Stability and periodicity in the thermal and mechanical evolution of the early continental lithosphere

We describe a simplified thermal and dynamical model of the Archean continental lithosphere that is described by the evolution in time of two state variables: the thickening factor f, which describes the thickness of the crustal layer relative to a reference section, and the depth-averaged lithospheric temperature T ― ′ . These quantities are explicitly linked by the advection of heat when extensional or convergent strain occurs (f drives T ― ′ ), and by the temperature-dependent gravitational potential energy that drives extension or convergence ( T ― ′ drives f). Thus a feedback loop exists in which the evolution of the thermal state lags the induced strain because of the time required for thermal diffusion. The evolution of the system from an arbitrary initial condition can be represented as a trajectory through the f – T ― ′ phase-space. The ratio of thermal diffusion timescale to viscous creep timescale defines an “energy parameter” Ψ that determines whether the system is stable to small disturbances. At moderate values of Ψ oscillatory solutions are possible (both finite-amplitude limit cycles, and decaying oscillations) if the viscosity of the lithosphere is only weakly dependent on temperature. Oscillations can be self-sustaining if the ratio of crustal to lithospheric thickness is less than about 0.27. Perturbations grow for thinner crust if lithosphere is sufficiently weak. If either the perturbation or the energy parameter Ψ is sufficiently large, runaway extension may occur. Thicker crust is generally stable to small disturbances and, if disturbed by external forces, will show decaying cycles of extensional and convergent strain. The feedback mechanism between thermal and mechanical states may be suppressed for typical lithospheric parameter values but, if it applies, it suggests a possible explanation for why the continental crust develops a thickness typically about 38 km, why tectonic reactivation cycles in sedimentary basins are commonly observed, and why periodic reactivation of orogenic zones occurs on timescales of order 108 years.