Spectral analysis of multi-year GNSS code multipath time-series

In the presented study multi-year time series of changes in the L1 pseudo-range multipath are analysed. Data from 8 stations of the EUREF Permanent Network (EPN) were used in the study. Periodic components present in the signal and their stability over time were analysed. Also, the type of background noise was determined, based on the spectral index. In some cases, the presence of weak components with a 1/2 and 1/3 of the Chandler period has also been found. Time-frequency analysis shows that periodic signals are not stationary in most of the examined cases, and particular signal components occur only temporarily. The analysed signals were characterised by pink noise in the lower frequency range and by white noise for higher frequencies, which is also characteristic for time series of coordinates obtained from GNSS measurements.

Theories of Polar Motion from Tisserand to Poincaré (1890 – 1910)

The discovery by Seth C. Chandler (1891) that the motion of the pole (the reality of which had been established by K.F. Küstner and by the simultaneous latitude observations at Honolulu and Berlin by German astronomers) resulted from two components i.e. a free circular motion with a period of 427 days and a forced elliptical motion with a period of 365.25 days, raised considerable interest in the scientific community of astronomers and geophysicists.The celebrated Mécanique Céleste of Tisserand (1890) had been published just one year before at a time when doubts still persisted and arguments could be presented in favor of the fixed pole. Starting with Tisserand’s arguments, we describe in this paper the impact of the successive contributions by A. Greenhill, S. Newcomb, Th. Sloudsky, S. Hough, G. Herglotz, A. Love, J. Larmor and H. Poincaré to the solution of the problems raised by the Chandler period.The lines of reasoning taken by these eminent scientists were rigorously correct so that, after about one hundred years, contemporary researchers, who benefit from a far better knowledge of the inner structure of the Earth and are able to take advantage of modern computing power, do not contradict any of their conclusions and instead refine them with an accuracy which was not imaginable one century ago.

Excitation of the Chandler Wobble

The redistribution of air and water masses between the Pacific and Indian oceans during the El Niño/Southern oscillation (ENSO) changes the components of the Earth’s inertia tensor and shifts the position of the pole of the Earth’s rotation. The spectrum of the ENSO has components with periods of about 6, 3.6, 2.8, and 2.4 years. These periods are all the multiples of the Chandler period T = 1.2 yr. and the principal period of nutation 18.6 yr. A nonlinear model for the Chandler polar motion has been constructed based on this empirical fact. In this model, the ENSO excites the Chandler polar motion by acting on the Earth at the frequencies of combinative resonance. At the same time, the Chandler polar motion induces a polar tide in the atmosphere and the World Ocean, which orders the ENSO. As a result, the dominant components in the noise spectrum of the ENSO are those with the periods indicated above.

On the Chandler periodicity (Polar Motion, LOD and Climate)

The 14-month Chandler period is associated with the free nutation of the Earth about its spin axis. The observed value of the Chandler period comes usually from the analysis of astronomical series of polar motion data as well as from superconducting gravimeter measurements. At the observation level a periodicity of about 420–440 days also was noticed in microseismic activities. Recently we found evidence of a signal with period similar to the Chandler one in the Sardinia rainfall time series.

Dissipation and Ellipticity of the Chandler Wobble

The Chandler wobble, one of the main feature of the Earth’s polar motion, is related to the properties of the mantle and liquid core as well as the mobility of the oceans. The equilibrium pole tide and mantle anelasticity both lengthen the Chandler period, moreover, the former imposes a slight ellipticity on the pole path, and the latter is responsible for the wobble energy dissipation. On the basis of the perturbation principles, we derive the theoretical Qω of the Chandler wobble, assuming that the wobble energy is totally dissipated within the mantle. The theoretical ellipticity and orientation of the semimajor axis of the Chandler wobble path for an anelastic Earth are given. Compared with the results for the elastic Earth, the effect of mantle anelasticity does not change the wobble ellipticity significantly, but slightly changes the orientation of the semimajor axis in the opposite direction. This paper has also proved that the effect of the Earth’s 3-axis feature on the wobble ellipticity is only about 19% of that of the equilibrium pole tide. Analysis of the polar motion data obtained by using modern geodetic techniques shows that the observed ellipticity and orientation of the semimajor axis agree with the theoretical results. We can deduce that the pole tide in the globe should be close to equilibrium.

Nature and Properties of the Chandler Motion and Mechanism of its Damping and Excitation

The analytical studies of the Chandler motion of the Earth’s pole on the basis of the special approach to the problem, using the canonical and noncanonical equations in the Andoyer elastic variables (Barkin, et al. 1995; Barkin, 1996; in press) have been fulfilled. The Earth is considered as an isolated celestial body with the anelastic (in general case) external envelope (the mantle) and an invariant central part (the core).The interpretation of the Chandler motion of the body, deformed by its own rotation, was given in the case of an elastic envelope. It was shown that the body rotates as a fictitious rigid body with different moments of inertia. The analytical solution of the problem let us explain the next properties of the motion of the deformable bodies: 1) observed period of the Earth’s polar motion; 2) ellipticity of the pole trajectory and difference of the eccentricities of the Chandler and Euler motions; 3) nonuniform velocity of the counter-clockwise polar motion along the Chandler ellipse; 4) orientation of this ellipse (its minor axis is located in the meridian plane, at 14.5 W degrees).The influence of the dissipation on the damping of the Chandler polar motion was studied. The analytical solution of the problem was obtained for the simplest treatment of the delay of the tides caused by the Earth’s rotation (Getino & Ferrándiz 1991; Kubo, 1991). This model explains the characteristic behaviour of the amplitude of the Chandler motion in the periods 1905–1920, 1943–1960 (Vondrák, & Cyril, 1966). The excitation of the Chandler motion can be explained by the upper and lower envelope displacements (Barkin, 1999) with Moon-Sun forced attraction with a period of 412 days, close to the Chandler period.