Dissipation analysis as a guide to mode selection during crustal extension and implications for the styles of sedimentary basins

We analyze the initial modes of continental extension with the aim of providing an improved understanding of the dynamic development of sedimentary basins. We first examine simple two-layer crustal-scale models which consist of a frictional-plastic upper crust bonded to a linear viscous lower crust of equal thickness. The mode of deformation is predicted by using an analytical analysis of the rate of internal dissipation of energy and the gravitational rate of work. It is assumed that models deform in the mode in which the total rate of work is minimized. For strain-softening models we predict the following modes of crustal extension: (1) pure shear, (2) multiple conjugate or parallel shear zones, (3) two shear zones, which form either one symmetric basin or two asymmetric basins, and (4) a single shear zone forming an asymmetric basin. The transitions between these modes are shown to depend on the trade off between gains'' that reduce the rate of energy dissipation and penalties'' that increase it. A single asymmetric basin is preferred for a strong brittle layer which has a high amount of strain softening (high plastic gain), a weak viscous layer and slow extension (low viscous penalty). A decrease in the plastic gain and/or an increase in the viscous penalty leads to modes with more shear zones in the upper crust. The pure shear mode is found for low strain softening, a high viscosity, and/or fast extension. Results of finite element calculations of equivalent simple two-layer models agree with the analytical mode predictions.