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.

Geochemical variation among small eruptive centers in the central SVZ of the Andes: An evaluation of subduction, mantle and crustal influences

Subduction zone magmatism is an important and extensively studied topic in igneous geochemistry. Recent studies focus on from where arc magmas are generated, how subduction components (fluids or melts) are fluxed into the source of the magmas, and whether or how the subduction components affect partial melting processes beneath volcanic arcs at convergent boundaries. ^ At 39.5°S in the Central Southern Volcanic Zone of the Andes, Volcano Villarrica is surrounded by a suite of Small Eruptive Centers (SEC). The SECs are located mostly to the east and northeast of the stratovolcano and aligned along the Liquine-Ofqui Fault Zone, the major fracture system in this area. Former studies observed the geochemical patterns of the SECs differ distinctively from those of V. Villarrica and suggested there may be a relationship between the compositions of the volcanic units and their edifice sizes. This work is a comprehensive geochemical study on the SECs near V. Villarrica, using a variety of geochemical tracers and tools including major, trace and REE elements, Li-Be-B elements, Sr-Nd-Pb isotopes and short-lived isotopes such as U-series and 10Be. In this work, systematic differences between the elemental and isotopic compositions of the SECs and those of V. Villarrica are revealed and more importantly, modeled in terms of magmatic processes occurring at continental arc margins. Detailed modeling calculations in this work reconstruct chemical compositions of the primary magmas, source compositions, compositions and percentages of different subduction endmembers mixed into the source, degrees of partial melting and different time scales of the SECs and V. Villarrica, respectively. Geochemical characteristics and possible origins of the two special SECs—andesitic Llizan, with crustal signatures, and Rucapillan, to the northwest toward the trench, are also discussed in this work. ^

An investigation into the Hawaiian mantle from a xenolithic perspective

Salt Lake Crater (SLC), on the island of Oahu, Hawaii, is best known for its wide variety of crustal and mantle xenoliths. SLC is only the second locality in oceanic regimes where deeper portions of the upper mantle (i.e., garnet-bearing xenoliths) have been sampled. These garnet-bearing xenoliths, that contain clinopyroxene (cpx), orthopyroxene (opx), olivine, and garnet, are the focus of this study Opx is present in small amounts. Cpx has exsolved opx, spinel, and garnet. In addition, many xenoliths contain spinel-cored garnets. In some xenoliths, opx crystals contain exsolved cpx and spinel. Olivine, cpx, and garnet are in chemical equilibrium with each other. Opx is not in chemical equilibrium with the other dominant minerals. ^ The origin of these xenoliths is interpreted on the basis of liquidus phase relations in the simplified system CaO-MgO-Al2O3-SiO 2 (CMAS) system at 3.0 and 5.0 GPa. The occurrence of spinel-cored garnets and the Ol-Cpx-Gt assemblage suggests that the depth of crystallization of the SLC xenoliths examined was ∼100–110 km (i.e., uppermost asthenosphere). ^ The experimental study is concerned with the equilibrium melting of garnet clinopyroxenite at 2.0–2.5 GPa and it explores the role of such melting process in the generation of tholeiitic and alkalic lavas in ocean island basalts (OIBs). The starting material is a tholeiitic picrite in terms of its normative composition. Its solidus temperature is 1295 ± 15°C and 1332 ± 15°C at 2.0 and 2.5 GPa, respectively. At 2.0 GPa, the liquidus phase is opx that is in reaction relation with the melt. It reacts out at ∼40°C below the liquidus as cpx and spinel appear. Garnet appears long after opx disappearance. Opx is absent in runs at 2.5 GPa. Cpx and garnet appear simultaneously on the liquidus at 2.5 GPa, and are the only assemblage throughout the melting interval. At both the pressures, the partial melts are olivine-hypersthene normative at high melt fraction ( F), becoming moderately to strongly nepheline-normative, as F decreases. It is concluded that the involvement of CO 2 (and perhaps H2O) is necessary for the generation of alkalic melts in most OIBs. ^