Normal mode study of the Earth's rigid body motions

Abstract

In this paper it is shown that the earth's rigid body (rb) motions can be represented by an analytical set of eigensolutions to the equation of motion for elastic‐gravitational free oscillations. Thus each degree of freedom in the rb motion is associated with a rb normal mode. We study both cases of nonrotating and rotating earth models and show that the rb modes do incorporate neatly into the earth's system of normal modes of free oscillation. The excitation formulae for the rb modes are also obtained, based on normal mode theory. Physical implications of the results are summarized and the fundamental differences between rb modes and seismic modes are emphasized. In particular, we ascertain that the Chandler wobble, being one of the rb modes belonging to the rotating earth, can be studied using the established theory of normal modes.