Modelling the pole tide and its effect on the Earth's rotation

Summary. The pole tide is the response of the ocean to incremental centrifugal forces associated with the Chandler wobble. The tide has a potentially important effect on the period and damping of the wobble, but it is at present not well constrained by observations. Here, we construct both analytical and numerical models for the pole tide. The analytical models consider the tide first in a global ocean and then in an enclosed basin on a beta-plane. The results are found to approach equilibrium linearly with decreasing frequency and inversely with increasing basin depth. The numerical models solve Laplace's tidal equations over the world's oceans using realistic continental boundaries and bottom topography. The results indicate that the effects of the non-equilibrium portion of the deep ocean tide on the Chandler wobble period and damping are negligible.     

A Hamiltonian approach to dissipative phenomena between the Earth's mantle and core, and effects on free nutations

The Hamiltonian formalism was recently applied by Getino (1995a,b) for the study of the rotation of a non-rigid earth with a heterogeneous and stratified liquid core. That earth model is generalized here by including the effect of the dissipation arising from the mantle-core interaction, using a model similar to that of Sasao, Okubo & Saito (1980), which includes both viscous and electromagnetic coupling. First, a solution for the free nutations is obtained following a classical approach, which in our opinion is more familiar to most of the readers than the Hamiltonian treatment. This solution provides a theoretical basis clear enough to study both the qualitative and quantitative effects of the dissipations considered in the hypotheses. The main qualitative features are, besides the delays, that the free core nutation (FCN) suffers an exponential damping, while the chandler wobble (CW) is not damped at first order, by the dissipation considered. The numerical values obtained for the complex compliances agree with the most recent experimental computations.
Next, the problem is studied under a Hamiltonian formalism, and a solution equivalent to the above is obtained. Besides its interest from a theoretical point of view, this formalism is necessary in order to apply canonical perturbation methods in order to obtain analytical nutation series.     

Coseismic and post-seismic signatures of the Sumatra 2004 December and 2005 March earthquakes in GRACE satellite gravity

The GRACE satellite mission has been measuring the Earth's gravity field and its temporal variations since 2002 April. Although these variations are mainly due to mass transfer within the geofluid envelops, they also result from mass displacements associated with phenomena including glacial isostatic adjustment and earthquakes. However, these last contributions are difficult to isolate because of the presence of noise and of geofluid signals, and because of GRACE's coarse spatial resolution (>400 km half-wavelength). In this paper, we show that a wavelet analysis on the sphere helps to retrieve earthquake signatures from GRACE geoid products. Using a wavelet analysis of GRACE geoids products, we show that the geoid variations caused by the 2004 December ( M _w= 9.2) and 2005 March ( M _w= 8.7) Sumatra earthquakes can be detected. At GRACE resolution, the 2004 December earthquake produced a strong coseismic decrease of the gravity field in the Andaman Sea, followed by relaxation in the area affected by both the Andaman 2004 and the Nias 2005 earthquakes. We find two characteristic timescales for the relaxation, with a fast variation occurring in the vicinity of the Central Andaman ridge. We discuss our coseismic observations in terms of density changes of crustal and upper-mantle rocks, and of the vertical displacements in the Andaman Sea. We interpret the post-seismic signal in terms of the viscoelastic response of the Earth's mantle. The transient component of the relaxation may indicate the presence of hot, viscous material beneath the active Central Andaman Basin.     

Geomagnetic effects of the Earth's ellipticity

We analyse the external field generated by a uniform distribution of magnetic susceptibility contained in an oblate spheroidal shell when it is magnetized by an internal magnetic field of arbitrary complexity. The situation is more relevant to the Earth than that of a spherical shell considered by Runcorn (1975a ) (in the context of lunar magnetism), because of the larger flattening of the Earth than that of the Moon. We find that, to first order in the susceptibility, each internal harmonic in a spheroidal harmonic expansion of the magnetic potential generates just one non-vanishing external field coefficient, unlike in the spherical case when all harmonics vanish identically. The field generated is proportional to the susceptibility, thickness of the shell and square of the Earth's eccentricity, and hence it appears that this field amplification mechanism will be very ineffective for the Earth.     

Oceanic excitation of daily to seasonal signals in Earth rotation: results from a constant-density numerical model

Velocity and mass fields from a constant-density, near-global ocean model, driven with observed twice-daily surface wind stresses and atmospheric pressures for the period October 1992-September 1993, are used to calculate oceanic excitation functions for the length of day (LOD) and for polar motion (PM), and results are analysed as a function of the frequency band. Variable currents and mass redistributions are both important in determining oceanic excitation functions. For bands with periods longer than one month, wind-driven variability is the primary cause of oceanic excitation signals. At higher frequency bands, larger deviations from the inverted barometer response occur, and pressure-driven signals contribute more significantly to the variance in the excitation functions. Oceanic LOD excitation is generally small compared to that of the atmosphere, except for the 2-10 day band. At these scales, adding oceanic to atmospheric excitation series does not lead to better agreement with the observed LOD, although this result may be related to data quality issues. With regard to the excitation of PM, the ocean is in general as important as the atmosphere at most time scales. Combined oceanic and atmospheric excitation series compare visibly better with geodetic series than do atmospheric series alone, pointing to the ocean as a source of measurable signals in PM.