Glaciation-induced perturbations in the Earth's rotation: A new appraisal

Abstract

We revisit the theory and predictions of glaciation-induced perturbations in both the rotation rate of the Earth (or J̇2) and the wander of the rotation pole with respect to the surface geography. The two most common theoretical formulations associated with polar wander driven by the surface loading of a viscoelastic Earth [e.g., Sabadini et al., 1982; Wu and Peltier, 1984] appear to disagree (by one) on the number of rotational normal modes associated with a surface gravitational response having N normal modes. We show, using a generalized theory, that the two formalisms yield essentially equivalent predictions. We next consider a benchmark compárison of recent predictions of present-day polar wander speed due to glacial isostatic adjustment (henceforth GIA). These comparisons confirm the validity of certain previous analyses [e.g., Spada et al., 1992a]. They also reveal that predictions of polar wander speed can be sensitive to an assumption of incompressibility. Previous studies have noted that predictions of J̇2/rotation rate, as a function of lower mantle viscosity, differ significantly in form from analogous predictions of polar wander speed. We investigate these differences by considering the contribution to the predicted anomalies from the individual normal modes of relaxation. We find that the normal mode structure of the J̇2/rotation rate predictions is fundamentally different from that which characterizes the polar wander response, and this difference reflects the distinct physical mechanisms which govern these anomalies. Finally, using a large suite of forward computations, as well as the calculation of a set of Frechet kernels, we investigate the sensitivity of our predictions to variations in the viscoelastic Earth model. We find, for example, that a previously noted sensitivity of polar wander speed predictions to variations in lithospheric thickness is only valid for Earth models with relatively weak lower mantle viscosities (