The effects of the solid inner core and nonhydrostatic structure on the Earth's forced nutations and Earth tides

Recent highly accurate nutation results from very long baseline interferometry (VLBI) disagree with the 1980 International Astronomical Union (IAU) nutation model by about 2 milliarcseconds (mas). Most of the discrepancy is at the retrograde annual frequency, and it has been interpreted as being due to a nonhydrostatic core-mantle boundary (CMB) ellipticity [Gwinn et al., 1986]. The ellipticity affects the eigenfrequency of the free core nutation (FCN) normal mode, predominantly a relative rotation about an equatorial axis between the fluid outer core (OC) and the solid mantle. This interpretation in terms of a nonhydrostatic CMB shape is consistent with inferences from diurnal tidal gravity measurements [Levine et al., 1986; Neuberg et al., 1987]. The theory that this interpretation is based on assumes that the inner core (IC)is a fluid. Furthermore, the Earth is presumed to be everywhere hydrostatically prestressed, and so it is inconsistent to use results from this theory to infer information about nonhydrostatic structure. In this paper, we extend the theoretical results to include the effects of a solid IC, and of nonhydrostatic structure. The presence of the IC is responsible for a new, nearly diurnal, prograde normal mode (for a hydrostatically prestressed Earth, the frequency is (1 – 1/471) cycles per day) that involves a relative rotation between the IC and OC about an equatorial axis. We call this newly modeled normal mode the free inner core nutation (FICN). The FICN causes a perturbation in the prograde semiannual nutation amplitude of close to 0.2 mas, but the contribution to the retrograde annual nutation is only 0.003 mas, not enough to explain the VLBI discrepancy. Its effects on the diurnal Earth tide are negligible. Nonhydrostatic structure affects the eigenfrequency of this mode and causes the nutation and Earth tide amplitudes to depend on IC-OC boundary, CMB, and outer surface topography at all spatial scales. The dependence, though, falls off as the (l - 1)th power of the ratio of the IC radius divided by the OC radius, for the simplified case of a homogeneous, rigid IC and mantle, and homogeneous, incompressible OC (l, here, is the angular order in the spherical harmonic expansion of the boundary shape). For small l, nonhydrostatic effects on the FICN are of the same order as hydrostatic effects for this specialized case. Neither the IC nor the nonhydrostatic terms significantly affect the conclusions about the values of the CMB ellipticity.

[1]  Thomas A. Herring,et al.  Forced nutations of the Earth: Influence of inner core dynamics: 3. Very long interferometry data analysis , 1991 .

[2]  P. M. Mathews,et al.  Forced nutations of the Earth: Influence of inner core dynamics: 2. Numerical results and comparisons , 1991 .

[3]  Thomas A. Herring,et al.  Forced nutations of the Earth: Influence of inner core dynamics: 1. Theory , 1991 .

[4]  J. Wahr,et al.  The possibility of lateral structure inside the core and its implications for nutation and Earth tide observations , 1989 .

[5]  D. J. Doornbos,et al.  Models of the core-mantle boundary and the travel times of internally reflected core phases , 1989 .

[6]  W. Peltier,et al.  Core-mantle boundary topography and whole-mantle convection , 1989 .

[7]  A. Souriau,et al.  Ellipticity and density at the inner core boundary from subcritical PKiKP and PcP data , 1989 .

[8]  J. Neuberg,et al.  Stacking gravity tide observations in central Europe for the retrieval of the complex eigenfrequency of the nearly diurnal free-wobble , 1987 .

[9]  Andrea Morelli,et al.  Topography of the core–mantle boundary and lateral homogeneity of the liquid core , 1987, Nature.

[10]  T. Jordan,et al.  Aspherical structure of the core‐mantle boundary from PKP travel times , 1986 .

[11]  J. Levine,et al.  Gravity tide measurements with a feedback gravity meter , 1986 .

[12]  John M. Wahr,et al.  The effects of mantle anelasticity on nutations, earth tides, and tidal variations in rotation rate , 1986 .

[13]  Thomas A. Herring,et al.  Erratum: Correction to ``Geodesy by Radio Interferometry: Studies of the forced nutations of the Earth, 1, Data Analysis'' , 1986 .

[14]  Thomas A. Herring,et al.  Geodesy by radio interferometry: Studies of the forced nutations of the Earth. II: Interpretation , 1986 .

[15]  Robert W. Clayton,et al.  Lower mantle heterogeneity, dynamic topography and the geoid , 1985, Nature.

[16]  D. L. Anderson,et al.  Preliminary reference earth model , 1981 .

[17]  J. Wahr,et al.  An excitation mechanism for the free ‘core nutation’ , 1981 .

[18]  J. Wahr.  A normal mode expansion for the forced response of a rotating earth , 1981 .

[19]  John M. Wahr,et al.  Body tides on an elliptical, rotating, elastic and oceanless earth , 1981 .

[20]  John M. Wahr,et al.  The forced nutations of an elliptical, rotating, elastic and oceanless earth , 1981 .

[21]  F. A. Dahlen,et al.  The Effect of A General Aspherical Perturbation on the Free Oscillations of the Earth , 1978 .

[22]  Martin L. Smith.  Wobble and nutation of the Earth , 1977 .

[23]  F. Gilbert,et al.  An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra , 1975, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[24]  Martin L. Smith.  The Scalar Equations of Infinitesimal Elastic-Gravitational Motion for a Rotating, Slightly Elliptical Earth , 1974 .

[25]  F. Dahlen.  On the Static Deformation of an Earth Model with a Fluid Core , 1974 .

[26]  Robert A. Phinney,et al.  Representation of the Elastic ‐ Gravitational Excitation of a Spherical Earth Model by Generalized Spherical Harmonics , 1973 .

[27]  D. E. Cartwright,et al.  Corrected Tables of Tidal Harmonics , 1973 .

[28]  W. Farrell.  Deformation of the Earth by surface loads , 1972 .

[29]  F. Dahlen.  The Normal Modes of a Rotating, Elliptical Earth , 1968 .

[30]  K. E. Bullen,et al.  An Introduction to the Theory of Seismology , 1964 .

[31]  A. R. Edmonds,et al.  Angular Momentum in Quantum Mechanics , 1957 .

[32]  J. Wahr,et al.  The earth's forced nutations - Geophysical implications , 1990 .

[33]  E. Ivins,et al.  On the Ellipticity of the Core-Mantle Boundary from Earth Nutations and Gravity , 1988 .

[34]  Véronique Dehant,et al.  Nutations and Inelasticity of the Earth , 1988 .

[35]  Raymond Jeanloz,et al.  Convection and anisotropy of the inner core , 1988 .

[36]  T. Sasao,et al.  A Simple Theory on the Dynamical Effects of a Stratified Fluid Core upon Nutational Motion of the Earth , 1980 .

[37]  C. Counselman.  Geodesy by Radio Interferometry , 1977 .

[38]  J. Gillis,et al.  Classical dynamics of particles and systems , 1965 .

[39]  Walter Munk,et al.  The rotation of the earth , 1960 .