Love numbers for diurnal tides: relation to wobble admittances and resonance expansions

Abstract

Wobble-related centrifugal and gravitational forces result in contributions to the Love numbers that are proportional to wobble admittances of the Earth and its core regions. We examine the nature of such forces on the basis of the recent work of Buffett et al. (1993) and present expressions relating the Love numbers to the wobble admittances. These expressions are qualitatively different from those of Sasao et al. (1980). By using a semianalytic theory for wobbles, we obtain a corresponding theory for the Love numbers and resonance formulae to describe their frequency dependence in the diurnal tidal band. In this formulation, the Earth's properties enter through a set of basic parameters (ellipticities, compliances, etc., of the whole Earth and its core regions). This analytic structure offers, for the first time, possibilities for the estimation of such parameters from data on nutation amplitudes and tides in a mutually consistent fashion. It also assures that use of a "modified preliminary reference Earth model (modifed PREM)" set of values for the basic parameters, which yields a free core nutation period in agreement with estimates from very long baseline interferometry (VLBI) data, will lead to resonances in the Love numbers at the corresponding nearly diurnal free wobble (NDFW) eigenfrequency. No other method is currently available for placing the resonance at the observed frequency. We present and discuss tables of values of (1) the parameters occurring in the resonance formulae for the wobbles and the Love numbers and (2) the wobble admittances and the Love numbers at various frequencies in the diurnal band, all computed using modified PREM in an approximation which takes account of all wobble-related effects but treats the Earth otherwise as spherical and static. Such detailed information on the admittances of wobbles, of the outer and inner cores, in particular, is not available elsewhere in the literature. We present comparisons of other workers' and our values for the Love numbers, to help to elucidate the sources of the differences among them. The influence of the NDFW eigenfrequency implied by the model used is notable: for the ψ₁ tide which is nearest this eigenfrequency, we obtain k = 0.5382, h = 1.0812, and l = 0.0687, while the Wahr (1981b) values, for model 1066A, which has an NDFW eigenfrequency differing significantly from the VLBI estimate, are k = 0.466, h = 0.937, l = 0.0736.