Maximum likelihood estimates of polar motion parameters

Abstract

IntroductionThe frequency Fc and quality factor Qc of the Chandler wobble, the Earth's free nutation with a nearly 14 month period, are of geophysical interest because they provide information about the Earth's elastic and anelastic properties at a frequency well below the seismic band. Smith and Dahlen [1981] provide a thorough review of the relationships between Fc, Qc and the Earth's physical properties.Estimates of Fc and Qc are made from observations of polar motion, the movement of the rotation axis with respect to geographical coordinates. In this study we use the monthly polar motion series of the Intemational Latitude Service (ILS) [Yumi and Yokoyama, 1980], for the period January 1900 through December 1978, with supplementary data for the period 1979-85. The ILS data form the longest available series that has been reduced in a homogeneous way, and should provide the most reliable estimates. For the period 1979-85, both the Satellite Laser Ranging (SLR) data [BIH Annual Reports] and optical astrometry data [International Latitude Observatory of Mizusawa (ILOM)] are available. We smoothed and then interpolated both SLR and ILOM series with a cubic spline to obtain pole positions at the same intervals as the ILS series. The results from the combined ILS/SLR and ILS/ILOM series were essentially identical, and the remainder of this paper will refer to the results obtained with the ILSflLOM series. We use estimators that were developed by Jeffreys in two papers appearing in 1940 and 1968. The symbols Fc and Qc denote the true values of the polar motion parameters, while F and Q indicate estimates. We refer to the estimator from the 1940 paper by the Roman numeral I, and to estimates derived from it as F(I), Q(I). Similarly, F(II) and Q(II) refer to the estimators in Jeffreys' 1968 paper. Both I and II were developed from maximum likelihood arguments, assuming that a Gaussian random process is the cause of polar motion near the Chandler frequency. While this may not be correct, Monte Carlo experiments demonstrate that it is probably not a critical assumption, particularly for estimator II. The Monte Carlo experiments also permit an evaluation of estimator bias and variance in the presence of noise. The discrete polar motion equation [Wilson, 1985] is the foundation for understanding Jeffreys' maximum likelihood estimators. This equation relates time samples of pole position, M, to time samples of the excitation axis position, X. Using the complex pole coordinate description in which the real part is associated with motion along the

On the variability of the Chandler frequency

“…Our preferred value of F is that from EOP93C010092, the longest series which is reasonably homogeneous. The value obtained (0.8433 _+ 0.003 cpy) equivalent to a period of (433.1 mean solar days (msd) +__ 1.7 msd) is fully consistent with the results reported previously by Wilson and Vicente [1980, 1981, 1990] for the ILS series, which comprises a subset of the data used to obtain EOP93CO1. procedures which are not fully consistent.…”

Hydrological and oceanic effects on polar motion from GRACE and models

“…If there were no excitation sources, however, the Chandler wobble would freely decay with a time constant of about 68 years to the minimum rotational energy state of rotation about the figure axis. Therefore, since the CW was first discovered in 1891, excitation sources or mechanisms have been investigated by many authors [Munk and MacDonald, 1960;Wilson and Haubrich, 1976;Wilson and Vicente, 1990;Furuya et al, 1996;Kuehne et al, 1996;Gross, 2000]. Atmospheric processes (wind and surface pressure variations) were the initial proposed mechanisms to excite the Chandler wobble.…”

“…where P = Px-i Py is the polar motion vector, s c = 2pF c (1 + i/2Q), Fc is the Chandler wobble frequency (about 0.8432 cycle/yr), Q = 179 is the quality factor determined by the Earth's physical properties [Wilson and Vicente, 1990] and its reciprocal (1/Q) is the associated dissipation factor, and c = (c 1…”

“…[18] Another significant component of the polar motion is the Chandler wobble (CW), which is a resonance in the Earth's rotation with a period of about 433.0 d and a quality factor Q of 179 [Wilson and Vicente, 1990] because the Earth is not rotating about its figure axis [Munk and MacDonald, 1960;Eubanks, 1993]. If there were no excitation sources, however, the Chandler wobble would freely decay with a time constant of about 68 years to the minimum rotational energy state of rotation about the figure axis.…”

Importance of Wind for the Excitation of Chandler Wobble as Inferred from Wobble Domain Analysis.

“…We integrated both the inferred and AAM excitations from the beginning date of available AAM data with the same Chandler period and Q as those assigned in calculating the inferred excitation. In the following, we fix the Q value to be 179 (Wilson and Vicente, 1990; see also, Furuya and Chao, 1996), while the Chandler period is tuned in order to achieve the best agreement with AAM-induced wobble. For numerical integration, we modified the discrete form of equation (2a) in Wilson (1985) as follows: (6) where ‡™ is the sampling interval (1 day Table 1).…”