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

Abstract

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.