A refined solution to the first terrestrial Pb-isotope paradox

The first terrestrial Pb-isotope paradox refers to the fact that on average, rocks from the Earth's surface (i.e. the accessible Earth) plot significantly to the right of the meteorite isochron in a common Pb-isotope diagram. The Earth as a whole, however, should plot close to the meteorite isochron, implying the existence of at least one terrestrial reservoir that plots to the left of the meteorite isochron. The core and the lower continental crust are the two candidates that have been widely discussed in the past. Here we propose that subducted oceanic crust and associated continental sediment stored as garnetite slabs in the mantle Transition Zone or mid-lower mantle are an additional potential reservoir that requires consideration. We present evidence from the literature that indicates that neither the core nor the lower crust contains sufficient unradiogenic Pb to balance the accessible Earth. Of all mantle magmas, only rare alkaline melts plot significantly to the left of the meteorite isochron. We interpret these melts to be derived from the missing mantle reservoir that plots to the left of the meteorite isochron but, significantly, above the mid-ocean ridge basalt (MORB)-source mantle evolution line. Our solution to the paradox predicts the bulk silicate Earth to be more radiogenic in Pb-207/Pb-204 than present-day MORB-source mantle, which opens the possibility that undegassed primitive mantle might be the source of certain ocean island basalts (OIB). Further implications for mantle dynamics and oceanic magmatism are discussed based on a previously justified proposal that lamproites and associated rocks could derive from the Transition Zone.

Petrology and geochemistry of early cretaceous bimodal continental flood volcanism of the NW Etendeka, Namibia. Part 1: Introduction, mafic lavas and re-evaluation of mantle source components

The bimodal NW Etendeka province is located at the continental end of the Tristan plume trace in coastal Namibia. It comprises a high-Ti (Khumib type) and three low-Ti basalt (Tafelberg, Kuidas and Esmeralda types) suites, with, at stratigraphically higher level, interstratified high-Ti latites (three units) and quartz latites (five units), and one low-Ti quartz latite. Khumib basalts are enriched in high field strength elements and light rare earth elements relative to low-Ti types and exhibit trace element affinities with Tristan da Cunha lavas. The unradiogenic Pb-206/Pb-204 ratios of Khumib basalts are distinctive, most plotting to the left of the 132 Ma Geochron, together with elevated Pb-207/Pb-204 ratios, and Sr-Nd isotopic compositions plotting in the lower Nd-143/Nd-144 part of mantle array (EM1-like). The low-Ti basalts have less coherent trace element patterns and variable, radiogenic initial Sr (similar to0.707-0.717) and Pb isotope compositions, implying crustal contamination. Four samples, however, have less radiogenic Pb and Sr that we suggest approximate their uncontaminated source. All basalt types, but particularly the low-Ti types, contain samples with trace element characteristics (e.g. Nb/Nb-*) suggesting metasediment input, considered source-related. Radiogenic isotope compositions of these samples require long-term isolation of the source in the mantle and depletions (relative to unmodified sediment) in certain elements (e.g. Cs, Pb, U), which are possibly subduction-related. A geodynamic model is proposed in which the emerging Tristan plume entrained subducted material in the Transition Zone region, and further entrained asthenosphere during plume head expansion. Mixing calculations suggest that the main features of the Etendeka basalt types can be explained without sub-continental lithospheric mantle input. Crustal contamination is evident in most low-Ti basalts, but is distinct from the incorporation of a metasedimentary source component at mantle depths.

Elasticity, yielding and episodicity in simple models of mantle convection

We explore the implications of refinements in the mechanical description of planetary constituents on the convection modes predicted by finite-element simulations. The refinements consist in the inclusion of incremental elasticity, plasticity (yielding) and multiple simultaneous creep mechanisms in addition to the usual visco-plastic models employed in the context of unified plate-mantle models. The main emphasis of this paper rests on the constitutive and computational formulation of the model. We apply a consistent incremental formulation of the non-linear governing equations avoiding the computationally expensive iterations that are otherwise necessary to handle the onset of plastic yield. In connection with episodic convection simulations, we point out the strong dependency of the results on the choice of the initial temperature distribution. Our results also indicate that the inclusion of elasticity in the constitutive relationships lowers the mechanical energy associated with subduction events.

Stirring in 3-d spherical models of convection in the Earth's mantle

On a global scale basalts from mid-ocean ridges are strikingly more homogeneous than basalts from intraplate volcanism. The observed geochemical heterogeneity argues strongly for the existence of distinct reservoirs in the Earth's mantle. It is an unresolved problem of Geodynamics as to how these findings can be reconciled with large-scale convection. We review observational constraints, and investigate stirring properties of numerical models of mantle convection. Conditions in the early Earth may have supported layered convection with rapid stirring in the upper layers. Material that has been altered near the surface is transported downwards by small-scale convection. Thereby a layer of homogeneous depleted material develops above pristine mantle. As the mantle cools over Earth history, the effects leading to layering become reduced and models show the large-scale convection favoured for the Earth today. Laterally averaged, the upper mantle below the lithosphere is least affected by material that has experienced near-surface differentiation. The geochemical signature obtained during the previous episode of small-scale convection may be preserved there for the longest time. Additionally, stirring is less effective in the high viscosity layer of the central lower mantle [1, 2], supporting the survival of medium-scale heterogeneities there. These models are the first, using 3-d spherical geometry and mostly Earth-like parameters, to address the suggested change of convective style. Although the models are still far from reproducing our planet, we find that proposal might be helpful towards reconciling geochemical and geophysical constraints.

An anisotropic viscous representation of Mohr-Coulomb failure for use is modelling coupled mantle-continent dynamics

In mantle convection models it has become common to make use of a modified (pressure sensitive, Boussinesq) von Mises yield criterion to limit the maximum stress the lithosphere can support. This approach allows the viscous, cool thermal boundary layer to deform in a relatively plate-like mode even in a fully Eulerian representation. In large-scale models with embedded continental crust where the mobile boundary layer represents the oceanic lithosphere, the von Mises yield criterion for the oceans ensures that the continents experience a realistic broad-scale stress regime. In detailed models of crustal deformation it is, however, more appropriate to choose a Mohr-Coulomb yield criterion based upon the idea that frictional slip occurs on whichever one of many randomly oriented planes happens to be favorably oriented with respect to the stress field. As coupled crust/mantle models become more sophisticated it is important to be able to use whichever failure model is appropriate to a given part of the system. We have therefore developed a way to represent Mohr-Coulomb failure within a code which is suited to mantle convection problems coupled to large-scale crustal deformation. Our approach uses an orthotropic viscous rheology (a different viscosity for pure shear to that for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation - neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane which is formally equivalent in any symmetric formulation. It is also important to allow strain-weakening of the material. The material should remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-Integration-point finite element code and will show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion, and comparisons between mantle convection models using the von Mises versus the Mohr-Coulomb yield criteria. The formulation itself is general and applies to 2D and 3D problems, although it is somewhat more complicated to identify the slip plane in 3D.

Anisotropy model for mantle convection

The paper presents a new theory for modeling flow in anisotropic, viscous rock. This theory has originally been developed for the simulation of large deformation processes including folding and kinking in multi-layered visco-elastic rock. The orientation of slip planes in the context of crystallographic slip is determined by the normal vector, the so-called director of these surfaces. The model is applied to simulate anisotropic natural mantle convection. We compare the evolution of the director and approximately steady states of isotropic and anisotropic convection. The isotropic case has a simple steady state solution, whereas the orthotropic convection model produces a continuously evolving patterning in tile core of the convection cell which makes only a near-steady condition possible, in which the thermal boundary layer appears to be well aligned with the flow and hence as observed in seismic tomomgraphy strong anistropic.