Modeling of nutation and precession: New nutation series for nonrigid Earth and insights into the Earth's interior

Abstract

[1] The analytical formulation of the theories of nutation and wobble reveals the combinations of basic Earth parameters that govern the nutation-wobble response of the Earth to gravitational (tidal) forcing by heavenly bodies and makes it possible to estimate several of them through a least squares fit of the theoretical expressions to the high-precision data now available. This paper presents the essentials of the theoretical framework, the procedure that we used for least squares estimation of basic Earth parameters through a fit of theory to nutation-precession data derived from an up-to-date very long baseline interferometry data set, the results of the estimation and their geophysical interpretation, and the nutation series constructed using the estimated values of the parameters. The theoretical formulation used here differs from earlier ones in the incorporation of anelasticity and ocean tide effects into the basic structure of the dynamical equations of the theory and in the inclusion of electromagnetic couplings of the mantle and the solid inner core to the fluid outer core, though this generalization comes at the cost of making some of the system parameters complex and frequency dependent; it is also more complete, as it takes account of nonlinear terms in these equations, including effects of the time-dependent deformations produced by zonal and sectorial tides, which had been traditionally neglected in nonrigid Earth theories. Among the geophysical results obtained from our fit are estimates for the dynamic ellipticity e of the Earth (e = 0.0032845479 with an uncertainty of 12 in the last digit), for the dynamical ellipticity e f of the fluid core (3.8% higher than its hydrostatic equilibrium value, rather than $5% as hitherto), and for the two complex electromagnetic coupling constants. Our best estimates for the RMS radial magnetic fields at the core mantle boundary and at the inner core boundary, based on the estimates for these coupling constants, are~6.9 and 72 gauss, respectively, when the magnetic field configurations are restricted to certain simple classes. The field strength needed at the inner core boundary could be lower if the density of the core fluid at this boundary or the ellipticity of the solid inner core were lower than that for the Preliminary Reference Earth Model. Our estimate for the resonance frequency of the prograde free core nutation mode, with an uncertainty of $10%, constitutes the first firm detection of the resonance associated with this mode; the period found is $1025 days, double that with electromagnetic couplings ignored. (Throughout this work, ''days,'' referring to periods, stands for ''mean solar days.'') A new nutation series (MHB2000) is constructed by direct solution of the linearized dynamical equations (with our best fit values adopted for all the estimated Earth parameters) for each forcing frequency, and adding on the contributions from the nonlinear terms and other effects not included in the linearized equations. This series gives a considerably better...

Determination of the Earth's pole tide Love number k2 from observations of polar motion using an adaptive Kalman filter approach

“…The result for the imaginary part (0.0030, corresponding to Q = 97) differs significantly from the initial value (0.0036, corresponding to Q = 82). Consequently DyMEG requires a lower damping than proposed by the value for the pole tide Love number provided by the Conventions of the IERS in combination with the (real valued) correction for the effect of equilibrium ocean pole tides following Smith and Dahlen [1981] and Mathews et al [2002]. Up to now no runs have been performed with DyMEG using the alternative ocean pole tide model of Desai [2002] (cf.…”

“…Since PREM is a substantially simplified representation of the real Earth, the accuracy of this value can not be quantified. The contribution of equilibrium ocean pole tides is incorporated by adding a surcharge of 0.044 [Smith and Dahlen, 1981;Mathews et al, 2002]. Consequently the effective pole tide Love number k 2 equals 0.3517 + 0.0036i.…”

Free core nutation resonance parameters from VLBI and superconducting gravimeter data

“…η R and η; see, e.g., Mathews et al 2002). One has η(σ) = T (n) (σ) η R (σ), wherein, neglecting the ICW effects, where the last three bracketed terms express the CW, FCN, and FICN resonance, respectively, with…”

“…The authors interpreted the enhancement of the amplitude of the retrograde annual nutation induced by the resonance in terms of a departure of the core-mantle boundary from its hydrostatic figure. Using an improved theoretical background, Mathews et al (2002) built a nutation model (referred to as MHB) based on a limited number of parameters describing the Earth's interior and adjusted to VLBI data up to 1999. Comparisons of the VLBI nutation time series with this model reveal differences of the order of 200 microarc seconds (μas) in rms.…”

Time stability of the ICRF2 axes

“…This is particularly critical since several studies have used VLBI nutation series to infer interesting physical parameters relevant to the Earth's core and inner core (Mathews et al 2002;Koot et al 2008Koot et al , 2010Koot & Dumberry 2011).…”