On the excitation of the Earth's free wobble and reference frames

In this paper we study the excitation of the Earth's polar motion in connection with problems that are associated with the diversity of reference frames involved in observations and theoretical computations. Thus, following the dynamics of the Earth's polar motion, the kinematics that relates observations from different reference frames are developed. The conventional procedures of studying the seismic excitation of polar motion are then re-examined accordingly — subject constantly to the question: relative to what reference frame? It is concluded that an inconsistency in the reference frames has prevailed in the literature. In particular, it is asserted that the computed change in the polar motion associated with a (sudden) seismic source is in fact what would be observed in Tisserand's mean frame. The latter has no real-world counterpart from the standpoint of observations, which are invariably made with respect to some geographic reference frame. While this inconsistency is indeed far from trivial in a philosophical sense, the resultant discrepancy is small for all practical purposes thanks to the nearly spherical configuration of the Earth.