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A matter of first-order importance in understanding the evolution of the topography of continents is to evaluate the law that controls large-scale erosion independently of tectonic processes. Many studies have constructed models in which surface erosion plays an important feedback role to tectonics. However, it is difficult to evaluate quantitatively the nature of the erosion process from geological phenomena involving tectonics, because the latter typically convolves various controlling factors such as rheology (and the temperature and pressure conditions of the lithosphere), tectonic force, and the (un)loading caused by sedimentation and erosion. Fischer [Nature, 417, 933-936, 2002] showed that the ratio (R) of the surface elevation (h) to the thickness of crustal root (m) of major mountain belts on the Earth's continents decreases systematically with time after the last major thermotectonic event. Although Fischer invoked phase changes in the lower crust to explain the observed behaviour of R, it may possibly also be explained without considering any tectonic process, as such regarding it only as a product of surface erosion and concomitant isostatic rebound.
In this study, using a local isostasy model, we attempt to infer the long-term erosion rate of mountain belts directly from R. One advantage of this approach is that only the relative movements of the surface and Moho are considered and broad, regional vertical motions (that may involve thermal processes, for example) affecting continents can be neglected. A quantitative investigation of the potential effect of phase changes in the locally thickened crust due to thermal relaxation and pressure decrease during erosional unloading, as suggested by Fischer, leads us to conclude that the temporal evolution of R, as a first-order approximation, is primarily controlled by surface erosion and its related rebound only. In such a case, it is possible to place constraints on the erosion process without considering tectonic influences. That R is observed to decrease with time and that observed m (crustal root) has long-term viability, given the adopted simple isostasy model, is assured as long as the density of the lower crust is greater than that of the upper crust. This, in turns, allows the evaluation of a long-term erosion rates from the observed data and leads us to investigate models where the proportionality between elevation and erosion rate is linear as well as non-linear.
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