Strain refraction, viscosity ratio and multi-layer deformation: A mechanical approach

A solution for the deformation of viscous layers during a two-dimensional general deformation is derived. Layer deformation is found to consist of components of pure shear, simple shear and pure rotation when considered with respect to the layer orientation. It is shown that for external bulk pure shear the layer deformation is typically vastly different to that outside the layer, ranging from pure to simple to super shear depending on layer orientation and viscosity contrast. Treagus' method for determining viscosity ratio from cleavage refraction is re-evaluated and is found to applicable under bulk pure shear. However, the presence of earlier LPS (layer-parallel shortening) can lead to erroneous viscosity ratio estimates. A new approach is developed, relying on the variation of cleavage orientation with layer orientation that is found to be robust with respect to LPS. The method is applied to examples from the Irish Variscides and the new approach has implications for determining whether or not LPS occurred in this foreland setting.