Flexural models of continental lithosphere based on the long-term erosional decay of topography

Abstract

The most easily observed geophysical characteristic of continents is their surface topography. Topographic power in the spectral range 1000-100 km has been computed for North American geological provinces and is found to decrease systematically as the tectonic age of the underlying crust increases. These data have been quantitatively modelled in terms of topographic erosion and stress relaxation within the continental lithosphere through geological time spans. The lithosphere is treated as a thin (Maxwell) viscoelastic plate which deforms flexurally in response to the vertical surface loads of topography and its erosion. Effective rheological model parameters are flexural rigidity D, a measure of the lithosphere's elastic strength, and viscous relaxation time constant τ, a measure of its viscosity. Erosion is assumed to occur at a rate linearly proportional to the height of topography at any given time, the proportionality being determined by the erosion time constant ∂. The models are constructed in space and time frequency domains using simple linear systems theory. Two loading schemes are considered. Model 1 assumes that a flexurally competent lithosphere is suddenly loaded by topography which subsequently erodes whereas model 2 ignores the emplacement and erosion of topography during orogenesis when the lithosphere is thermally activated and considers only the load effected by erosion beginning some time later when the lithosphere has cooled and strengthened. Both models predict that the remnant topography of very old regions such as the Canadian Shield can be maintained, in fact is favoured, by a viscoelastic lithosphere with τ as small as 1-10Ma. The continued existence of such topography does not necessarily imply significant long-term lithospheric strength. Model 1 results indicate low values of the flexural rigidity D, ∼ 1021-1022Nm, which are interpreted to characterize not so much presentday D but that which was effective when topography was formed. Model 2 more successfully reproduces the data and constrains the product ∼D to values, ∼ 1024-1025Nm Ma, which compare very favourably to those found from studies of individual loads on continental lithosphere. The model results show that the erosion time constant τ is probably wavenumber-dependent and falls in the range 200–400 Ma for the topographic wavelengths under consideration.