S U M M A R YAccurate predictions of stress distribution in the lithosphere are of major importance for approaching more realistic numerical models of the mantle-lithosphere system. Since stress fields in the lithosphere computed in convection models differ substantially between viscous and viscoelastic rheologies, it is essential to employ a viscoelastic rheology when accurate stresses are to be predicted in mantle convection models involving the lithosphere. This difference in stress distribution and magnitude has important implications for accurate modelling of stress-dependent processes like power-law creep, shear heating and plasticity. A further requirement for computation of accurate stress fields is to ensure numerically divergence-free solutions in the Boussinesq approximation. We present the technical background required for implementation of numerically incompressible solutions and for implementation of a Maxwell viscoelastic rheology in the frame of the finite element method (FEM). We employ the Jaumann invariant stress derivative in our implementation and demonstrate that the choice of the invariant stress derivative is irrelevant for geodynamic simulations. We discuss potential numerical advantages of a viscoelastic rheology when large viscosity variations are applied in thermal convection models. Due to the physical transition from effectively viscous to elastic behaviour in a viscoelastic model, the introduction of viscosity cut-offs generally applied in viscous models can be avoided.
[1] Archean cratons belong to the most remarkable features of our planet since they represent continental crust that has avoided reworking for several billions of years. Even more, it has become evident from both geophysical and petrological studies that cratons exhibit deep lithospheric keels which equally remained stable ever since the formation of the cratons in the Archean. Dating of inclusions in diamonds from kimberlite pipes gives Archean ages, suggesting that the Archean lithosphere must have been cold soon after its formation in the Archean (in order to allow for the existence of diamonds) and must have stayed in that state ever since. Yet, although strong evidence for the thermal stability of Archean cratonic lithosphere for billions of years is provided by diamond dating, the long-term thermal stability of cratonic keels was questioned on the basis of numerical modeling results. We devised a viscoelastic mantle convection model for exploring cratonic stability in the stagnant lid regime. Our modeling results indicate that within the limitations of the stagnant lid approach, the application of a sufficiently high temperature-dependent viscosity ratio can provide for thermal craton stability for billions of years. The comparison between simulations with viscous and viscoelastic rheology indicates no significant influence of elasticity on craton stability. Yet, a viscoelastic rheology provides a physical transition from viscously to elastically dominated regimes within the keel, thus rendering introduction of arbitrary viscosity cutoffs, as employed in viscous models, unnecessary.
[1] Ultralow velocity zones (ULVZs) are relatively thin regions directly above the core-mantle boundary (CMB) that exhibit marked seismic P-and S-velocity reductions. A viable explanation for the reduction is the presence of melt fractions within ULVZs. Since melt was found to be denser than solid in melting experiments at lowermost mantle pressures, partially molten ULVZs should exhibit negative buoyancy. Using published experimental data, we present a melting model based on Clapeyron slopes for the formation of ULVZs as partially molten regions above the CMB and apply the resulting melting curves and latent heat effects in fully dynamic, regionally constant viscosity convection simulations of the lowermost mantle. We find that the height of the ULVZs depends only moderately on Rayleigh number but strongly decreases with increasing excess density of melt over solid. The models predict excess density of at least 1% to explain observed heights. The combined effect of topography and latent heat of melting reduces the vigor of mantle convection only very slightly, while if combined with a decrease of the ULVZ viscosity, mantle flow velocities are significantly enhanced near the CMB, and overall mantle temperatures are notably increased. ULVZ heights are found to be insensitive to ULVZ viscosity (for the range isoviscous to 1/100 the viscosity of the ambient mantle).
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