Rotationally consistent Love numbers

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SUMMARY The Love number k2 at a 14-month period is used to characterize the deformation of the solid earth during the Chandler wobble. Traditionally, the value of k2(CW), ∼0.31, is inferred from observations of the Chandler wobble period, after the effects of the oceans have been subtracted. However, during wobble the core is almost completely decoupled from the mantle; consistency requires that we view that inference as a mantle-only value of the Love number. This in turn implies that k2= 0.35, almost 13 per cent higher than the traditionally accepted value. The use of rotationally consistent Love numbers leads to equations for predicting the effects of a given rotational excitation that are distinctly different from previous versions. Furthermore, formulations of the excitation itself—such as the ‘effective angular momentum functions’ of Barnes et al.—are seriously modified, with the excitation functions up to ∼14 per cent larger. Rotationally consistent Love numbers imply that the solid earth is much more anelastic at a 14-month period than previously considered. Popular ‘constant Q’ and ‘power-law Q’ models of anelasticity are unable to simultaneously fit observations of k2 at seismic, nine-day, and Chandler frequencies. Alternative anelastic relaxation models such as those proposed by Ivins hold much more promise.