Modelling of compression and extension of the continental lithosphere: towards rehabilitation of the necking-level model

We present a dynamic model of continental lithosphere deformation under extension or compression, focusing on the role of an effective mechanical parameter called "necking level" or "necking depth", a widely used concept in basin modelling studies. Though it has generally been assumed that "necking depth" depends strongly upon the rheological structure of the lithosphere (especially the depth distribution of its strong layers), such a dependency has never been demonstrated. Our model, which accommodates small deformations of a thin inhomogeneous plate induced by in-plane as well as by mantle boundary forces (applied to the model sides and base, respectively), shows that "necking depth" is a function of the horizontal position and depends mainly on the relative thicknesses and strengths of the rigid layers in the uppermost crust and below the Moho. Using different yield strength envelopes we demonstrate that the final structure of the lithosphere formed as a result of deformation and its consequent isostatic adjustment can be closely approximated by a model with a flat necking level. In the process of extension and compression of the continental lithosphere all boundaries, including the topographic surface and the Moho, deform. As a result, the total disturbance of the isostatic equilibrium state (specified as a load) is only a part of the topographic weight. Estimates of the correct load can be made using the depth to the necking level inferred from lithosphere structure, composition and thermal state. The final topography of lithospheric interfaces depends on both necking depth and effective flexural rigidity. Any attempt to estimate simultaneously strain distribution, necking depth and effective flexural rigidity, however, represents an ill-posed problem and is not possible without reliance upon strong independent assumptions constraining lithosphere structure. (C) 2010 Elsevier Ltd. All rights reserved.