V. Dehant, Royal Observatory of Belgium. | 2003-08-08

# Bomford Prize Presentation: Nutation, observation and theory.

Due to the gravitational attraction of the Moon and the Sun and also the planets, the Earth deforms and undergoes polar motion, variations of the length-of-day and nutations. The amplitudes of these induced deformations and forced motions are additionally modified by the ocean and the atmosphere. These nutations can be observed by using Very Long Baseline Interferometry (VLBI) and can be computed from an Earth model involving physical parameters for the Earth’s interior. The comparison of the observation and the theory leads to a better understanding of the physics of the Earth’s interior, which in turn, allows to readjust the model.

My work in the nutation field can be described by different steps improving the nutation models and starting from the adopted nutation model by the IAU and the IUGG based on the rigid Earth nutation series of Kinoshita (1977) convolved with the model of Wahr’s (1981) nutation for an ellipsoidal rotating Earth, primarily in hydrostatic equilibrium, with an elastic inner core, a liquid core and an elastic mantle.

First, I introduced mantle inelasticity in the input model. This work was completed for my Ph. D. in 1986 (Dehant, 1986, 1988). In that same year, Herring et al. (1986) pointed out that the discrepancy between the observed and computed Free Core Nutation (FCN) could explain the large residuals on the retrograde annual nutation. Indeed this nutation frequency is close to the FCN normal mode frequency that can be excited when an angle between the rotation axis of the core and the rotation axis of the mantle exists. While the theoretical value for an Earth a priori in hydrostatic equilibrium is 460 days in inertial space, the observed value is 432 days. This discrepancy can be resolved by changing the core equatorial radius with respect to the polar radius by 500 meters (increase of the core flattening). We (work in collaboration with J. Wahr and P. Defraigne) have then searched for a physical mechanism causing this increased flattening. We have computed, for a steady state convection, the convective fluxes derived from the buoyancy forces associated with mass heterogeneities inside the mantle. The mass heterogeneities are deduced from three dimensional images of the mantle determined by the seismologists (tomography, 3D-lateral heterogeneities in seismic velocities). Phase transitions inside the mantle have been incorporated in the computation (Dehant and Wahr, 1991) and the model has been constrained by other geophysical data as the geoid and the tectonic plate velocities (Defraigne, Dehant and Wahr, 1996). The fluxes derived in this model deform the surface and the interfaces, and in particular deform the core mantle boundary resulting in an increase of the core flattening. A new transfer function for nutation has been derived (Dehant and Defraigne, 1997) which includes all those effects.

In parallel, we worked on the rigid Earth nutation theory and computed a new series (Roosbeek and Dehant, 1998). We compared it with the ephemerides and with other theories (Dehant et al., 1999a). From this comparison, it can be seen that our rigid Earth nutation series is precise enough (better than 10 microarcsecond) and thus there is no needed at present to derive a more accurate rigid Earth nutation series. The situation concerning the Earth’s transfer function is rather different as explained here below.

Comparisons have been performed for the non-rigid Earth nutation series with the VLBI observations. This has shown that our transfer function still suffers from a lack of dissipation needed to explain the large out-of-phase parts missing in the retrograde annual nutation and in the 18.6 year nutations. The core, and in particular the core-mantle boundary electromagnetic torque, are the major actors in the next development of nutation theory. This future work is in the line of my responsibilities in the Special Bureau for the Core in the frame of the International Earth Rotation Service (IERS) (see Dehant et al., 1999c).

To be able to further compare observation and theory, we decided to incorporate the atmospheric and oceanic corrections. We adopted the torque approach (see Dehant et al., 1996, de Viron et al., 1999), which consists in computing the pressure torque, the gravitational torque and the friction torque exerted by the fluid on the Earth. There are still unexplained differences between our results and the results coming from the angular momentum approach (which consists in considering that the variation of the Earth’s angular momentum can be directly deduced from the variations in the atmospheric angular momentum and in the ocean angular momentum). We are still working on that problem.

Within the WG on "Non rigid Earth nutation theory" which I chaired, many points in the theoretical nutation computation and in the comparison with observation have been discussed and the most important findings are described in Dehant et al. (1999b).

Another research activity that I conducted in the frame of the nutation is the computation of the nutations of the planet Mars. Nutations being sensitive to the state of the core (due to the resonance at the FCN period), their observation would provide us with information about the interior of Mars. This is one of the principal aims of the Netlander geodesy experiment, which will fligh in 2005.

I wish to thank the Central Bureau of the IAG for providing me this prize and the Belgian National Committee for Geodesy and Geophysics for presenting me for this prize. Additionally, I would like to acknowledge my colleagues P. Defraigne, O. de Viron, F. Roosbeek and T. Van Hoolst, the present Director of Royal Observatory of Belgium P. Pâquet, my Ph. D. adviser P. Melchior, my colleagues M. Feissel, S. Mathews, J. Wahr, colleagues from the Observatoire de Paris, colleagues from the Institut de Physique du Globe de Strasbourg, all the members and correspondents of the WG on "Non rigid Earth nutation theory", all the members of the Netlander team, my family and friends.

My work in the nutation field can be described by different steps improving the nutation models and starting from the adopted nutation model by the IAU and the IUGG based on the rigid Earth nutation series of Kinoshita (1977) convolved with the model of Wahr’s (1981) nutation for an ellipsoidal rotating Earth, primarily in hydrostatic equilibrium, with an elastic inner core, a liquid core and an elastic mantle.

First, I introduced mantle inelasticity in the input model. This work was completed for my Ph. D. in 1986 (Dehant, 1986, 1988). In that same year, Herring et al. (1986) pointed out that the discrepancy between the observed and computed Free Core Nutation (FCN) could explain the large residuals on the retrograde annual nutation. Indeed this nutation frequency is close to the FCN normal mode frequency that can be excited when an angle between the rotation axis of the core and the rotation axis of the mantle exists. While the theoretical value for an Earth a priori in hydrostatic equilibrium is 460 days in inertial space, the observed value is 432 days. This discrepancy can be resolved by changing the core equatorial radius with respect to the polar radius by 500 meters (increase of the core flattening). We (work in collaboration with J. Wahr and P. Defraigne) have then searched for a physical mechanism causing this increased flattening. We have computed, for a steady state convection, the convective fluxes derived from the buoyancy forces associated with mass heterogeneities inside the mantle. The mass heterogeneities are deduced from three dimensional images of the mantle determined by the seismologists (tomography, 3D-lateral heterogeneities in seismic velocities). Phase transitions inside the mantle have been incorporated in the computation (Dehant and Wahr, 1991) and the model has been constrained by other geophysical data as the geoid and the tectonic plate velocities (Defraigne, Dehant and Wahr, 1996). The fluxes derived in this model deform the surface and the interfaces, and in particular deform the core mantle boundary resulting in an increase of the core flattening. A new transfer function for nutation has been derived (Dehant and Defraigne, 1997) which includes all those effects.

In parallel, we worked on the rigid Earth nutation theory and computed a new series (Roosbeek and Dehant, 1998). We compared it with the ephemerides and with other theories (Dehant et al., 1999a). From this comparison, it can be seen that our rigid Earth nutation series is precise enough (better than 10 microarcsecond) and thus there is no needed at present to derive a more accurate rigid Earth nutation series. The situation concerning the Earth’s transfer function is rather different as explained here below.

Comparisons have been performed for the non-rigid Earth nutation series with the VLBI observations. This has shown that our transfer function still suffers from a lack of dissipation needed to explain the large out-of-phase parts missing in the retrograde annual nutation and in the 18.6 year nutations. The core, and in particular the core-mantle boundary electromagnetic torque, are the major actors in the next development of nutation theory. This future work is in the line of my responsibilities in the Special Bureau for the Core in the frame of the International Earth Rotation Service (IERS) (see Dehant et al., 1999c).

To be able to further compare observation and theory, we decided to incorporate the atmospheric and oceanic corrections. We adopted the torque approach (see Dehant et al., 1996, de Viron et al., 1999), which consists in computing the pressure torque, the gravitational torque and the friction torque exerted by the fluid on the Earth. There are still unexplained differences between our results and the results coming from the angular momentum approach (which consists in considering that the variation of the Earth’s angular momentum can be directly deduced from the variations in the atmospheric angular momentum and in the ocean angular momentum). We are still working on that problem.

Within the WG on "Non rigid Earth nutation theory" which I chaired, many points in the theoretical nutation computation and in the comparison with observation have been discussed and the most important findings are described in Dehant et al. (1999b).

Another research activity that I conducted in the frame of the nutation is the computation of the nutations of the planet Mars. Nutations being sensitive to the state of the core (due to the resonance at the FCN period), their observation would provide us with information about the interior of Mars. This is one of the principal aims of the Netlander geodesy experiment, which will fligh in 2005.

##### Acknowledgements

I wish to thank the Central Bureau of the IAG for providing me this prize and the Belgian National Committee for Geodesy and Geophysics for presenting me for this prize. Additionally, I would like to acknowledge my colleagues P. Defraigne, O. de Viron, F. Roosbeek and T. Van Hoolst, the present Director of Royal Observatory of Belgium P. Pâquet, my Ph. D. adviser P. Melchior, my colleagues M. Feissel, S. Mathews, J. Wahr, colleagues from the Observatoire de Paris, colleagues from the Institut de Physique du Globe de Strasbourg, all the members and correspondents of the WG on "Non rigid Earth nutation theory", all the members of the Netlander team, my family and friends.

##### References

**Defraigne P., Dehant V. and Wahr J.M., 1996,**"Internal loading of an homogeneous compressible Earth with phase boundaries.", Geophys. J. Int., 125, pp. 173-192.**Dehant V., 1986,**"Intégration des équations aux déformations d'une Terre elliptique, inélastique, en rotation uniforme et à noyau liquide.", Ph.D. Thesis, Université catholique de Louvain, Louvain-la-Neuve, Belgium, in French, 298 pp.**Dehant V., 1988,**"Nutations and inelasticity of the Earth.", in: Proc. of the 128th IAU Symp. on `Earth's Rotation and Reference Frames for Geodesy and Geodynamics', Washington, USA, 1986, eds. A.K. Babcock and G.A. Wilkins, Reidel Publ. Comp., pp. 323-330.**Dehant V. and Wahr J.M., 1991,**"The response of a compressible, non-homogeneous Earth to internal loading: Theory.", J. Geomag. Geoelectr., 43, pp. 157-178.**Dehant V. and Defraigne P., 1997,**"New transfer functions for nutations of a non-rigid Earth.", J. Geophys. Res., 102, pp. 27,659-27,688.**Dehant V., Bizouard Ch., Hinderer J., Legros H. and Lefftz M., 1996,**"On atmospheric pressure perturbation on precession and nutations.", Phys. Earth planet. Inter., 96, 1, pp. 25-40.**Dehant V., Bretagnon P., Francou G., Rocher P., Simon J.-L., Kinoshita H., Souchay J., Roosbeek F., Defraigne P., Herring T. and Mathews P.M., 1999a,**"Comparison between the different rigid and non-rigid Earth nutation theories.", in: 'Proc. Journées Systèmes de Référence Spatio-temporels 1998', ed. N. Capitaine, Paris, France, pp. 113-117.**Dehant V., Arias F., Bizouard Ch., Bretagnon P., Brzezinski A., Buffett B., Capitaine N., Defraigne P., de Viron O., Feissel M., Fliegel H., Forte A., Gambis D., Getino J., Gross R., Herring T., Kinoshita H., Klioner S., Mathews P.M., McCarthy D., Moisson X., Petrov S., Ponte R.M., Roosbeek F., Salstein D., Schuh H., Seidelmann K., Soffel M., Souchay J., Vondrak J., Wahr J.M., Weber R., Williams J., Yatskiv Y., Zharov V. and Zhu S.Y., 1999b,**"Considerations concerning the non-rigid Earth nutation theory.", Celest. Mech., 72, 4, pp. 245-310.**Dehant V., Cardin Ph., Chulliat A., Defraigne P., de Viron O., Dormy E., Greff-Lefftz M., Hinderer J., Holme R., Hulot G., Jackson A., Jault D., Kuang W., Legros H., Le Mouel J-L., Noir J., Pais A., Roosbeek F. and Van Hoolst T., 1999c,**"Special Bureau for the Core.", Technical Note of the IERS, ins press.**de Viron O., Bizouard Ch., Salstein D. and Dehant V., 1999,**"Atmospheric torque on the Earth rotation and comparison with atmospheric angular momentum variations.", J. Geophys. Res, 104, B3, pp. 4861-4875.**Herring T.A., Gwinn C.R. and Shapiro I.I., 1986,**"Geodesy by Radio Interferometry: Studies of the Forced Nutations of the Earth. 1. Data Analysis.", J. Geophys. Res., 91, B5, pp. 4745-4754.**Kinoshita H., 1977,**"Theory of the rotation of the rigid Earth.", Celest. Mech., 15, pp. 277-326.**Roosbeek F. and Dehant V., 1998,**"RDAN97: an analytical development of rigid Earth nutation series using the torque approach.", Celest. Mech. Dynamical Astron., 70, pp. 215-253.**Wahr J.M., 1981,**"The forced nutations of an elliptical, rotating, elastic and oceanless Earth.", Geophys. J.R. astron. Soc., 64, pp. 705-727.