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The long term rheological behaviour of the continental lithosphere is investigated by means of isostatic response functions Q(k), gravity normalized by topography in the wavenumber k domain, and by the erosional decay of continental topography.

Q(k) has been modelled in the past assuming time-independent topographic loads and lithospheric rheology. New models are developed which describe the response of a thin (Maxwell) viscoelastic plate lithosphere to topography which erodes. The rate of erosion is assumed to be linearly proportional to the topography remaining at any given time. Model parameters are D, the plate`s flexural rigidity; , its viscoelastic relaxation time constant; and , the erosion time constant of harmonic topography. Model predictions of time-dependent Q(k,t) and power spectra of continental topography are compared to calculations of each for several North American tectonic provinces.

The results show that a viscoelastic lithosphere with as small as 1-10 Ma can support the remnant topography of very old regions such as the Canadian Shield. In general, viscoelastic models provide better agreement than elastic models with the observed topography decay data. The results do not tightly constrain parameters D and but possible values are comparable with those based on other studies. appears to be wave-number dependent, lying in the range 200-400 Ma for topographic wavelengths in the range 100-1000 km.

The observed response function Q(k) suggest that stresses induced by erosion through time are almost completely relaxed at the present, a result which precludes pure elasticity as a viable lithosphere rheology. The effects of erosion on Q(k) can explain why previous analyses have returned values of D lower than those based on other kinds of data.

One feature of the Canadian Shield Q(k) not explicable in terms of the rheological models is its directional anisotropy. A model in which the lithosphere is loaded at its base by forces associated with small scale upper mantle convection as well as by surface topography is proposed as a possible explanation.

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