Rheological modelling and deformation instability of lithosphere under extension

SUMMARY Continental break‐up, which precedes oceanic accretion, probably results from an unstable extension of the lithosphere, analogous to necking of metals when they are submitted to tension. By reason of complexity of the rheology, no conclusion about lithospheric extension stability may be reached by an a priori analysis. We thus examine directly the evolution, when the lithosphere is stretched, of lateral inhomogeneities, represented in our example by small‐scale variations of thickness. The rheological model is derived from the hypotheses of Brace & Kohlstedt (1980) and is consistent with the results of rock mechanics. The lithosphere consists of three or four layers of varying thicknesses and mechanical properties. The brittle upper crust and, eventually, the brittle part of the mantle are assimilated to perfectly plastic media and are described, in a state of uniform extension, by a constant viscosity. In the lower crust and ductile mantle lithosphere, the effective viscosity is supposed to be exponential. The mechanical model relies on a perturbation method developed, by Fletcher & Hallet (1983), among others. Contrary to previous published results, no unstable behaviour of the lithosphere is observed unless the latter is more dense than the asthenosphere, in which case a gravitational instability may develop. This discrepancy can be explained by differences in assumptions concerning the variation of strength in the lithosphere, as yet poorly constrained by the data. We observe a great sensitivity of the results to the strength stratification and to the artificial discontinuities of density or viscosity implied by the models.