Rheological models and interpretation of postglacial uplift

SUMMARY This paper investigates four generalized Maxwell bodies (GMBs) and the classical Maxwell body (CMB) with respect to their potential to explain postglacial uplift. The GMBs are the Lomnitz body, defined by a logarithmic creep law, the Q power‐law body, defined by a power‐law dependence of the quality factor on frequency, the Caputo body, defined by a special stress‐strain relation with memory, and the Burgers body. The Burgers body is a 4‐parameter model, the other GMBs have 3 and the CMB has only 2 parameters. Theoretical uplift curves are calculated for simple space‐time models of the Canadian and Fennoscandian deglaciations, and hedgehog inversion yields the successful model parameters. The GMBs explain the data better than the CMB. The parameters of the Burgers body are only rather weakly constrained because of trade‐offs among them. From the success of the GMBs we conclude that long time‐scale transient creep is a possible rheological behaviour of mantle rocks. Viscosity extrapolation from the time constant of postglacial uplift, about 10 ka, to the time constant of mantle convection, roughly 100 Ma, is made with the effective viscosity and yields approximately 10 22 Pas ( Q power‐law body), 10 23 Pas (Caputo body) and 10 25 Pas (Lomnitz body). Hence, postglacial uplift does not strongly constrain the long time‐scale mantle viscosity. It provides only a lower bound , about 10 21 Pas; this value follows from data interpretation with the CMB model in which steady‐state creep is present alone. Rayleigh number estimates for whole‐mantle convection are clearly supercritical for the CMB, the Q power‐law body and the Caputo body, but only about critical or even subcritical for the Lomnitz body. Both postglacial uplift and mantle convection is satisfactorily explained by the CMB, the Q power‐law body and the Caputo body.