Compressible rotational deformation

In recent years a number of studies have investigated the influence of compressibility on geophysical observables such as postglacial rebound deformation rates and the geoid. Some of these studies indicate that long-term signatures such as the geoid might be sensitive to compressibility. As both load relaxation and tidal-effective relaxation of the equatorial bulge are operative in a dependent way, polar wander can potentially be more sensitive to compressible rheologies if the interference between the two relaxation mechanisms is constructive. This has motivated us to study the influence of compressibility on true polar wander by means of spherical, laterally homogeneous, self-gravitating analytical earth models. As we wish to study both short-term rotational changes and polar wander on geological time-scales, we employ a Maxwell viscoelastic model instead of a Newtonian viscous model. The latter is commonly used in geoid modelling. The purpose of this paper is to concentrate on the basic physical aspects of the differences between compressible and incompressible rotational deformation, rather than applying the procedures to fine-graded multi-layered PREM models with realistic forcing functions. An important issue of our method concerns the analytical instead of numerical way of solving the differential equations by the propagator matrix method. Compressible viscoelastic relaxation has usually been treated numerically until now. The results show that homogeneous earth models do not have significant differences on long time-scales between compressible and the corresponding incompressible cases. Compressibility introduces a denumerably infinite set of short-time relaxation modes. The relaxation times of these dilatation modes can be approximated analytically. Two-layer core-mantle models show relatively large differences between incompressible and compressible Maxwell rheologies. Simplified models of true polar wander triggered by Heaviside loads show that differences of several tens of per cent between incompressible and compressible Maxwell rheologies are possible. True polar wander is decreased in the compressible case on both short and long time-scales, which means that smaller viscosities are required to explain polar-wander measurements than in the incompressible case.