Generalized Maxwell bodies and estimates of mantle viscosity

Summary. Three generalized Maxwell bodies (GMBs) are discussed whose transient-creep properties make them interesting alternatives t o the classical Maxwell body (CMB) in interpretations of post-glacial uplift. The first GMB is defined by its relaxation spectrum, the second by its quality factor and the third by its stress-strain relation. In each case the GMB is characterized by three parameters only: the unrelaxed modulus, the steady-state viscosity or a time constant, and a dimensionless parameter representative of the transient-creep properties. This is one parameter less than needed for the Burgers body which has mainly been used so far to model transient creep. The GMB models are described in some detail and numerical results for their viscoelastic moduli, relaxation spectra, and relaxation and creep functions are given. For practical applications it is most important that the viscoelastic moduli can be calculated a t arbitrary frequencies. In the second part of the paper post-glacial-uplift data from Canada and Fenno-scandia are interpreted with the GMB rheologies described. Otherwise the Earth model used and the assumptions on the form and history of the ice load are very simple. Effective viscosities of the successful models, i.e. inverse creep rates a t times representative of mantle convection, fall in the range lOZ2-lOz4P (1O2'-1OZ3Pa s) and are in part considerably larger than mantle viscosities derived under the assumption of a CMB rheology. Hence. post-glacial-uplift data constrain mantle viscosity less than has been believed until recently. Key words: viscoelasticity, rheology, mantle viscosity, post-glacial uplif