Oblique convergence of the crust driven by basal forcing: implications for length-scales of deformation and strain partitioning in orogens

SUMMARY We investigate the effects of oblique convergence on crustal thickening by modelling the crust as a thin viscous sheet. Crustal deformation is driven by basal velocity boundary conditions representing the kinematics of the underlying convergent mantle lithosphere, which is assumed to detach and subduct. The crustal sheet is coupled to the basal velocity field by a weak simple shear layer, which exerts a traction on the base of the sheet. The use of basal velocity boundary conditions with a thin-sheet model is shown to be valid provided coupling with the base is weak and deformation extends over a horizontally wide zone in comparison to the thickness of the sheet. The effect of the mantle lithosphere on crustal deformation can be shown to depend on the non-dimensional Ampferer number, Am, which represents the relative strengths of the crust and the weak basal shear zone. Analytical and numerical model results for small amounts of normalized convergence show that the ratio of horizontal length-scales for normal and transcurrent crustal deformation is 2, for both linear and non-linear viscous rheologies. The length-scales depend on the relative strength of the crust and the basal shear zone, convolved with a forcing length-scale from the boundary conditions. For obliquely incident velocities, the length-scale ratio is between 2 and 1, the exact value depending on the power-law exponent of the rheology, and the relative magnitude of the normal and transverse velocity components driving deformation. The model results for the ratio of normal to transcurrent deformation length-scales are different from those found by using a side-driven viscous thin-sheet model (England, Houseman & Sonder 1985; Sonder, England & Houseman 1986). We propose that this difference may be used as a test to distinguish the primary driving mechanism for large-scale orogenic deformation. If the deformation mechanism corresponds to pure shear of the whole lithosphere without significant basal tractions, we expect the deformation length-scale to be determined by the scale of the applied boundary conditions and buoyancy forces in the crust. The normal/transcurrent length-scale ratio for this case, in early stages of deformation, will be approximately 4. Alternatively, if the results presented here are more appropriate, then we expect the deformation length-scale to be determined by the intrinsic relative strengths of the crust and underlying basal shear zone. The corresponding normal/transcurrent length-scale ratio for this case, in early stages of deformation, will be between 2 and 1. On the basis of a comparison of the predicted length-scales of deformation with the length-scale over which the velocity boundary conditions are applied, we suggest that long, narrow, linear orogens such as the Andes are controlled by basal boundary conditions, whereas the Himalayan-Tibetan orogen has dimensions consistent with either basally or side-driven deformation.

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