastic mantle. Taking into account the various pressure and gravitational torques appearing between the different parts of the model as well as the elasto-gravitational deformations with the help of a Love number approach, we propose a fully developed set of equations for the conservation of angular momentum. The homogeneous system relative to the free case yields four normal modes: besides the classical Chandler Wobble and Free Core Nutation, two new eigenmodes appear: the Inner Core Wobble and the Free Inner Core Nutation. The simplicity of our model allows us to find analytical expressions for these rotational modes and to show the relative importance of the various coupling mechanisms which are involved. We also compare our values to numerical values proposed by two recent studies. The rotational response is then computed as a function of two different forcing mechanisms: one derived from an external potential like the tidal gravitational potential of nearly diurnal frequency, and another associated with a surface pressure like the pressure induced by atmospheric or oceanic loading.

Stacking gravity tide measurements and nutation observations in order to determine the complex eigenfrequency of the nearly diurnal free wobble

The resonance due to the nearly diurnal free wobble, observed in the diurnal tesseral tides and in the associated nutations, is used to determine the frequency and the damping of this wobble. The data are stacked to provide a least squares estimation of the resonance parameters: frequency, quality factor, and complex strengths. Some previous papers presented the same kind of analysis using either tidal or nutation data sets; in both cases, the frequency was about −(1 + 1/435) cycle/sidereal day, but the quality factor was larger for nutation data than for tidal data. In this paper we analyze simultaneously both sets of data, and we focus our attention on the determination of the free core nutation period and quality factor. We have analyzed a series of tidal data sets provided by the International Center for Earth Tides (ICET), and nutation data sets gathered from published matter. Our final result is obtained from a global stacking using four independent nutation data sets and three superconducting gravimeter data sets together. The values of the fitted parameters are found to be λFCN = −(1 + 1/(434.1 ± 0.9)) cycle/sidereal day and Q ≃ 54,000 (36,000; 109,000).

The NetLander very broad band seismometer

Abstract The interior of Mars is today poorly known, in contrast to the Earth interior and, to a lesser extent, to the Moon interior, for which seismic data have been used for the determination of the interior structure. This is one of the strongest facts motivating the deployment on Mars of a network of very broad band seismometers, in the framework of the 2007 CNES-NASA joint mission. These seismometers will be carried by the Netlanders, a set of 4 landers developed by a European consortium, and are expected to land in mid-2008. Despite a low mass, the seismometers will have a sensitivity comparable to the present Very Broad Band Earth sensors, i.e. better than the past Apollo Lunar seismometers. They will record the full range of seismic and gravity signals, from the expected quakes induced by the thermoelastic cooling of the lithosphere, to the possible permanent excitation of the normal modes and tidal gravity perturbations. All these seismic signals will be able to constrain the structure of Mars’ mantle and its discontinuities, as well as the state and size of the Martian core, shortly after for the centennial of the discovery of the Earth core by Oldham (Quart. J. Geol. Soc. 62(1906) 456–475).

RDAN97: An Analytical Development of Rigid Earth Nutation Series Using the Torque Approach

New series of rigid Earth nutations for the angular momemtum axis, the rotation axis and the figure axis, named RDAN97, are computed using the torque approach. Besides the classical J2 terms coming from the Moon and the Sun, we also consider several additional effects: terms coming from J3 and J4 in the case of the Moon, direct and indirect planetary effects, lunar inequality, J2 tilt, planetary‐tilt, effects of the precession and nutations on the nutations, secular variations of the amplitudes, effects due to the triaxiality of the Earth, new additional out‐of‐phase terms coming from second order effect and relativistic effects. Finally, we obtain rigid Earth nutation series of 1529 terms in longitude and 984 terms in obliquity with a truncation level of 0.1 μ (microarcsecond) and 8 significant digits. The value of the dynamical flattening used in this theory is HD=(C-A)/C=0.0032737674 computed from the initial value pa=50′.2877/yr for the precession rate. These new rigid Earth nutation series are then compared with the most recent models (Hartmann et al., 1998; Souchay and Kinoshita, 1996, 1997; Bretagnon et al., 1997, 1998. We also compute a benchmark series (RDNN97) from the numerical ephemerides DE403/LE403 (Standish et al., 1995) in order to test our model. The comparison between our model (RDAN97) and the benchmark series (RDNN97) shows a maximum difference, in the time domain, of 69 μas in longitude and 29 μas in obliquity. In the frequency domain, the maximum differences are 6 μas in longitude and 4 μ as in obliquity which is below the level of precision of the most recent observations (0.2 mas in time domain (temporal resolution of 1 day) and 0.02 mas in frequency domain).

Space geodesy monitors mass transports in global geophysical fluids

Large-scale mass transports in the Earth system produce variations in Earths rotation, gravity field, and geocenter. Although relatively small, these global geodynamic effects have been measured by space geodetic techniques to increasing, unprecedented accuracy, opening up important new avenues of research that will lead to a better understanding of global mass transport processes and the Earths dynamic responses. To take full advantage of these advances, the International Earth Rotation Service (IERS), the organization that monitors the rotational motions of the Earth and related properties, saw the need in 1998 to create an infrastructure to facilitate the link between the space geodetic measurement and the geodynamic “global change” research communities [Dehant et al., 1997]. Hence was born the IERS Global Geophysical Fluids Center (GGFC).

New transfer functions for nutations of a nonrigid Earth

There are differences between the observed values of nutation and the computed ones based on the International Astronomical Union (IAU) 1980 adopted nutation series. These differences can be expressed in the frequency domain where they may reach several milliarc seconds, a level that is too large for practical use. This paper aims to resolve part of these differences by computing a new theoretical model accounting for additional geophysical effects. A new transfer function is computed, based on an Earth initially in a nonhydrostatic equilibrium corresponding to the steady state associated with the present mantle convection. The mantle mass anomalies are deduced from seismic tomography data, and the flow-induced boundary deformations are computed from internal loading for an Earth made up of a viscous inner core, a liquid outer core, a viscous mantle, and a solid lithosphere. In this way, a new core-mantle boundary (CMB) flattening is obtained, which gives the observed free core nutation (FCN) period. Furthermore, the global Earth dynamical flattening induced by the mass anomalies in the mantle associated with tomography and by the mass anomalies due to the computed boundary deformations, is in agreement with the J2 form factor (or the observed precession constant). In addition to this nonhydrostatic initial state, the rheology of the mantle is considered as inelastic. The transfer function for nutation is then obtained by numerical integration of motion equations from the Earths center up to the surface to provide a model which is completely self-consistent. In order to validate our model, the transfer function is convolved with new rigid Earth nutations, ocean corrections are applied and the final results are then compared with the observed nutations or with the International Earth Rotation Service (IERS) nutation series. The residuals between our model and the observation are about 3 times smaller than those between the IAU 1980 adopted model and the observation. However, our model still presents residuals above the observational error; this is particularly true for the out-of-phase part of the residuals, while the in-phase part gives very small residuals (improvement of about 1 order of magnitude). A further step in this study is a refinement of the modeling of geophysical fluids (core, ocean, and atmosphere).

Atmospheric torque on the Earth and comparison with atmospheric angular momentum variations

The purpose of this paper is to compute atmospheric torques on the Earth, including the oceans, with an emphasis on the equatorial components. This dynamic approach is an alternative method to the classical budget-based angular momentum method for viewing atmospheric effects on Earths orientation in space. The expression of the total torque interaction between the atmosphere and the Earth is derived from the angular momentum balance equation. Such a torque is composed of three parts due to pressure, gravitation, and friction. Each of these torque components is evaluated numerically by a semi-analytical approach involving spherical harmonic approximations, and their orders of magnitude are intercompared. For the equatorial components the pressure and gravitational torques have far larger amplitudes than that of the friction torque; these two major torques have the same order of magnitude but opposite signs, and the value of the sum of the torques is shown to be close to the equatorial components of the atmospheric angular momentum time derivative s, as would be expected in a consistent model-based analysis system. The correlation between the two time series is shown to be very good at low frequency and decrease slowly with increasing frequency. The correlation is still significant (≥ 0.7) up to 0.5 cycle per day, but the correlation coefficient reduces to 0.5 at the diurnal frequency band, indicating the difficulty of calculating rapidly changing model-based torques within an atmospheric analysis system.

Network science landers for Mars

Abstract The NetLander Mission will deploy four landers to the Martian surface. Each lander includes a network science payload with instrumentation for studying the interior of Mars, the atmosphere and the subsurface, as well as the ionospheric structure and geodesy. The NetLander Mission is the first planetary mission focusing on investigations of the interior of the planet and the large-scale circulation of the atmosphere. A broad consortium of national space agencies and research laboratories will implement the mission. It is managed by CNES (the French Space Agency), with other major players being FMI (the Finnish Meteorological Institute), DLR (the German Space Agency), and other research institutes. According to current plans, the NetLander Mission will be launched in 2005 by means of an Ariane V launch, together with the Mars Sample Return mission. The landers will be separated from the spacecraft and targeted to their locations on the Martian surface several days prior to the spacecrafts arrival at Mars. The landing system employs parachutes and airbags. During the baseline mission of one Martian year, the network payloads will conduct simultaneous seismological, atmospheric, magnetic, ionospheric, geodetic measurements and ground penetrating radar mapping supported by panoramic images. The payloads also include entry phase measurements of the atmospheric vertical structure. The scientific data could be combined with simultaneous observations of the atmosphere and surface of Mars by the Mars Express Orbiter that is expected to be functional during the NetLander Missions operational phase. Communication between the landers and the Earth would take place via a data relay onboard the Mars Express Orbiter.

Considerations concerning the non-rigid Earth nutation theory.

This paper presents the reflections of the Working Group of which the tasks were to examine the non-rigid Earth nutation theory. To this aim, six different levels have been identified: Level 1 concerns the input model (giving profiles of the Earths density and theological properties) for the calculation of the Earths transfer function of Level 2; Level 2 concerns the integration inside the Earth in order to obtain the Earths transfer function for the nutations at different frequencies; Level 3 concerns the rigid Earth nutations; Level 4 examines the convolution (products in the frequency domain) between the Earths nutation transfer function obtained in Level 2, and the rigid Earth nutation (obtained in Level 3). This is for an Earth without ocean and atmosphere; Level 5 concerns the effects of the atmosphere and the oceans on the precession, obliquity rate, and nutations; Level 6 concerns the comparison with the VLBI observations, of the theoretical results obtained in Level 4, corrected for the effects obtained in Level 5.Each level is discussed at the state of the art of the developments.