Free wobble/nutation of the Earth : a new approach for hydroAppalachian Mountainsstatic Earth models

Abstract

One of the two conventional approaches to formulate a theory to describe the Earth's wobble/nutations is to regard these as among the set of free oscillations of a rotating oblate Earth model. This theory, now standard, predicts the eigenperiods of the Chandler wobble and free core nutation (FCN). Very-long-baseline interferometry and superconducting gravimetry data indicate a significant discrepancy between the inferred and theoretically-predicted values of FCN period. The widely-accepted explanation for this discrepancy is that the core-mantle boundary's ellipticity departs from its hydrostatic equilibrium value. However the standard theory for a hydrostatic Earth model has two mathematical shortcomings, which should be removed before abandoning hydrostatic equilibrium as the reference state. These shortcomings are: (1) the treatment of the governing equations in interior regions is not consistent with the treatment of the boundary conditions at surfaces of discontinuity in material properties; (2) formulation of the boundary conditions does not treat material properties properly. To remove these shortcomings, in this thesis spherical polar coordinates are replaced by a non-orthogonal coordinate system (ro,θ,ø), named after Clairaut. A set of new variables in Clairaut coordinates is introduced, generalizing the conventional notation for a spherical-layered Earth model. The governing equations and boundary conditions, written in these new variables, give a consistent description of free wobble/nutation accurate to first order in ellipticity. A program to compute wobble/nutation eigenperiods has been written, and preliminary numerical results obtained, but either the program still contains errors or truncation is too severe.