We have analysed more than four years of data from the Strasbourg superconducting gravimeter to retrieve the period and damping of the nearly diurnal-free wobble (NDFW). The removal of noise spikes is found to be crucial for an accurate determination of tidal-wave amplitudes and phases. A new simple algorithm is derived which allows an analytical solution for the NDFW period and damping using the complex gravimetric factors of three resonant diurnal waves. The results show a huge reduction of the confidence intervals when compared with a previous investigation from a Lacoste Romberg spring meter operated at the same station. Our results are in close agreement with values obtained from two other European superconducting gravimeters. The results are also compared with respect to values inferred from very long baseline interferometry (VLBI) measurements.
A first-order form of the Euler's equations for rays in an ellipsoidal model of the Earth is obtained. The conditions affecting the velocity law for a monotonic increase, with respect to the arc length, in the angular distance to the epicentre, and in the angle of incidence, are the same in the ellipsoidal and spherical models. It is therefore possible to trace rays and to compute travel times directly in an ellipsoidal earth as in the spherical model. Thus comparison with the rays of the same coordinates in a spherical earth provides an estimate of the various deviations of these rays due to the Earth's flattening, and the corresponding travel-time differences, for mantle P-waves and for shallow earthquakes. All these deviations are functions both of the latitude and of the epicentral distance. The difference in the distance to the Earth's centre at points with the same geocentric latitude on rays in the ellipsoidal and in the spherical model may reach several kilometres. Directly related to the deformation of the isovelocity surfaces, this difference is the only cause of significant perturbation in travel times. Other differences, such as that corresponding to the ray torsion, are of the first order in ellipticity, and may exceed 1 km. They induce only small differences in travel time, less than 0.01 s. Thus, we show that the ellipticity correction obtained by Jeffreys (1935) and Bullen (1937) by a perturbational method can be recovered by a direct evaluation of the travel times in an ellipsoidal model of the Earth. Moreover, as stated by Dziewonski & Gilbert (1976), we verify the non-dependence of this correction on the choice of the velocity law.
Linear equations governing the rotation of the Earth are developed for a model with a Maxwell homogeneous mantle and a homogeneous inviscid fluid core having a differential rotation relative to the mantle. We find four eigenfrequencies for the equatorial perturbations in rotation. Two are well known: the rotational nearly diurnal frequency and the Chandlerian frequency with a damping related to the relaxation time of the Earth. The other two frequencies, one being a heavily damped long-period oscillation and the other one zero, are related to the relaxation modes, but are nevertheless coupled with the rotational eigenfrequencies. We investigate the kinetic and deformation energy resulting from both impulsive and time-constant geophysical sources. Using a generalized notation, we derive an analytical solution for the rotations of the Earth and its fluid core due to various excitation sources at the Earth's surface and at the core-mantle boundary. We obtain some results concerning phenomena acting at the CMB which are able to produce a significant shift of the rotation axis.
