A forward approach to the problem of nonlinear viscoelasticity and the thickness of the mechanical lithosphere

Abstract

The physical significance of the mechanical lithosphere is clarified using a nonlinear Maxwell flexure model. This model reconciles high‐temperature creep data for rock with the observed long‐term strength of the mechanical lithosphere. An approximate correspondence is established between the nonisothermal Maxwell model and an elastic flexure model to define an effective lithosphere thickness h e . The model calculations are essentially forward, since h e does not depend in a significant way upon the nominal or prescribed value of beam thickness, depending rather upon such variables as temperature and creep activation energy. The effective thickness of the Maxwell model, though a function of time, is stable enough over appropriate time scales to explain the long‐term integrated strength of the lithosphere. The strength index Σ is defined as the ratio of axial stress to the axial stress that would be present in a purely elastic fiber suffering the same strain. The base of the effective lithosphere is marked by a critical isopleth of strength, Σ c ≅ 0.3. This critical level (though not its position) is independent of time since loading. The strength index also maps out zones of predominant rheology. The narrowness of the transition zone between the elastic lithosphere and the viscous asthenosphere explains the success of the elastic plate in modeling many examples of lithosphere flexure. The elastic plate approximation may apply best where the lithosphere is relatively young and hot. Isolated, weak zones in the continental crust may or may not weaken the lithosphere as a whole, depending upon the distribution of these zones and the manner in which they deform. In general, such weakening is likely to be most effective when the base of the crust occurs at midlithospheric depths.