Body tides on an elliptical, rotating, elastic and oceanless earth

Abstract

Summary. The Earth's deformation caused by the luni-solar tidal force is defined as the 'body tide'. We compute the effects of the Earth's rotation and elliptical stratification on the body tide for a number of modern elastic structural models. Rotation and ellipticity within the mantle are found to affect tidal observations by about 1 per cent. A consequence is an improved estimate for the fluid core resonance in the diurnal tidal band. Agreement between results for the different structural models is very good. As a result, the results computed here can be used to model the tidal effects of a globally averaged, oceanless, rotating, elliptical and elastic earth to an accuracy of at least one part in 300. The combined gravitational force of the Sun and Moon on the Earth consists of a dominant portion which affects the Earth's orbit in space, plus a smaller remainder: the luni-solar tidal force. Although the tidal force exerts no net force on the Earth, it induces a response consisting of deformation (the body tide), changes in the Earth's angular orientation in space (forced precession and nutation), and changes in the Earth's rotation rate. We will describe, below, a simultaneous computation of the Earth's deformational and rotational tidal response which systematically includes the effects of the Earth's rotation and elliptical material stratification. Since the deformation is observed primarily by geodesists and the Earth's rotation by astronomers, it is conventional (and useful) to separate the solution into deformational and rotational components and to consider these terms separately. We will primarily be concerned in this paper with the body tide. The motivation for the present work is the hope that accurate observations of the body tide can improve our knowledge of the Earth's structure and dynamical behaviour. This question is likely to become increasingly important in light of the recent, rapid development of precise geodetic techniques. Seismological and astrometric observations indicate that the