Wobble and nutation of the Earth

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.