Can we Predict Hidden Tectonic Shortening at Plateau Margin?

We study coupling between lithospheric-scale tectonic shortening and surface erosion in the model setup which includes rheologically weak plateau and relatively strong indenting foreland. The question we address is how much of the tectonic shortening is transmitted to the plateau depending on lithospheric rheology and erosion rate. In the modelling we employ a thermo-mechanical lagrangian explicit material-point code which incorporates highly nonlinear visco-elasto-plastic rheology as well as surface processes in form of fluvial and landsliding erosion. We show that at low fluvial erosion rates, plate convergence is effectively transmitted into tectonic shortening inside the plateau region. In contrast, when erosion rate is high, the entire convergence could be completely taken by a single exhumation fault at the plateau rim. We call this hidden shortening. We studied a full spectrum of intermediate cases when convergence is partly transmitted into the plateau and partly taken by the exhumation channel, varying crustal rheology, convergence rate and erosion rate. Apparent and hidden shortening as well as denudation rates were measured by tracking of material tracers. Model results allow us to quantify relationship between amount of hidden shortening (relative part of the shortening rate transmitted to the plateau) from one side and ratio of exhumation and convergence rates from another side. In first approximation this relation does not depend on lithospheric rheology or convergence rate and therefore can be used in various tectonic settings. This relation could be used in two ways. When exhumation rates are known along the orographic front, amount of hidden shortening could be predicted. Alternatively, when the amount of shortening taken by the exhumation front is known, the average exhumation rate along the plate boundary could be predicted. In the case of Himalayas-Tibet, the total recent convergence rate is 5 to 6 cm/year from which according to the GPS data, about 30-40 % is taken by Himalayas. From our model this corresponds to the average exhumation rate of 5-7 mm/year. Taking into account that the exhumation rate varies from 0 to 13-14 mm/year along Himalayas, the above estimation looks quite reasonable.