40Ar/39Ar constraints on a temporal link between gold mineralization, magmatism, and continental margin transtension in the Jiaodong Gold Province, eastern China

The Jiaodong gold province is the largest gold repository in China. Both mineralization and granitoid hosts are spatially related to the crustal-scale Tan-Lu strike-slip fault system, which developed along the Mesozoic continental margin in eastern China. A series of Ar-40/Ar-39 laser incremental heating analyses of hydrothermal sericite/muscovite from three major gold deposits (Jiaojia, Xincheng, and Wangershan) and igneous biotite from the granodiorite hosts were performed to establish a possible temporal link between gold mineralization, magmatism, and movement along the Tan-Lu fault zone. Magmatic biotite crystals yield well-defined and concordant plateau ages between 124.5+/-0.4 Ma and 124.0+/-0.4 Ma (2sigma), whereas sericite and muscovite samples (a total of 30 single separates) give reproducible plateau ages ranging from 121.0+/-0.4 Ma to 119.2+/-0.2 Ma (2sigma). An integration of our Ar-40/Ar-39 results with age data from other major gold deposits in Jiaodong demonstrates that widespread gold mineralization occurred contemporaneously during a 2-3-m.yr. period. Most gold deposits show intimate spatial associations with abundant mafic to intermediate dikes. The mafic dikes have K-Ar ages of 123.5-119.6 Ma, in excellent agreement with those of the gold deposits. These newly obtained Ar-40/Ar-39 ages, in combination with other independent geological and geochronological data on granodioritic intrusions (130-126 Ma), volcanic rocks (1243.6-114.7 Ma), and deformed rocks within strike-slip faults (132-120 Ma) in Jiaodong or adjacent areas, also support the idea that gold mineralization postdated the granodioritic magmatism but was contemporaneous with mafic magmatism and volcanism, all controlled by the transtensional motion along the Tan-Lu fault in the Early Cretaceous.

Petrology and geochemistry of early cretaceous bimodal continental flood volcanism of the NW Etendeka, Namibia. Part 2: Characteristics and petrogenesis of the high-Ti latite and high-Ti and low-Ti voluminous quartz latite eruptives

As a result of their relative concentration towards the respective Atlantic margins, the silicic eruptives of the Parana (Brazil)-Etendeka large igneous province are disproportionately abundant in the Etendeka of Namibia. The NW Etendeka silicic units, dated at similar to132 Ma, occupy the upper stratigraphic levels of the volcanic sequences, restricted to the coastal zone, and comprise three latites and five quartz latites (QL). The large-volume Fria QL is the only low-Ti type. Its trace element and isotopic signatures indicate massive crustal input. The remaining NW Etendeka silicic units are enigmatic high-Ti types, geochemically different from low-Ti types. They exhibit chemical affinities with the temporally overlapping Khumib high-Ti basalt (see Ewart et al. Part 1) and high crystallization temperatures (greater than or equal to980 to 1120degreesC) inferred from augite and pigeonite phenocrysts, both consistent with their evolution from a mafic source. Geochemically, the high-Ti units define three groups, thought genetically related. We test whether these represent independent liquid lines of descent from a common high-Ti mafic parent. Although the recognition of latites reduces the apparent silica gap, difficulty is encountered in fractional crystallization models by the large volumes of two QL units. Numerical modelling does, however, support large-scale open-system fractional crystallization, assimilation of silicic to basaltic materials, and magma mixing, but cannot entirely exclude partial melting processes within the temporally active extensional environment. The fractional crystallization and mixing signatures add to the complexity of these enigmatic and controversial silicic magmas. The existence, however, of temporally and spatially overlapping high-Ti basalts is, in our view, not coincidental and the high-Ti character of the silicic magmas ultimately reflects a mantle signature.

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.

The igneous charnockite—high-K alkali-calcic I-type granite—incipient charnockite association in Trivandrum Block, southern India

The Pan-African (640 Ma) Chengannoor granite intrudes the NW margin of the Neoproterozoic high-grade metamorphic terrain of the Trivandrum Block (TB), southern India, and is spatially associated with the Cardamom hills igneous charnockite massif (CM). Geochemical features characterize the Chengannoor granite as high-K alkali-calcic I-type granite. Within the constraints imposed by the high temperature, anhydrous, K-rich nature of the magmas, comparison with recent experimental studies on various granitold source compositions, and trace- and rare-earth-element modelling, the distinctive features of the Chengannoor granite reflect a source rock of igneous charnockitic nature. A petrogenetic model is proposed whereby there was a period of basaltic underplating; the partial melting of this basaltic lower crust formed the CM charnockites. The Chengannoor granite was produced by the partial melting of the charnoenderbites from the CM, with subsequent fractionation dominated by feldspars. In a regional context, the Chengannoor I-type granite is considered as a possible heat source for the near-UHT nature of metamorphism in the northern part of the TB. This is different from previous studies, which favoured CM charnockite as the major heat source. The Occurrence of incipient charnockites (both large scale as well as small scale) adjacent to the granite as well as pegmatites (which contain CO2, CO2-H2O, F and other volatiles), suggests that the fluids expelled from the alkaline magma upon solidification generated incipient charnockites through fluid-induced lowering of water activity. Thus the granite and associated alkaline pegmatites acted as conduits for the transfer of heat and volatiles in the Achankovil Shear Zone area, causing pervasive as well as patchy charnockite formation. The transport Of CO2 by felsic melts through the southern Indian middle crust is suggested to be part of a crustal-scale fluid system that linked mantle heat and CO2 input with upward migration of crustally derived felsic melts and incipient charnockite formation, resulting in an igneous charnockite - I-type granite - incipient charnockite association.

A new estimate for the composition of weathered young upper continental crust from alluvial sediments, Queensland, Australia

We present new major element, trace element and Nd-isotope data for 30 alluvial sediments collected from 25 rivers in Queensland, E Australia. Samples were chosen to represent drainage from the region's most important lithologies, including Tertiary intraplate volcanic rocks, a Cretaceous igneous province (and sedimentary rocks derived thereof) as well as Proterozoic blocks. In most chemical and isotopic aspects, the alluvial sediments represent binary or ternary mixing relationships, with absolute abundances implied to reflect the proportion of lithologies in the catchments. When averaged, the studied sediments differ from other proxies of upper continental crust (UCC) mainly in their relative middle rare earth element enrichment (including an elevated Sm/Nd ratio), higher relative Eu abundance and higher Nb/Ta ratio. These features are inherited from eroded Tertiary intraplate basalts, which commonly form topographic highs in the studied region. Despite the high degree of weathering strong to excellent coherence between similarly incompatible elements is found for all samples. From this coherence, we suggest revisions of the following upper crustal element ratios: Y/Ho = 26.2, Yb/Tm = 6.37, Th/W = 7.14, Th/Tl = 24 and Zr/Hf = 36.9. Lithium, Rb, Cs and Be contents do not seem depleted relative to UCC, which may reflect paucity of K-feldspar in the eroded catchments. Nickel, Cr, Pb, Cu and Zn concentrations are elevated in polluted rivers surrounding the state capital. River sediments in the Proterozoic Georgetown Inlier are elevated in Pb, Cu and Zn but this could be a natural phenomenon reflecting abundant sulphide mineralisation in the area. Except for relative Sr concentrations, which broadly anticorrelate with mean annual rainfall in catchments, there is no obvious relationship between the extent of weathering and climate types, which range from and to tropical. The most likely explanation for this observation is that the weathering profiles in many catchments are several Myr old, established during the much wetter Miocene period. The studied sediment compositions (excluding those from the Proterozoic catchments) are used to propose a new trace element normalisation termed MUQ (MUd from Queensland), which serves as an alternative to UCC proxies derived from sedimentary rocks. Copyright (C) 2005 Elsevier Ltd

Provenance of long-travelled dust determined with ultra-trace-element composition: A pilot study with samples from New Zealand glaciers

We report high-precision inductively coupled plasma mass spectrometric (ICP-MS) compositional data for 39 trace elements in a variety of dust deposits, trapped sediments and surface samples from New Zealand and Australia. Dusts collected from the surface of alpine glaciers in the Southern Alps, New Zealand, believed to have undergone long-distance atmospheric transport from Australia, are recognizable on account of their overabundances of Pb and Cu with respect to typical upper crustal values. Long-travelled dust from Australia therefore scavenges these and other metals (e.g. Zn, Sb and Cd) from the atmosphere during transport and deposition. Hence, due to anthropogenic pollution, long-travelled Australian dusts can be recognized by elevated metal contents. The relative abundance of 25 other elements that are not affected by atmospheric pollution, mineral sorting (Zr and Hf) and weathering/solubility (alkali and earth alkali elements) reflects the geochemistry of the dust source sediment. As a result, we are able to establish the provenance of dust using ultra-trace-element chemistry at regional scale. Comparison of long-travelled dust chemistry with potential Australian sources shows that fits of variable quality are obtained. We propose that the best fitting potential source chemistry most likely represents the major dust source area. A binary mixing model is used to demonstrate that admixture of small quantities of local dust provides an even better fitting dust chemistry for the long-travelled dusts. Copyright (c) 2005 John Wiley & Sons, Ltd.

Integrated Pb- and S-isotope investigation of sulphide minerals from the early Archaean of southwest Greenland

We present high-spatial resolution secondary ion mass spectrometry (SIMS) measurements of Pb and S isotopes in sulphides from early Archaean samples at two localities in southwest Greenland. Secondary pyrite from a 3.71 Ga sample of magnetite-quartz banded iron formation in the Isua Greenstone Belt, which has previously yielded unradiogenic Pb consistent with its ancient origin, contains sulphur with a mass independently fractionated (MIF) isotope signature (Delta(33)S =+3.3 parts per thousand). This reflects the secondary mineralization of remobilized sedimentary S carrying a component modified by photochemical reactions in the early Archaean atmosphere. It further represents one of the most extreme positive excursions so far known from the early Archaean rock record. Sulphides from a quartz-pyroxene rock and an ultramafic boudin from the island of Akilia, in the Godth (a) over circle bsfjord, have heterogeneous and generally radiogenic Pb isotopic compositions that we interpret to represent partial re-equilibration of Pb between the sulphides and whole rocks during tectonothermal events at 3.6, 2.7 and 1.6 Ga. Both these samples have Delta(33)S=0 (within analytical error) and therefore show no evidence for MIF sulphur. These data are consistent with previous interpretations that the rock cannot be proven to have a sedimentary origin. Our study illustrates that SIMS S-isotope measurements in ancient rocks can be used to elucidate early atmospheric parameters because of the ability to obtain combined S and Pb-isotope data, but caution must be applied when using such data to infer protolith. When information from geological context, petrography and chronology (i.e. by Pb isotopes) is combined and fully evaluated, Delta(33)S signatures from sulphides and their geological significance can be interpreted with a higher degree of confidence. (c) 2005 Elsevier B.V All rights reserved.

Theoretical and numerical analysis of large-scale heat transfer problems with temperature-dependent pore-fluid densities

Purpose - In many scientific and engineering fields, large-scale heat transfer problems with temperature-dependent pore-fluid densities are commonly encountered. For example, heat transfer from the mantle into the upper crust of the Earth is a typical problem of them. The main purpose of this paper is to develop and present a new combined methodology to solve large-scale heat transfer problems with temperature-dependent pore-fluid densities in the lithosphere and crust scales. Design/methodology/approach - The theoretical approach is used to determine the thickness and the related thermal boundary conditions of the continental crust on the lithospheric scale, so that some important information can be provided accurately for establishing a numerical model of the crustal scale. The numerical approach is then used to simulate the detailed structures and complicated geometries of the continental crust on the crustal scale. The main advantage in using the proposed combination method of the theoretical and numerical approaches is that if the thermal distribution in the crust is of the primary interest, the use of a reasonable numerical model on the crustal scale can result in a significant reduction in computer efforts. Findings - From the ore body formation and mineralization points of view, the present analytical and numerical solutions have demonstrated that the conductive-and-advective lithosphere with variable pore-fluid density is the most favorite lithosphere because it may result in the thinnest lithosphere so that the temperature at the near surface of the crust can be hot enough to generate the shallow ore deposits there. The upward throughflow (i.e. mantle mass flux) can have a significant effect on the thermal structure within the lithosphere. In addition, the emplacement of hot materials from the mantle may further reduce the thickness of the lithosphere. Originality/value - The present analytical solutions can be used to: validate numerical methods for solving large-scale heat transfer problems; provide correct thermal boundary conditions for numerically solving ore body formation and mineralization problems on the crustal scale; and investigate the fundamental issues related to thermal distributions within the lithosphere. The proposed finite element analysis can be effectively used to consider the geometrical and material complexities of large-scale heat transfer problems with temperature-dependent fluid densities.

Chemical characterization of earth's most ancient clastic metasediments from the Isua Greenstone Belt, southern West Greenland

New and published major and trace element abundances of elastic metasediments (mainly garnet-biotite-plagioclase schists) from the similar to 3.8 Ga Isua Greenstone Belt (IGB), southern West Greenland, are used in an attempt to identify the compositional characteristics of the protoliths of these sediments. Compositionally, the metasediments are heterogeneous with enrichment of LREE (La/Sm-chord = 1.1-3.9) and variable enrichment and depletion of HREE (Gd/Yb-chord = 0.8-4.3). Chondrite-normalized Eu is also variable, spanning a range from relative Eu depletion to enrichment (Eu/Eu* = 0.6-1.3). A series of geochemical and geological criteria provides conclusive evidence for a sedimentary origin, in disagreement with some previous studies that questioned the presence of genuine elastic metasediments. In particular, trace element systematics of IGB metasediments show strong resemblance to other well-documented Archaean clastic sediments, and are consistent with a provenance consisting of ultramafic, malic and felsic igneous rocks. Two schists, identified as metasomatized mafic igneous rocks from petrographic and field evidence, show distinct compositional differences to the metasediments. Major element systematics document incipient-to-moderate source weathering in the majority of metasediments, while signs of secondary K-addition are rare. Detailed inspection of Eu/Eu*, Fe2O3 and CIW (chemical index of weathering) relationships reveals that elevated iron contents (when compared to averages for continental crust) and strong relative enrichment in Eu may be due to precipitation of marine Fe-oxyhydroxides during deposition or diagenesis on the seafloor. Some of the IGB metasediments have yielded anomalous Nd-142 and W-182 isotopic compositions that were respectively interpreted in terms of early mantle differentiation processes and the presence of a meteorite component. Alternatively, W and possibly Nd isotopes could have been affected by thermal neutron capture on the Hadean surface. The latter process was tested in this study by analysis of Sm isotope compositions, which serve as an effective monitor for neutron capture effects. As no anomalous variation from terrestrial values was detected, we infer that isotope systematics (including W-182 and Nd-142) of IGB metasediments were not affected by neutron capture, but reflect decay of radioactive parent isotopes. Copyright (c) 2005 Elsevier Ltd.

Dinosaur sanctuary on the Chatham Islands, Southwest Pacific: First record of theropods from the K-T boundary Takatika Grit

Cretaceous-Tertiaty (K-T) boundary (ca. 65 Ma) sections on a Southwest Pacific island containing dinosaurs were unknown until March 2003 when theropod bones were recovered from the Takatika Grit on the remote Chatham Islands (latitude 44 degrees S, longitude 176 degrees W), along the Chatham Rise. Tectonic and palaeontologic evidence support the eastward extension of a ca. 900 km land bridge that connected the islands to what is now New Zealand prior to the K-T boundary. The Chathams terrestrial fauna inhabited coastal, temperate environments along a low-lying, narrow, crustal extension of the New Zealand subcontinent, characterised by a tectonically dynamic, volcanic landscape with eroding hills (horsts) adjacent to flood plains and deltas, all sediments accumulating in grabens. This finger-like tract was blanketed with a conifer and clubmoss (Lycopodiopsida) dominated forest. The Chatham Islands region would have, along with New Zealand, provided a dinosaur island sanctuary after separating from the Gondwana margin ca. 80 Ma. (c) 2005 Elsevier B.V. All rights reserved.

The effect of energy feedbacks on continental strength

The classical strength profile of continents(1,2) is derived from a quasi-static view of their rheological response to stress-one that does not consider dynamic interactions between brittle and ductile layers. Such interactions result in complexities of failure in the brittle-ductile transition and the need to couple energy to understand strain localization. Here we investigate continental deformation by solving the fully coupled energy, momentum and continuum equations. We show that this approach produces unexpected feedback processes, leading to a significantly weaker dynamic strength evolution. In our model, stress localization focused on the brittle-ductile transition leads to the spontaneous development of mid-crustal detachment faults immediately above the strongest crustal layer. We also find that an additional decoupling layer forms between the lower crust and mantle. Our results explain the development of decoupling layers that are observed to accommodate hundreds of kilometres of horizontal motions during continental deformation.

Partitioning of deformation within a subduction channel during exhumation of high-pressure rocks: a case study from the Western Alps

The metamorphic belt of the Western Alps was subjected to widespread extensional tectonism at the end of the Eocene (ca. 45-35 Ma). Extension was accommodated by hinterland-directed movements along gently inclined extensional shear zones, which facilitated rapid exhumation of high-pressure and ultra-high-pressure rocks. This deformation resulted in a normal metamorphic sequence. Extension in the inner parts of the Western Alps was coeval with shortening at the front of the belt (foreland-directed thrusts), which took place during decompression, and emplaced higher grade metamorphic units over lower grade metamorphic rocks, thus forming an inverse metamorphic sequence. Two mechanisms for this extensional episode are discussed: (1) collapse of an overthickened lithosphere, and (2) internal readjustments within the orogenic wedge due to subduction channel dynamics. We favour the latter mechanism because it can account for the development of the observed inverse and normal metamorphic sequences along foreland-directed thrusts and hinterland-directed detachments, respectively. This hypothesis is supported by published structural, metamorphic and geochronological data from four geological transects through the Western Alps. This study also emphasizes the importance of post-shearing deformation (e.g. horizontal buckling versus vertical flattening), which can modify the distribution of hinterland- and foreland-directed shear zones in orogenic belts. (c) 2006 Elsevier Ltd. All rights reserved.

Timing and chemistry of fluid-flow events in the Lawn Hill Platform, Northern Australia

Mudrocks and carbonates of the Isa superbasin in the Lawn Hill platform in northern Australia host major base metal sulfide mineralization, including the giant strata-bound Century Zn-Pb deposit. Mineral paragenesis, stable isotope, and K-Ar dating studies demonstrate that long-lived structures such as the Termite Range fault acted as hot fluid conduits several times during the Paleoproterozoic and Mesoproterozoic in response to major tectonic events. Illite and chlorite crystallinity studies suggest the southern part of the platform has experienced higher temperatures (up to 300 degrees C) than similar stratigraphic horizons in the north. The irregular downhole variation of illite crystallinity values provides further information oil the thermal regime in the basin and shows that clay formation was controlled not only by temperature increase with depth but also by high water/rock ratios along relatively permeable zones. K-Ar dating of illite, in combination with other data, may indicate three major thermal events in the central and northern Lawn Hill platform Lit 1500, 1440 to 1400, and 1250 to 1150 Ma. This study did not detect the earlier Century base metal mineralizing event at 1575 Ma. 1500 Ma ages are recorded only in the south and correspond to the age of the Late Isan orogeny and deposition of the Lower Roper superbasin. They may reflect exhumation of a provenance region. The 1440 to 1300 Ma ages are related to fault reactivation and a thermal pulse at similar to 1440 to 1400 Ma possibly accompanied by fluid flow, with subsequent enhanced cooling possibly due to thermal relaxation or further crustal exhumation. The youngest thermal and/or fluid-flow event at 1250 to 1150 Ma is recorded mainly to the cast of the Tern-lite Range fault and may be related to the assembly of the Rodinian supercontinent. Fluids in equilibrium with illite that formed over a range of temperatures, at different times in different parts of the platform. have relatively uniform oxygen isotope compositions and more variable hydrogen isotope compositions (delta O-18 = 3.5-9.7 parts per thousand V-SMOW; delta D = -94 to -36 parts per thousand V-SMOW). The extent of the 180 enrichment and the variably depleted hydrogen isotope compositions suggest the illite interacted with deep-basin hypersaline brines that were composed of evaporated seawater and/or highly evolved meteoric water. Siderite is the most abundant iron-rich gangue phase in the Century Zn-Pb deposit, which is surrounded by all extensive ferroan carbonate alteration halo. Modeling suggests that the ore siderite formed at temperatures of 120 degrees to 150 degrees C, whereas siderite and ankerite in the alteration halo formed at temperatures of 150 degrees to 180 degrees C. The calculated isotopic compositions of the fluids are consistent with O-18-rich basinal brines and mixed inorganic and organic carbon Sources (6180 = 3-10 parts per thousand V-SMOW, delta C-13 = -7 to -3 parts per thousand V-PDB). in the northeast Lawn Hill platform carbonate-rich rocks preserve marine to early diagenetic carbon and oxygen isotope compositions, whereas ferroan carbonate cements in siltstones and shales in the Desert Creek borehole are O-18 and C-13 depleted relative to the sedimentary carbonates. The good agreement between temperature estimates from illite crystallinity and organic reflectance (160 degrees-270 degrees C) and inverse correlation with carbonate delta O-18 values indicates that organic maturation and carbonate precipitation in the northeast Lawn Hill platform resulted from interaction with the 1250 to 1150 Ma fluids. The calculated isotopic compositions of the fluid are consistent with evolved basinal brine (delta O-18 = 5.1-9.4 parts per thousand V-SMOW; delta C-13 = -13.2 to -3.7 parts per thousand V-PDB) that contained a variable organic carbon component from the oxidation and/or hydrolysis of organic matter in the host sequence. The occurrence of extensive O-18- and C-13-depleted ankerite and siderite alteration in Desert Creek is related to the high temperature of the 1250 to 1150 Ma fluid-flow event in the northeast Lawn Hill platform, in contrast to the lower temperature fluids associated with the earlier Century Zn-Pb deposit in the central Lawn Hill platform.

Construction of an Intraplate Fault System Model of South Australia, and Simulation Tool for the iSERVO Institute Seed Project

To foster ongoing international cooperation beyond ACES (APEC Cooperation for Earthquake Simulation) on the simulation of solid earth phenomena, agreement was reached to work towards establishment of a frontier international research institute for simulating the solid earth: iSERVO = International Solid Earth Research Virtual Observatory institute (http://www.iservo.edu.au). This paper outlines a key Australian contribution towards the iSERVO institute seed project, this is the construction of: (1) a typical intraplate fault system model using practical fault system data of South Australia (i.e., SA interacting fault model), which includes data management and editing, geometrical modeling and mesh generation; and (2) a finite-element based software tool, which is built on our long-term and ongoing effort to develop the R-minimum strategy based finite-element computational algorithm and software tool for modelling three-dimensional nonlinear frictional contact behavior between multiple deformable bodies with the arbitrarily-shaped contact element strategy. A numerical simulation of the SA fault system is carried out using this software tool to demonstrate its capability and our efforts towards seeding the iSERVO Institute.

Anisotropic viscous models of large-deformation Mohr-Coulomb failure

We have developed a way to represent Mohr-Coulomb failure within a mantle-convection fluid dynamics code. We use a viscous model of deformation with an orthotropic viscoplasticity (a different viscosity is used for pure shear to that used 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. We also allow for strain-weakening of the material. The material can 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 show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion. The formulation itself is general and applies to 2- and 3-dimensional problems.