Constraints on deep-Earth properties from space-geodetic data

The amplitude of the Earth's nutation driven by a given component of the tidal potential is governed primarily by three parameters pi which are composites of a larger number of 'basic' Earth parameters (ellipticities, compliances, moments of inertia, etc., of the Earth and its core regions). We obtain estimates of the pi by least-squares fitting of nutation amplitudes estimated from very long baseline interferometry (VLBI) data to theoretical expressions based on an analytical formulation of nutation theory which incorporates the role of the solid inner core. We show how the estimates obtained, as well as the overall fit, vary with the ellipticity assumed for the inner core, and examine how the results are affected when otherwise unmodelled effects of ocean tides and mantle anelasticity are taken into account. Considering two anelasticity models, we find that the fit obtained with the use of one of them is noticeably worse than if the other is used or if no anelasticity correction is made. Independent of the corrections applied, the χ2 of the fit is found to be smallest if the ellipticity es of the solid inner core is taken as about half that of the Preliminary Reference Earth Model (PREM). Independent estimates of the ellipticity ef of the fluid core and other basic parameters on which the pi depend cannot be obtained from the estimates of the pi alone. Nevertheless, with certain assumptions that are less restrictive than those hitherto employed in the literature, we find ef to be 5.0% higher than the PREM value if the best-fit value is assigned to es, and 4.7% higher if es = es(PREM);; these values for ef are in accord with the estimate of Gwinn et al. (J. Geophys. Res., 91: 4755-4765, 1986), and correspond to a nonhydrostatic flattening of about 465 m and 435 m, respectively, of the core-mantle boundary. Our parameter estimates have implications for the value of the static part k0 of the second-degree Love number k which seem to be hard to reconcile with information from other sources. Observational estimates of the amplitudes of the 18.6 year nutations are also found to be not satisfactorily matched with theoretical expectations. A careful re-examination of data analysis and theory is needed to resolve these problems