Pascale Defraigne

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.

Time transfer to TAI using geodetic receivers

The classical time transfer method used to realize International Atomic Time (TAI) is based on the common view technique, with GPS observations collected by C/A code receivers. The resulting clock offsets between the laboratory clock and GPS time are obtained from a fixed procedure defined by the Consultative Committee for Time and Frequency (CCTF). A similar procedure can be applied to the Receiver INdependent EXchange (RINEX) observation files produced by geodetic receivers driven by a stable external frequency. If the link between the receiver clock and the external clock is stable and precisely determined, the geodetic receivers can then be used for time transfer to TAI. In that case, we propose some modifications to the CCTF procedure to adapt it for the links between geodetic receivers, in order to take advantage of the P codes available on L1 and L2. This new procedure forms the ionosphere-free combination of the P1 and P2 codes as given by the 30 s RINEX observation files, the standard of the International GPS Service. The procedure is tested using the Ashtech Z-XII3T geodetic receivers and the results are compared with those obtained with the classical CCTF procedure based on the C/A code by computing the fractional frequency stability (Allan deviation) of the time links. Over short baselines, the two techniques are equivalent, while the new technique provides a factor 2 improvement for a transatlantic time link. For time links between a time receiver and a geodetic receiver, the differential satellite delays (P1-C/A or P2-C/A) must additionally be introduced. We show here that these biases do not, however, alter the long-term (>3 days) stability of the time transfer results. The corrections associated with tidal station displacement are also investigated, and the results indicate that they do not significantly improve the results at the present level of precision.

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).

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).

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.

The Netlander Ionosphere and Geodesy Experiment

Abstract The NEtlander Ionosphere and Geodesy Experiment (NEIGE) of the Netlander Mission to Mars has two series of scientific objectives: (1) to determine Mars orientation parameters in order to obtain information about the interior of Mars and about the seasonal mass exchange between atmosphere and ice caps; and (2) to determine the total electron content (TEC) and the scintillation of radio signals in order to study the large- and small-scale structure of the ionosphere of Mars. These two sets of information will be derived from measurements of amplitudes and Doppler shifts of radio links at UHF and X-band between the Netlander microstations on the Mars surface and an orbiter and between this orbiter and the Earth (at X-band).

Chandler wobble and Free Core Nutation for Mars

Abstract The NetLander Ionospheric and Geodesic Experiment (NEIGE) of the 2007 NetLander/Mars Sample Return mission will allow the determination of Mars’ orientation parameters. Two normal rotational modes of Mars are studied here which can play an important role in these quantities: the Free Core Nutation (FCN) and the Chandler wobble (CW). The influence of various rheological and structural assumptions about the planet on the periods of these modes is investigated. Special attention is paid to the effects of inelasticity and the possible presence of a solid inner core. It is found that inelasticity has an almost negligible effect on the FCN period but can change the CW period by several days. The presence of an inner core, on the other hand, almost does not influence the CW period but can cause important changes to the FCN period. For the FCN, also nonhydrostatic effects can have a large impact on the period. These additional factors determining the FCN period, besides core size and density, certainly complicate the procedure for deriving information on the core of Mars such as the core radius, but more importantly offer the possibility to study and constrain a wide variety of inner core outer core and mantle properties.

GPS Time and Frequency Transfer: PPP and Phase-Only Analysis

To compute precise point positioning (PPP) and precise time transfer using GPS code and phase measurements, a new software named Atomium was developed by the Royal Observatory of Belgium. Atomium was also adapted to perform a phase-only analysis with the goal to obtain a continuous clock solution which is independent of the GPS codes. In this paper, the analysis strategy used in Atomium is described and the clock solutions obtained through the phase-only approach are compared to the results from the PPP mode. It is shown that the phase-only solution improves the stability of the time link for averaging times smaller than 7 days and that the phase-only solution is very sensitive to the station coordinates used. The method is, however, shown to perform better than the IGS clock solution in case of changes in the GPS receiver hardware delays which affects the code measurements.

The free core nutation period stays between 431 and 434 sidereal days

We determine the parameters of the Free Core Nutation (FCN) from the resonance induced in the forced nutations by a least-squares analysis of VLBI observations. By applying the procedure to consecutive observation series, we deduce the time evolution of the FCN period, and show that it varies only between 431 and 434 sidereal days. These bounds are within the limits of uncertainty arising from noise in the data. We therefore find no evidence for time variation of the FCN period.