This article develops 'broad-band' Liouville equations which are capable of determining the effects on the rotation of the Earth of a periodic excitation even at frequencies as high as semi-diurnal; these equations are then used to predict the rotational effects of altimetric, numerical and 32-constituent spherical harmonic ocean-tide models. The rotational model includes a frequency-dependent decoupled core, the effects of which are especially marked near retrograde diurnal frequencies; and a fully dynamic oceanic response, whose effects appear to be minor despite significant frequency dependence. The model also includes solid-earth effects which are frequency dependent as the result of both anelasticity at long periods and the fluid-core resonance at nearly diurnal periods.The effects of both tidal inertia and relative angular momentum on Earth rotation (polar motion, length of day, 'nutation' and Universal Time) are presented for 32 long-and short-period ocean tides determined as solutions to the author's spherical harmonic tide theory. The lengthening of the Chandler wobble period by the pole tide is also re-computed using the author's full theory. Additionally, using the spherical harmonic theory, tidal currents and their effects on rotation are determined for available numerical and altimetric tide height models. For all models, we find that the effects of tidal currents are at least as important as those of tide height for diurnal and semi-diurnal constituents.
Standard time series analysis techniques have been applied to the homogeneous polar motion data recently published by the ILS‐IPMS [Yumi and Yokoyama, 1980] in order to study some of the more controversial features apparently possessed by the older ILS data. The magnitude and direction of the secular trend unbiased by the presence of harmonics in the data were determined, yielding a rate of polar wander ∼3.52×10−3 arc sec/yr (which extrapolates to ∼0.98°/m.y.) in direction 80.1°W longitude. The long‐period Markowitz wobble, which dominates the retrograde power spectrum of the data, has a signal to noise ratio in that spectrum of 21:1; its period is well‐determined as 31 years. Variations with time of the annual wobble and Chandler wobble were investigated using complex demodulation; the annual wobble was found to undergo relatively insignificant variations in amplitude and phase, in contrast to some analyses of the older ILS data, while the amplitude modulation and 1925–1940 phase change of the Chandler wobble were reconfirmed.
In this work, various formulations describing the excitation of Earth rotation, originating with the effective angular momentum functions of Barnes et al. [1983], are assessed in the context of zero or complete coupling between the core and the mantle. Popular formulations have assumed zero coupling for the length of day component but are ambiguous for polar motion. Versions are developed here for the case of arbitrary core‐mantle coupling, and employed to derive consistent formulations for both extremes of coupling. Even for complete decoupling, all of the formulations can differ from each other noticeably, depending on the treatment of the oceans and the parameter values employed. It is recommended that agencies responsible for archiving atmospheric and other excitation data consider distributing “bare bones,” parameter‐free time series. A possible inconsistency in all formulations to date is the role of the degree 2 solid earth Love number. If the Chandler wobble takes place with a (near) absence of core‐mantle coupling, then prior estimates of the Love number have in reality been measuring its mantle‐only component. By implication the mantle may be much more anelastic at a 14‐month period than had previously been recognized.
Dynamic tidal theory is generalized in order to predict the oceanic response to atmospheric pressure variations. The oceans are found to exhibit distinct dynamic behavior when forced at periods less than 1 week; depending on the harmonic type of forcing, the amplitude of the response can differ by ∼ 20% or more from the static response. Even at roughly 2 months the traditional “inverted barometer” may not be sufficiently accurate for applications in which detection of long‐term sea level trends or vertical crustal motion is the goal. For forcing at periods of order 1 year the oceanic response differs by at most a few percent from the static (not the inverted barometer) response; thus calculations of meteorological excitation of the annual and Chandler wobbles can employ the static approximation without reservation.
Secular polar motion has been recorded in ILS data over the past 75 years, an amount greater by a factor of ten than the 'true polar wandering' deduced from paleomagnetic data. In this work, the possibility that the secular trend is an observational artifact of the continental drift of the ILS stations is directly examined by consideration of several absolute plate velocity models earlier proposed by Minster et al.(1 974), Kaula (1 9 7 9 , and Solomon, Sleep & Richardson (1975). The assumptions underlying those models are discussed; in general, the absolute velocity models are more likely to be valid when geologically short timescales are considered.The corrections to the ILS data due to the stations' motion fail by an order of magnitude to explain the ILS trend; even by taking into account possible plate hyperactivity and non-rigidity, the corrections could explain no more than 30 per cent of the trend. The corrections are small because the absolute plate velocities of North America and Eurasia are small and primarily east-west. Consequently, the rotation pole is undergoing significant motion of its own relative to the surface of the Earth.The Kimura z term found by the ILS observations provides an independent means of estimating the relative motion between Eurasia and North America. It also contains other geophysical information; the 7.5-yr periodicity discovered by Naito & Ishii (1 974) may be widespread.Lastly, tectonically induced changes in the zenith direction, such as at Mizusawa, are probably too small to be detected, contrary to earlier proposals.
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