On the variability of the Chandler frequency

Abstract

Abstract. We have estimated the Chandler frequency from a variety of polar motion time series derived from optical and space geodetic data which span various time periods from 1846 through the early 1990s. Estimates of F vary, depending upon which time series is employed, but the variation is not significant when associated intervals of confidence are considered; thus there is no evidence that the true Chandler frequency has varied. Using a maximum likelihood method, our preferred estimate of F is 0.8433 cycles per tropical year (cpy), _+0.003 cpy, or equivalently a period of 433.1 mean solar days (msd), _+ 1.7 msd. Estimates are given on the condition that the Gaussian statistical model of the excitation process is valid, and new approaches which employ observations of the polar motion excitation process should eventually provide better estimates, which may differ from those determined here. IntroductionThe theory of the motion of the Earth around its center of mass is developed in such a way that the motion is separated into two distinct parts which affect the terrestrial and celestial coordinates in different ways. The first of these is a free motion, which exists independently of external forces. Originally There are two issues to resolve when examining whether variability in estimates of F should be interpreted as variability in F. In the first place, the analysis is only meaningful when the component is above the noise level in the data. This condition is met in the case of the Chandler wobble, with a signal amplitude of a few hundred milli arc seconds (mas) and noise levels ranging from 10 mas or more in older optical data to below 1 mas in recent space geodetic data. The second issue is the adoption of an estimation technique firmly tied to the physical aspects of the problem that can provide meaningful statements of confidence, taking into consideration uncertainty introduced by both noise and the finite duration of the data set. The analysis method in this paper, based on the maximum likelihood principle described by Jeffreys [1940, 1968], meets these requirements, as discussed in section 3. 20,439

The Earth’s variable Chandler wobble

“…The theoretical computation of σ c leads to a period of 430.3 days and a quality factor Q = 88 (Mathews et al 2002). The theoretical period is consistent with other estimates of the observed Chandler period based on analyses of polar motion time series (e.g., Vicente & Wilson 1997). However, there is no consensus on the value of Q: depending on the time interval and the analysis method, it ranges from 50 (Furuya & Chao 1996;Kuehne et al 1996) to 180 (Vicente & Wilson 1997;Aoyama et al 2003).…”

“…In the absence of forcing, the CW would have a period of 430.3 days (Mathews et al 2002) fixed mainly by the whole planet's dynamical ellipticity and, more marginally, by mantle and ocean deformabilities, and would lose most of its energy after a few tens of years because of dissipation in the mantle and in the oceans. Observation of the Earth's polar motion, however, reveals a prograde oscillation whose pseudo period can be as far as 20 days from the above value (e.g., Vondrák 1988;Vicente & Wilson 1997). It gains energy at some times (e.g., Danjon & Guinot 1954) so that it never disappears.…”

“…(1) of Vicente & Wilson 1997), and comparing it against the RHS directly given by fluid layer angular momentum time series. Nevertheless, the noise behavior of χ f and χ g around the Chandler frequency and their weak amplitude compared with the seasonal excitation can make this approach difficult.…”

Dynamical Modeling and Excitation Reconstruction as Fundamental of Earth Rotation Prediction

“…This rst order equation is based on the linearisation of the original EulerLiouville equation and is a simple but an adequate approximation of the real system, Munk and MacDonald (1960), Wilson and Chen (1996), Vicente and Wilson (2002), Bizouard and Seoane (2010). In the works of Vicente and Wilson (1997), Spiridonov and Tsurkis (2008), Furuya and Chao (1996) (1) has the form Developed in the works of Wilson (1985), Wilson and Chen (1996), Vicente and Wilson (2002) and improved in Zhou et al (2005) Jereys-Wilson lter is a convenient way to reconstruct the excitation from discrete equally spaced observations…”

Search for the 531-day-period wobble signal in the polar motion based on EEMD

“…Some researchers have suggested that the CW is highly variable with respect to its amplitude (e.g., Carter, 1981Carter, , 1982Höpfner, 2003;Chen et al, 2009Chen et al, , 2013a, some have considered it to have double or multiple frequencies (e.g., Chao, 1983;Pan, 2012), and some have considered its frequency to be invariant (e.g., Okubo, 1982;Vicente and Wilson, 1997;Gross et al, 2003;Seitz and Schmidt, 2005). If the CW is frequency modulated as Carter (1981Carter ( , 1982 suggested, namely, the frequency is governed by the magnitude, it will create an infinite number of sidebands, arranged symmetrically about the carrier and spaced at integer multiples of the modulating frequency (Carter, 1981).…”