Study of the high‐frequency structure of polar motion derived from LAGEOS ranging data
Authors: Caporali Alessandro , Cenci Alberto , Fermi Marco 
Published: February 2008

The spectrum of polar motion at or near 1 cycle per day contains very valuable information. For example, the celestial ephemeris pole of the International Astronomical Union (IAU) 1980 nutation theory has, by definition, no body fixed nor space fixed motions. But the theory is also known to be affected by a nonnegligible error at the annual frequency, so that one expects the nutation error to be visible in body fixed coordinates as a (nearly) diurnal polar motion. In addition, if polar coordinates are determined from satellite tracking data, absence of dirurnal changes of the pole coordinates is a direct consequence of use of a correct dynamical model of the orbit. There is no reason to search for the nearly diurnal free wobble associated to the free core nutation, due to very stringent upper limits recently set by very long baseline interferometry (VLBI) observations. The requirements of dense and uniform data distribution, both temporally and geographically, for constructing meaningful spectra have been, in the past, incompatible with the available data. But uniformily dense data sets are now obtained from laser ranging to the LAGEOS satellite. To investigate the spectrum of polar motion near diurnal frequencies, we have selected six LAGEOS arcs with the criteria that the temporal and spatial distribution of the range data be as uniform as possible with arcs long enough to provide an acceptable spectral resolution. For each of these arcs an accurate ephemeris has been determined using a reduced version of the NASA GEM T1 dynamical model and the IAU 1980 nutation theory. Station coordinates and the three Earth rotation parameters at 1‐day interval were least squares adjusted simultaneously with the six Keplerian parameters, along‐track acceleration, and solar radiation coefficient. Then the orbit and station coordinates were constrained to the previously found values and the pole coordinates estimated at six hourly intervals. The resulting time series, when compared with an independent VLBI determination at 5‐day intervals, show excellent agreement and stability. They also indicate the presence of a diurnal signal. Spectral analysis yields amplitudes of the diurnal signal ranging from 3.8 milliarc seconds (mas) (1 mas = 0.001″) to 1.4 mas, with one exception of 12.8 mas. The signal has positive frequency in all cases, in the sense that the recovered polar motion is counterrotating relative to the Chandler wobble. We examine possible causes of the diurnal signal, such as nonuniform spatial and/or temporal data distribution, orbit mismodeling due to Earth/ocean tides, incorrect choice of the initial vector of state for the orbit, and error in the adopted nutation theory. Our analysis indicates that the diurnal signal, being repeatable and maintaining phase coherence between contiguous independent time series, is unlikely to originate from data distribution but is more probably due, perhaps in different proportions from arc to arc, to a combination of nutation and orbit errors. We show that these two causes are, in principle, separable: the diurnal polar motion associated with nutation has an amplitude and phase independent of the orbit of the satellite, while the diurnal polar motion due to orbit mismodeling varies in amplitude and phase with the orbital inclination and node. The diurnal signal should disappear form the spectra if the analysis is repeated with corrected nutation coefficients and a dynamical model consistent with the corrected nutation theory.