Wobble and nutation of the Earth

Summary Elastic‐gravitational normal mode theory is used to study theoretically the free wobble and free nutation of a suite of geophysically plausible rotating slightly elliptical earth models. We principally find that observations of wobble eigenfrequencies are not likely to constrain strongly the structure of the Earth's fluid core, that the results of our calculations, together with Dahlen's estimate of the ocean correction, yield the observed Chandler wobble period within its observational uncertainty and that estimates of wobble excitation by earthquakes based on quasi‐static calculations of the Earth's response are correctly computed. Also we summarize several analytical treatments of both wobble and internal core modes of rotating Earth models and use that information to assess analytically and numerically the approximate theory exploited here. We show that the approximation we use is valid for the Earth's major free wobbles but not for studying internal modes in the fluid core.summary By exploiting the existence of analytic solutions to certain members of the general class of problems of interest to us here, we have been able to explore the range over which the numerical theory used here is valid. In particular, the theory is adequate to describe the major mantle wobbles of the Earth – namely the Chandler wobble and the nearly diurnal free wobble. It is also adequate to describe the response of the Earth to tidal potentials, at least to the extent that ‘internal’ modes in the fluid core do not participate in the Earth's response. The theory has been demonstrated to be sorely inadequate for two other classes of normal modes: internal core modes and the Chandler Wobble of the solid inner‐core. In both cases the failure of the theory is associated with the inability of our finite representation to adequately represent motion in the fluid. These failures are not evident from inspection of the numerical results alone; their detection was only made possible by the availability of analytic solutions. A corollary of these results is that recent published calculations of internal core modes for rotating geophysically plausible earth models by Crossley (1975) and Shen & Mansinha (1976) are almost surely invalid. The theoretical basis for those studies, like the one exploited here, is wholly inadequate to describe internal core modes.