Vertical averages of rheology of the continental lithosphere: relation to thin sheet parameters

Abstract

We calculate vertically-averaged rheologies for continental lithosphere subject to biaxial states of stress corresponding to extensional, compressional, and strike-slip regimes. We assume that brittle deformation occurs by Byerlee's Law and that ductile deformation occurs by steady-state creep mechanisms. Under these conditions, the vertically-averaged rheology may be approximated by a single power law over the range of strain rates from 10⁻¹³ to 10⁻¹⁷ s⁻¹. This is true not only when either brittle or ductile behavior dominates the strength of the lithospere, but also when the contributions of brittle and ductile behavior are comparable. The value of the power law exponent,n, and the strength of the lithosphere depend on: the depth and stress difference at the brittle-ductile transition, the temperature at the Moho, and the geothermal gradient. In the range of vertically-integrated stress between 10¹² and 10¹³ N m⁻¹n reaches a minimum of between 5 and 10; under other circumstancesn increases rapidly as brittle behavior dominates over ductile behavior. The strength of the lithosphere depends most strongly on the thermal state of the upper mantle but also is influenced by the stress supported in brittle portions of the lithosphere.