Discrete polar motion equations

Summary. A digital filter equation is derived which is appropriate for predicting polar motion from excitation axis displacements, or for inferring the excitation axis changes from observed polar motion. The result differs from previously published equations in its phase response. Two additional equations are presented which are useful if samples of the excitation and polar motion functions are required to be at the same time values.     

Meteorological excitation of the annual polar motion

Summary. Numerous studies have indicated that the annual term in the polar motion cannot be explained in any detail by meteorological/hydrological excitation and no reasonable alternative excitations have been put forward. Part of the problem has been that the hydrostatic adjustment of the oceans to the atmospheric pressure changes has traditionally been computed using the inverse barometer approach. This approach does not properly model the gravitational interaction between the atmosphere and oceans, and the inverse barometer theory is modified in this paper to account for this properly. The information necessary to compute the ocean tide and polar excitation caused by any change in the atmospheric pressure pattern is presented. The results of the application of this theory to two global atmospheric pressure data sets are examined and compared to results of other workers.
It is concluded that the atmosphere is observed well enough to answer the question of the annual excitation of polar motion and it is argued that the ground water excitation is the component with the largest error and remains the chief obstacle to the successful solution of this problem.     

Further evidence for oceanic excitation of polar motion

While the role of the atmosphere in driving variations in polar motion is well established, the importance of the oceans has been recognized only recently. Further evidence for the role of the oceans in the excitation of polar motion is presented. To estimate the equatorial excitation functions, χ ₁ and χ ₂ , for the ocean, we use velocity and mass fields from a constant-density ocean model, driven by observed surface wind stresses and atmospheric pressure, for the period 1993–1995; comparison with similar functions derived from a more complex density-stratified ocean model indicates the effectiveness of the simple constant-density modelling approach. Corresponding atmospheric excitation functions are computed from NCEP/NCAR re-analyses. Results indicate significant improvements in the agreement with the observed polar motion excitation when the simulated oceanic effects are added to atmospheric excitation. Correlations between the polar motion and the geophysical signals at periods of 15–150 days increase from 0.53 to 0.80 and from 0.75 to 0.88 for χ ₁ and χ ₂ , respectively. The oceanic signals are particularly important for seasonal variations in χ ₁ (correlation increases from 0.28 to 0.85 when oceanic excitation is included). A positive impact of the oceans on more rapid polar motion is also observed, up to periods as short as 5 days. The sensitivity of the results to different forcing fields and different amounts of friction in the oceans is also discussed.     

Gravitational torque on the inner core and decadal polar motion

A decadal polar motion with an amplitude of approximately 25 milliarcsecs (mas) is observed over the last century, a motion known as the Markowitz wobble. The origin of this motion remains unknown. In this paper, we investigate the possibility that a time-dependent axial misalignment between the density structures of the inner core and mantle can explain this signal. The longitudinal displacement of the inner core density structure leads to a change in the global moment of inertia of the Earth. In addition, as a result of the density misalignment, a gravitational equatorial torque leads to a tilt of the oblate geometric figure of the inner core, causing a further change in the global moment of inertia. To conserve angular momentum, an adjustment of the rotation vector must occur, leading to a polar motion. We develop theoretical expressions for the change in the moment of inertia and the gravitational torque in terms of the angle of longitudinal misalignment and the density structure of the mantle. A model to compute the polar motion in response to time-dependent axial inner core rotations is also presented. We show that the polar motion produced by this mechanism can be polarized about a longitudinal axis and is expected to have decadal periodicities, two general characteristics of the Markowitz wobble. The amplitude of the polar motion depends primarily on the Y ¹₂ spherical harmonic component of mantle density, on the longitudinal misalignment between the inner core and mantle, and on the bulk viscosity of the inner core. We establish constraints on the first two of these quantities from considerations of the axial component of this gravitational torque and from observed changes in length of day. These constraints suggest that the maximum polar motion from this mechanism is smaller than 1 mas, and too small to explain the Markowitz wobble.     

Refined correlations between atmospheric and rapid polar motion excitations

In this work we employ Monte Carlo experiments to explore reports by others of a statistically significant correlation between atmospheric angular momentum variations and polar motion on timescales of days to months. Our experiments verify that the correlation between atmospheric and geodetic excitation is statistically different from zero at the 0.997 confidence level, and demonstrate that the correlations improve with more recent recreations of the older data sets. Additional Monte Carlo experiments reveal that, during the previous decade, about 60 per cent of the atmospheric excitation was effective in exciting rapid polar motion, and nearly 80 per cent of the geodetic excitation was atmospheric in origin on these timescales; with the older data sets, barely 50 per cent of the geodetic excitation could be ascribed to an atmospheric origin. Possible sources of the remaining polar motion excitation are briefly discussed. Our work implies that simply subtracting atmospheric angular momentum from geodetic data may not be the best way to remove the atmospheric contribution. We also present the first correlation results employing atmospheric excitation data corrected for the dynamic response of the oceans to barometric pressure forcing.     

A new derivation of the displacement potentials for motion in a homogeneous isotropic elastic medium

Summary. We give a derivation of the displacement potentials and the wave equations which they satisfy. The derivation is similar to one given by Richards but is more general and yields explicit formulas for the source terms. This generality is retained when the moment tensor representation of the source is used. Formulas for the source terms are given in both spherical and cylindrical coordinate systems and are evaluated for the particular case of a point source with second order moment tensor.