Normal modes of the viscoelastic earth

Summary A uniformly valid linear viscoelastic rheology is described which takes the form of a ‘generalized’ Burgers' body and which appears capable of reconciling the behaviour of the Earth's mantle across the complete spectrum of geodynamic time‐scales. This spectrum is bracketed by the short time‐scales of body wave and free oscillation seismology on which anelastic effects are dominant, and the long time‐scale of mantle convection on which the Earth behaves viscously. The parameters of the model which control the viscous response are fixed by post‐glacial rebound data whereas those which govern the anelasticity are to be determined by fitting the model to observations of seismic Q. The paper is concerned primarily with a discussion of the normal mode spectrum of the Earth as a generalized Burgers' body. Focusing upon the homogeneous model, it includes an initial analysis of the accuracy of first‐order perturbation theory as a method of calculating the respective Qs of the elastic gravitational free oscillations. Also considered are the quasi‐static modes of relaxation which only exact eigenanalysis can reveal. The importance of these modes is assessed within the context of a discussion of the effect of viscoelasticity upon the efficiency of Chandler wobble excitation.