factors that control the angle of shear bands in geodynamic numerical models of brittle deformation abstract numerical models of brittle deformation on geological timescales typically use a pressure dependent mohr coulomb or drucker prager plastic flow law to simulate plastic failure despite its widespread usage in geodynamic models of lithospheric deformation however certain aspects of such plasticity models remain poorly understood one of the most prominent questions in this respect is what are the factors that control the angle of the resulting shear bands recent theoretical work suggest that both roscoe 45 coulomb angles 45 2 where is the angle of internal friction and arthur angles 45 4 where is the dilation angle as well as all intermediate angles are possible published numerical models however show a large range of shear band angles with some codes favoring arthur angles whereas others yield coulomb angles in order to understand what causes the differences between the various numerical models here i perform systematic numerical simulations of shear localization around an inclusion of given length scale both numerical element type geometrical and rheological viscoplastic versus viscoelastoplastic effects are studied results indicate that the main factor controlling shear band angle is the non dimensional ratio between the length scale of the heterogeneity d and the size of the numerical mesh x coulomb angles are observed only in cases where the inclusion is resolved well d x 5 10 and in which it is located sufficiently far from the boundary of the box in most other cases either arthur or roscoe orientations are observed if heterogeneities are one element in size coulomb angles are thus unlikely to develop irrespective of the employed numerical resolution whereas differences in element types and rheology do have consequences for the maximum obtainable strain rates inside the shear bands they only have a minor effect on shear band angles shear bands initiated from random noise or from interactions of shear bands with model boundaries or other shear bands result in stress heterogeneities with dimensionless length scales d x 1 2 such shear bands are thus expected to form roscoe or arthur orientations consistent with the findings in previous numerical models

a two phase model for compaction and damage 3 applications to shear localization and plate boundary formation a new two phase theory employing a nonequilibrium relation between interfacial surface energy pressure and viscous deformation bercovici et al this issue provides a model for damage void generation and microcracking and thus a continuum description of weakening failure and shear localization here we demonstrate applications of the theory to shear localization with simple shear flow calculations in which one phase the matrix representing for example silicate is much stronger more viscous than the other phase the fluid this calculation is motivated as a simple model of plate boundary formation in a shear zone even without shear the two phases eventually separate due to gradients in surface tension however the influence of shear on phase separation is manifest in several ways as shear velocity increases the separation rate of the phases increases demonstrating a basic feedback mechanism accumulation of the fluid phase causes focused weak zones on which shear concentrates causing more damage and void generation and thus greater accumulation of fluid beyond a critical shear velocity phase separation undergoes intense acceleration and focusing leading to a tear localization in which the porosity becomes nearly singular in space and grows rapidly like a tear or crack at an even higher value of shear velocity phase separation is inhibited such that shear localization gives way to defocusing of weak zones suggestive of uniform microcracking and failure throughout the layer our two phase damage theory thus predicts a wide variety of shear localization and failure behavior with a continuum model applications of the theory to various fields such as granular dynamics metallurgy and tectonic plate boundary formation are numerous

structural reactivation in plate tectonics controlled by olivine crystal anisotropy structures formed during ancient tectonic events are commonly reactivated during subsequent tectonism numerical models point to mechanical anisotropy arising from the inherited orientation of crystals of the mineral olivine in the lithospheric mantle as the cause of this behaviour

viscous heating in silicate melts an experimental and numerical comparison 1 the transition from newtonian to non newtonian flow of silicate melts is commonly manifested as shear thinning at conditions of high stress and strain rate shear thinning may strongly influence the dynamics of magmatic flows but the details of its microscopic origins are not fully understood here we consider viscous heating and thermomechanical coupling as a potential cause of shear thinning we compare the results of laboratory uniaxial compression experiments of a silicate melt with the results of thermomechanical numerical simulations corresponding to the experimental setup both the experimental and numerical results concord and indicate that the reduction of the temperature dependent viscosity in flowing silicate melts is a result of viscous heating viscous heating was quantified for glasses with viscosities ranging from 108 to 1011 pa s and strain rates from 10 5 to 100 s 1 the results of 48 compression experiments indicate that the transition from newtonian to non newtonian flow in the silicate melt occurs at a brinkmann number i e ratio of heat gained to heat lost around 1 whereas brittle behavior dominates the melt deformation when the deborah number i e ratio of viscoelastic relaxation time to characteristic deformation time is larger than around 0 01 the observed viscous heating significantly contributes to the viscosity decrease observed in high stress strain rate experiments and questions our current understanding of the non newtonian deformation behavior of silicate melts

compression of oceanic lithosphere an analysis of intraplate deformation in the central indian basin intraplate compressional deformation in the central indian basin is expressed as linear e w trending topographic undulations and geoid anomlies with characteristic spacings of approximately 200 km to elucidate the nature of this deformation we develop models of an oceanic lithosphere in a state of horizontal compression the lithosphere is treated as a viscous or plastic layer of uniform strength which overlies a viscous half space in which strength decreases exponentially with depth we compare models in which deformation with a dominant wavelength develops in response to flexural buckling and the hydrodynamic growth of instabilities for the viscous flexural buckling model deformation is constrained to occur in the antisymmetric mode by flexural folding which is characterized by uniform bending of the layer in the hydrodynamic flow model a range of deformational styles are possible in a strong viscous lithosphere deformation of the layer occurs by flexural folding at a wavelength which agrees with that predicted from flexural buckling theory in a lithosphere of intermediate strength the layer deforms by folding characterized by thickening which localizes beneath topographic highs in a relatively weak lithosphere the layer incurs an even greater amount of localized thickening and deforms in the symmetric or pinch and swell mode by inverse boudinage if the layer has a plastic rheology deformation occurs by inverse boudinage independent of the yield stress results from models in which the layer folds either flexurally or with periodic thickening are consistent with the observed depth distribution of seismicity in the central indian basin and with experimental rock rheological data because of the trade off between buoyancy forces and layer strength in determining the dominant wavelength a lithosphere which was overlain by weak sediments when intraplate deformation initiated can be characterized by a compressive layer strength almost a factor of 3 less than a lithosphere which was initially sediment free for a range of plausible models which consider both a sediment covered and sediment free lithosphere the observed wavelength requires deviatoric stresses in the indian plate of several hundreds of mpa

lithospheric deformation during the early stages of continental collision numerical experiments and comparison with south island new zealand 1 the nature of lithospheric deformation during continental plate collision still remains unresolved while it has often been proposed that the mantle lithosphere is accommodated by distributed thickening of a viscous root an alternate hypothesis suggests that significant portions of convergent mantle lithosphere essentially undergo underthrusting or subduction to further consider this issue we model the thermochemical evolution of the lithosphere mantle system using arbitrary lagrangian eulerian finite element techniques we incorporate a mix of viscous thermally activated power law creep and plastic frictional coulomb with strain softening rheologies in the numerical experiments to treat disparate composition in the crust and mantle a range of rheological and mechanical parameters is explored to determine controls on the style of lithospheric deformation the models suggest that during the initial stages of plate collision the mantle lithosphere is characterized by plate like behavior and underthrusting subduction of the upper region in conjunction with distributed thickening and rayleigh taylor type viscous instability of the lower portion depending on the material rheology temperature regime and imposed convergence velocity the deforming mantle lithosphere demonstrates various combinations of these end member behavioral modes the modeling results are interpreted in the context of observed lithospheric deformation across south island new zealand a combined style of underthrusting and distributed thickening is consistent with the observed crustal structure in the young collisional orogen as well as seismic imaging of the geometry of the underlying lithosphere

on the initiation of subduction estimates of shear resistance associated with lithospheric thrusting and convergence represent lower bounds on the force necessary to promote trench formation three environments proposed as preferential sites of incipient subduction are investigated passive continental margins transform faults fracture zones and extinct ridges none of these are predicted to convert into subduction zones simply by the accumulation of local gravitational stresses subduction cannot initiate through the foundering of dense oceanic lithosphere immediately adjacent to passive continental margins the attempted subduction of buoyant material at a mature trench can result in large compressional forces in both subducting and overriding plates this is the only tectonic force sufficient to trigger the nucleation of a new subduction zone the ubiquitous distribution of transform faults and fracture zones combined with the common proximity of these features to mature subduction complexes suggests that they may represent the most likely sites of trench formation if they are even marginally weaker than normal oceanic lithosphere

a constitutive model for layer development in shear zones near the brittle ductile transition 1 the microstructure of ductile shear zones differs from that of surrounding wall rocks in particular compositional layering is a hallmark of shear zones as layered rocks are weaker than their isotropic protolith when loaded in simple shear layering may hold the key to explain localization of ductile deformation onto ductile shear zones i propose here a constitutive model for layer development a two level mixing theory allows the strength of the aggregate to be estimated at intermediate degrees of layering a probabilistic failure model is introduced to control how layers develop in a deforming aggregate this model captures one of the initial mechanism of phase interconnection identified experimentally by holyoke and tullis 2006a 2006b fracturing of load bearing grains this model reproduces the strength evolution of these experiments and can now be applied to tectonic modeling

convective instability of thickening mantle lithosphere mantle lithosphere being colder and therefore denser than the underlying mantle is prone to convective instability that can be induced by horizontal shortening numerical experiments on a cold layer with imposed horizontal shortening are carried out to examine the relative importance of mechanical thickening thermal diffusion and gravitational instability in deforming the layer this analysis is then used to develop a method for determining which of these styles dominates for a layer thickening at a given rate if viscosity is non newtonian the imposition of shortening decreases the lithospheric strength which causes perturbations to the lithosphere s temperature structure to grow exponentially with time once these perturbations become sufficiently large they then grow super exponentially with time eventually removing the lithospheric base because lithospheric viscosity is highly temperature dependent at most only the lower 30 per cent of the lithosphere participates in the downwelling associated with this initial super exponential growth event after this event however a downwelling develops that removes material advected into the region of downwelling by horizontal shortening the magnitude of this persistent downwelling depends on the rate and duration of shortening if the total amount of shortening does not exceed 50 per cent doubling of crustal thickness then this downwelling extends to a depth three to four times the thickness of undeformed lithosphere and forms a sheet significantly thinner than the width of the region undergoing shortening once shortening stops this downwelling is no longer replenished by the shortening process and should then detach due to its inherent gravitational instability the hottest 60 per cent of the mantle lithosphere could be removed in such an event which would be followed by an influx of hot buoyant asthenosphere that causes rapid surface uplift because more cold material is removed after the cessation of shortening than by the initial gravitational instability the former has a potentially greater influence on surface uplift the tibetan interior is thought to have been shortened by about 50 per cent in 30myr and afterwards at 8ma experienced a period of rapid uplift that may have resulted from the removal of a large downwelling finger of cold lithosphere generated by shortening

folding of oceanic lithosphere folding of the lithosphere just south of the bay of bengal appears as 1 undulations in acoustic basement topography and 2 as linear geoid undulations in the seasat altimeter data from the seasat data we find that the east west trending folds have wavelengths ranging from 130 to 250 km and clustering about 190 km the horizontal gravity disturbances due to the folds range in amplitude from 15 to 50 mgal elastic models of oceanic lithosphere have in the past been used to demonstrate the implausibility of lithosphere buckling or folding in response to compression these elastic models typically predict that compressive stresses of about 5 gpa are required to buckle oceanic lithosphere with an age comparable to that of the northeastern indian ocean 40 70 ma these stresses exceed the strength of lithospheric rock we use an elastic plastic model to show that oceanic lithosphere of this age should have a net compressive strength equal to about 12 of the elastic buckling stress we further demonstrate that loads approaching the net compressive strength cause the lithosphere to fold with a wavelength about 200 km i e the wavelength observed from seasat our results reinforce earlier speculation that this folding may be related to the himalayan orogeny

on the initiation of subduction zones analysis of the relation between intraplate stress fields and lithospheric rheology leads to greater insight into the role that initiation of subduction plays in the tectonic evolution of the lithosphere numerical model studies show that if after a short evolution of a passive margin time span a few tens of million years subduction has not yet started continued aging of the passive margin alone does not result in conditions more favorable for transformation into an active margin

shear heating induced lithospheric scale localization does it result in subduction abstract even though it is a well established fact that the earth is currently in a plate tectonics mode the question on how to break lithospheric plates and initiate subduction remains a matter of debate here we focus on shear heating as a potential mechanism to cause lithospheric shear localization and subsequent subduction initiation in oceanic plates it is shown that shear heating under some conditions i facilitates the formation of a lithospheric scale shear zone and ii is capable of stabilizing a lithospheric scale shear zone thus creating the necessary condition for subduction initiation to occur furthermore we demonstrate that not only the localization process is of importance but also the post localization stage where rapidly growing convective instabilities might prevent an incipient subduction zone from developing we develop scaling laws for both the localization and the post localization stages in the case of lithospheric localization the characteristic length scale equals a quarter of the dominant folding wavelength in the lithosphere thus of the order of the competent layer thickness this shows that oceanic lithosphere develops an intrinsic perturbation length scale that is largely independent of smaller scale heterogeneities we compare the subduction initiation potential of wet olivine and dry olivine rheologies and find that for earth like conditions a dry olivine rheology is more likely to result in subduction initiation a large plate age does not always increase the potential for subduction initiation as it increases the potential for convective instabilities to occur instead an optimal plate age exists for shear heating induced subduction initiation which is around 40 ma for a wet olivine rheology

continental lithosphere folding in central asia part ii constraints from gravity and topography abstract periodical sub parallel fold like structures observed in the western gobi have two characteristic dominant wavelengths of approximately 50 and 300 360 km we explain these observations in terms of independent quasi viscous folding of the crustal and upper mantle parts of the lithosphere due to horizontal transpressional stresses in central asia induced by the collision with the indian plate we derive a model for the mechanical response of the continental lithosphere to horizontal stresses for a rheologically layered plate with non newtonian power law rheology overlying a low viscosity asthenosphere the differentiation in the effective viscosity and thickness of the strong upper crust and upper mantle lithosphere along with the presence of a low viscosity lower crust between them leads to their partial decoupling during compressional deformation these features result in the appearance of different wavelengths of the folds in the western gobi region we derive simple semi analytical estimates for the dominant wavelengths and rates of growth of surface undulations constrained by data from experimental rock mechanics topography and gravity

mechanisms for the generation of plate tectonics by two phase grain damage and pinning abstract weakening and shear localization in the lithosphere are essential ingredients for understanding how and whether plate tectonics is generated from mantle convection on terrestrial planets we present a new theoretical model for the mechanism of lithospheric weakening and shear localization and hence plate generation through damage grain evolution and zener pinning in two phase polycrystalline lithospheric rocks grain size evolves through the competition of coarsening which drives grain growth with damage which drives grain reduction however in a two phase medium the interface between phases induces zener pinning which impedes grain growth and facilitates damage the size of the pinning surfaces is given by the roughness of the interface and damage to the interface causes smaller pinning surfaces which in turn drive down the grain size forcing the rheology into the grain size dependent diffusion creep regime this process allows damage and rheological weakening to co exist which is normally considered impossible in single phase assemblages moreover pinning greatly inhibits grain growth and shear zone healing which is much faster in single phase materials hence the resulting shear localization is rapid less than 1 myr but the healing time for a dormant weak zone is very slow greater than 100 myrs these effects therefore permit rapidly forming and long lived plate boundaries the model therefore provides a key ingredient and predictive theory for the generation of plate tectonics on earth and other planets

at what stress level is the central indian ocean lithosphere buckling internal contrasts in strength are responsible for lithospheric buckling these are quantified by comparing the indian ocean data to two dimensional visco elasto plastic numerical models where the material properties depend on temperature and pressure the central indian basin is known for its intraplate seismicity and long wavelength undulations of the sea floor and associated gravity signatures to simulate the amplitudes of undulations that reach 1 km within about 11 ma of compression and 60 km of shortening the required mean yield strength of the lithosphere is 400 mpa if either a hydrostatic fluid pressure is considered in the crust or a mechanical decoupling at the depth of the moho small crustal wavelengths are superimposed on the long wavelength deformation in agreement with observations it is then possible to match the alternative indication that buckling commenced only 4 ma ago with a total amount of shortening of 30 km and with a required yield strength of 200 mpa about 10 of homogeneous thickening accompanies buckling taking into account variable thermal conductivity demonstrates that a change in the geotherm is sufficient to increase buckling amplitudes by 10 within 5 ma fl 2000 elsevier science b v all rights reserved

strain localization in olivine aggregates at high temperature a laboratory comparison of constant strain rate and constant stress boundary conditions we performed high strain torsion experiments on aggregates of fo50 olivine to test the influence of imposed boundary conditions on localizing deformation we deformed both solid and thin walled cylinders of fo50 either at constant strain rate or at constant stress samples deformed in constant strain rate experiments reached a peak stress followed by weakening at a continually decreasing weakening rate in contrast samples deformed in constant stress experiments weakened at an accelerating weakening rate localization is manifested in samples deformed at constant stress as irregularities along strain markers s c foliations and torsional buckling of thin walled cylinders in contrast samples deformed at constant strain rate deformed homogeneously grain boundary maps created with electron backscatter diffraction data indicate that high strain regions in constant stress samples correlate with finer grain sizes and stronger crystallographic fabrics since the dominant deformation mechanism is grain size sensitive heterogeneous recrystallization leads to strain localization in finer grained regions however variations in strength are not large enough to initiate localization in constant strain rate experiments the magnitude of grain size heterogeneity remains relatively constant with increasing strain implying that shear zones are maintained throughout the experiments even as non localizing regions recrystallize based on our results we propose that deformation driven at constant stress in earth s lithosphere will easily localize even if structural heterogeneities are not initially present

spacing of faults at the scale of the lithosphere and localization instability 2 application to the central indian basin 1 tectonic deformation in the central indian basin cib is organized at two spatial scales long wavelength 200 km undulations of the basement and regularly spaced faults the fault spacing of order 7 11 km is too short to be explained by lithospheric buckling we show that the localization instability derived by montesi and zuber 2003 provides an explanation for the fault spacing in the cib localization describes how deformation focuses on narrow zones analogous to faults the localization instability predicts that localized shear zones form a regular pattern with a characteristic spacing as they develop the theoretical fault spacing is proportional to the depth to which localization occurs it also depends on the strength profile and on the effective stress exponent ne which is a measure of localization efficiency in the brittle crust and upper mantle the fault spacing in the cib can be matched by ne 300 if the faults reach the depth of the brittle ductile transition bdt around 40 km or ne 100 if the faults do not penetrate below 10 km these values of ne are compatible with laboratory data on frictional velocity weakening many faults in the cib were formed during seafloor spreading the preexisting faults near target locations separated by the wavelength of the localization instability were preferentially reactivated during the current episode of compressive tectonics the long wavelength undulations may result from the interaction between buckling and localization index terms 8010 structural geology fractures and faults 8020 structural geology mechanics 8159 tectonophysics evolution of the earth rheology crust and lithosphere keywords faults central indian basin fault spacing folds strength envelope diffuse plate boundary

viscoelastic mantle convection and lithospheric stresses summary accurate 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

three regimes of mantle convection with non newtonian viscosity and stagnant lid convection on the terrestrial planets numerical simulations of convection with strongly temperature dependent viscosity suggest that non newtonian viscosity convection dislocation creep passes through three convective regimes similar to those observed for newtonian viscosity convection diffusion creep the small viscosity contrast regime the transitional regime and the stagnant lid regime for realistic viscosity contrasts mantle convection is in the stagnant lid regime characterized by formation of a very viscous slowly creeping lid on top of an actively convecting mantle this explains the tectonic style observed on the terrestrial planets and the moon on the other hand this eliminates the possibility that the plates on earth could be mobile due to non newtonian viscosity the nature of the mobility of lithospheric plates on earth has yet to be explained

on the rheologically critical melt fraction abstract with increasing melt fraction the strength of partially molten granite decreases from a value characteristic of solid competent rock to a value nearly equal to that of the melt previously published mechanical and microstructural data indicate that deformation in partially molten rocks often involves brittle processes thus the pressure in the melt is expected to be important in determining strength when the volume changes during deformation strength and fluid flow will be coupled by such parameters as permeability k storage capacity per unit volume or storativity s melt compressibility f grain size d fluid viscosity and strain rate experiments on brittle rock at low temperatures show that the strain rate at which the internal fluid pressure can be maintained constant is approximately proportional to k s an evaluation of published experimental data suggests that this relation also holds for partially molten granites indicating that the strength of these rocks depends on their transport properties since the permeability is related to below a critical melt fraction rcmf the melt pressure will change if deformation is not iso volumetric by assuming a power law relationship between k and we estimate that rcmf f d m 1 n 1 where m and n relate permeability to grain size and respectively

dynamics of subduction initiation at preexisting fault zones we show that a new subduction zone can initiate at a preexisting dipping fault zone with reasonable plate forces consistent with what is observed in the western pacific the dynamics of subduction initiation within a viscoelastic medium has been systematically explored with the finite element method we investigate the compression of oceanic lithosphere with both force and velocity boundary conditions and track the thermal structure in which heat is transported by both advection and diffusion the viscosity of the medium is non newtonian and temperature dependent we also examine the influence of a perfectly plastic yield stress a new method to model the preexisting weak zone as a graded fault with remeshing is introduced the first 400 km of plate convergence is examined during which time there are profound changes in plate boundary dynamics initially topography across the plate boundary is characterized by over 1000 m of uplift close to the trench subsequently a bathymetric depression develops on the overriding plate with an initial subsidence rate of 125 m myr for a slab subducting at 2 cm yr tectonic subsidence of the overriding plate is primarily dependent upon the depth of slab penetration for a plate force of 4 10 12 n m subduction initiates even with a fault shear stress of 3 mpa the resistance most consistent with seismological observations however subduction will not initiate when this fault shear stress is 5 mpa our results are consistent with plate reconstructions which predict the initiation of subduction across preexisting weak zones within oceanic basins

dynamics of subduction initiation with different evolutionary pathways changes of plate motion may have induced subduction initiation si but the tectonic history of si is different from one subduction zone to another izu bonin mariana ibm si accompanied by strong backarc spreading and voluminous eruption of boninites contrasts with the aleutians which shows neither using finite element models we explore visco elasto plastic parameters and driving boundary conditions for si evolution with an imposed velocity we find three different evolutionary modes of si continuous without backarc spreading continuous with backarc spreading and a segmented mode with an increase in the coefficient of friction and a decrease in the rate of plastic weakening the amount of convergence needed for si increases from 20 to 220 km while the mode changes from segmented to continuous with backarc spreading and eventually to continuous without backarc spreading if the imposed velocity boundary condition is replaced with an imposed stress the amount of convergence needed for si is reduced and backarc spreading does not occur these geodynamic models provide a basis for understanding the divergent geological pathways of si first ibm evolution is consistent with subduction of an old strong plate with an imposed velocity which founders causing intense backarc spreading and boninitic volcanism second the new hebrides si is in the segmented mode due to its weak plate strength third the puysegur si is in the continuous without backarc spreading mode with no associated volcanic activities fourth the aleutians si has neither trench rollback nor backarc spreading because the slab is regulated by constant ridge push forces

spacing of faults at the scale of the lithosphere and localization instability 1 theory 1 large scale tectonic structures such as orogens and rifts commonly display regularly spaced faults and or localized shear zones to understand how fault sets organize with a characteristic spacing we present a semianalytical instability analysis of an idealized lithosphere composed of a brittle layer over a ductile half space undergoing horizontal shortening or extension the rheology of the layer is characterized by an effective stress exponent ne the layer is pseudoplastic if 1 ne 0 and forms localized structures if 1 ne 0 two instabilities grow simultaneously in this model the buckling necking instability that produces broad undulations of the brittle layer as a whole and the localization instability that produces a spatially periodic pattern of faulting the latter appears only if the material in the brittle layer weakens in response to a local perturbation of strain rate as indicated by 1 ne 0 fault spacing scales with the thickness of the brittle layer and depends on the efficiency of localization localization is more efficient for more negative 1 ne leading to more widely spaced faults the fault spacing is related to the wavelength at which different deformation modes within the layer enter a resonance that exists only if 1 ne 0 depth dependent viscosity and the model density offset the instability wavelengths by an amount al that we determine empirically the wave number of the localization instability is kjl j al 1 ne 1 2 h with h the thickness of the brittle layer j an integer and 1 4 al 1 2 if the strength of the layer increases with depth and the strength of the substrate decreases with depth

why is terrestrial subduction one sided subduction of the lithosphere at convergent plate boundaries takes place asymmetrically the subducted slab sinks downward while the overriding plate moves horizontally one sided subduction in contrast global mantle convection models generally predict downwelling of both plates at convergent margins two sided subduction we carried out two dimensional 2 d numerical experiments with a mineralogical thermomechanical viscoelastic plastic model to elucidate the cause of one sided subduction our experiments show that the stability intensity and mode of subduction depend mainly on slab strength and the amount of weak hydrated rocks present above the slab two sided subduction occurs at low slab strength sin 0 15 the weak interface is maintained by the release of fluids from the subducted oceanic crust as a consequence of metamorphism the resulting weak interplate zone localizes deformation at the interface and decouples the strong plates facilitating asymmetric plate movement our work suggests that high plate strength and the presence of water are major factors controlling the style of plate tectonics driven by self sustaining one sided subduction processes

plate tectonics on the early earth limitations imposed by strength and buoyancy of subducted lithosphere the tectonic style and viability of modern plate tectonics in the early earth is still debated field observations and theoretical arguments both in favor and against the uniformitarian view of plate tectonics back until the archean continue to accumulate here we present the first numerical modeling results that address for a hotter earth the viability of subduction one of the main requirements for plate tectonics a hotter mantle has mainly two effects 1 viscosity is lower and 2 more melt is produced which in a plate tectonic setting will lead to a thicker oceanic crust and harzburgite layer although compositional buoyancy resulting from these thick crust and harzburgite might be a serious limitation for subduction initiation our modeling results show that eclogitization significantly relaxes this limitation for a developed ongoing subduction process furthermore the lower viscosity leads to more frequent slab breakoff and sometimes to crustal separation from the mantle lithosphere unlike earlier propositions not compositional buoyancy considerations but this lithospheric weakness could be the principle limitation to the viability of plate tectonics in a hotter earth these results suggest a new explanation for the absence of ultrahigh pressure metamorphism uhpm and blueschists in most of the precambrian early slabs were not too buoyant but too weak to provide a mechanism for uhpm and exhumation

a simple parameterization of strain localization in the ductile regime due to grain size reduction a case study for olivine we propose a simple parameterization of the transition between dislocation creep and grain size sensitive creep under conditions characteristic of the lithospheric mantle and derived from the results of laboratory experiments on olivine rich rocks through numerical modeling and linear stability analysis we determine the conditions under which this transition takes place and potentially leads to strain localization we pay particular attention to the effect of cooling rate and strain rate which are likely to be dominant parameters in actively deforming tectonic areas we conclude that at constant temperature strain localization can only take place if the rheology of the material is nonlinearly related to grain size that strain localization is facilitated by syndeformation cooling that there is only a narrow region in the strain rate versus cooling rate parameter space where localization is likely to take place and that grain growth inhibits strain localization at fast cooling rates but may lead to grain growth localization at low cooling rates we draw attention to the potential consequences of our analysis of strain localization for the style of plate motions at the earth s surface

convective instability of a boundary layer with temperature and strain rate dependent viscosity in terms of available buoyancy summary cold mantle lithosphere is gravitationally unstable with respect to the hotter buoyant asthenosphere beneath it leading to the possibility that the lower part of the mantle lithosphere could sink into the mantle in convective downwelling such instabilities are driven by the negative thermal buoyancy of the cold lithosphere and retarded largely by viscous stress in the lithosphere because of the temperature dependence of viscosity the coldest and therefore densest parts of the lithosphere are unavailable for driving the instability because of their strength by comparing theory and the results of a finite element representation of a cooling lithosphere we show that for a newtonian fluid the rate of exponential growth of an instability should be approximately proportional to the integral over the depth of the lithosphere of the ratio of thermal buoyancy to viscosity both of which are functions of temperature and thus depth we term this quantity available buoyancy because it quantifies the buoyancy of material sufficiently weak to flow and therefore available for driving convective downwelling for non newtonian viscosity with power law exponent n and temperature dependent pre exponential factor b the instabilities grow superexponentially as described by houseman molnar 1997 and the appropriate timescale is given by the integral of the nth power of the ratio of the thermal buoyancy to b the scaling by the available buoyancy thus offers a method of determining the timescale for the growth of perturbations to an arbitrary temperature profile and a given dependence of viscosity on both temperature and strain rate this timescale can be compared to the one relevant for the smoothing of temperature perturbations by the diffusion of heat allowing us to define a parameter similar to a rayleigh number that describes a given temperature profile s tendency toward convective instability like the rayleigh number this parameter depends on the cube of the thickness of a potentially unstable layer therefore mechanical thickening of a layer should substantially increase its degree of convective instability and could cause stable lithosphere to become convectively unstable on short cales we estimate that convective erosion will in 10 myr reduce a layer thickened by a factor of two to a thickness only 20 to 50 per cent greater than its pre thickened value thickening followed by convective instability may lead to a net thinningof a layer if thickening also enhances the amplitude of perturbations to the layer s lateral temperature structure for the mantle lithosphere the resulting influx of hot asthenosphere could result in rapid surface uplift and volcanism

effects of elasticity on the rayleigh taylor instability implications for large scale geodynamics summary although parts of the lithosphere may be expected to behave elastically over certain timescales this effect is commonly ignored in models of large scale mantle dynamics recently it has been demonstrated that elasticity and in particular viscoelasticity may have a significant effect on the buckling instability and on the creation of lithospheric scale shearzones it is however less clear whether elasticity also has an effect on mantle convection and density driven lithospheric instabilities the focus of this work is therefore to study the effects of elasticity on the twolayer rayleigh taylor rt instability consisting of a maxwell viscoelastic layer overlying a viscous layer of lower density we analyse this problem by performing systematic numerical simulations that are compared with newly derived analytical solutions it is demonstrated that elasticity can be important for certain parameter combinations it leads to a speedup of the rt instability the cause for this speedup is that the rt instability is only sensitive to the viscous fraction of deformation in the viscoelastic layer elasticity reduces the viscous fraction of deformation at timescales shorter than the maxwell relaxation time t m t m g where is the viscosity and g the elastic shear module for plate tectonics on earth the parameters are such that the effect of elasticity on instability growth is negligible for most boundary conditions whereas elasticity does not or only slightly change the timescales for lithospheric detachment of the upper mantle it does significantly alter the response and stress build up in the overlying crust numerical simulations illustrate this effect for lithospheric detachment and show that peak stresses in a viscoelastic crust are smaller than stresses that develop in a viscous crust moreover if the timescale for delamination of the mantle lithosphere is equal or smaller than the maxwell relaxation time of the crust the topography of the crust is increased compared to viscous models

buckling of the oceanic lithosphere from geophysical data and experiments two major hypotheses have been advanced for the formation of the long wavelength 100 300 km undulations of oceanic basement and overlying sediments developed in the central indian ocean basin whole layer folding buckling and local thickening inverse boudinage using appropriately scaled two layer analogue models for the oceanic lithosphere comprising a brittle layer above a ductile layer we show that buckling of the entire brittle layer is likely to be the mode of deformation however the lithosphere asthenosphere boundary remains undisturbed we find a relationship between the thickness of the brittle layer and the wavelength of folding such that the wavelength is 7 times the brittle layer thickness

catastrophic initiation of subduction following forced convergence across fracture zones although the formation of subduction zones plays a central role in plate evolution the processes and geological settings that lead to the initiation of subduction are poorly understood using a visco elastoplastic model we show that a fracture zone could be converted into a self sustaining subduction zone after approximately 100 km of convergence modeled initiation is accompanied by rapid extension of the over riding plate and explains the inferred catastrophic boninitic volcanism associated with eocene initiation of the izu bonin mariana ibm subduction zone using global plate reconstructions we suggest that ibm nucleation was associated with a change in plate motion between 55 and 45 ma we estimate that the forces resisting ibm subduction initiation were substantially smaller than available driving forces

subduction initiation along the inherited weakness zone at the edge of a slab insights from numerical models summary a preexisting weakness zone in the lithosphere is required to initiate subduction here we focus on a new type of weakness zone a subduction transform edge propagator step fault which is inherited from a tear along the edge of a slab using coupled thermal mechanical models we show that step fault perpendicular convergence results in a dipping shear zone in any tectonic setting at a continental margin this shear zone dips towards the continent which is an excellent starting condition for ocean continent subduction if far field convergence persists step faults become new subduction boundaries the trench moves landward during the earliest stages of convergence when slab pull becomes a dominant driving force after 80 km convergence trench roll back commences the initial geometry and mechanical properties of the sub crustal step fault zone affect the results subduction initiation is facilitated by a wide 100 km and low viscosity weakness zone incipient subduction is easier for young oceanic lithosphere due to its lower flexural rigidity and is insensitive to the far field convergence rate as step faults are commonly associated with young oceanic lithosphere subduction initiation is thus relatively easy along them of particular interest are continent ocean margins where step faulting has occurred

how ductile are ductile shear zones three premises of ductile deformation in the middle and lower crust are widely accepted 1 rocks flow with power law viscous rheology 2 localization in ductile shear zones involves strain softening and 3 fluid flows into and is channelized within ductile shear zones ductile viscous shear zones should therefore initially develop along planes of maximum shear stress strain soften and rotate as material planes into the field of progressive extension however the mean stress or pressure within a weak elongate viscous band being stretched is higher than the surrounding matrix and this is difficult to reconcile with premise 3 in contrast mohr coulomb brittle faults always have lower pressure within the fault zone flow of fluid and melt into high temperature shear zones therefore implies that ductile shear zones are not perfectly viscous but have a pressure dependent viscoplastic rheology the continued pressure dependence may reflect significant microcracking on the grain scale even when localized deformation does not produce larger scale discrete fractures

analogue modelling of the initiation of subduction summary we report the results of experiments on the initiation of subduction using stratified analogue models in a large centrifuge where the experiments are driven only by the enhanced gravity of the centrifuge without the effect of external lateral stresses the scaled density of the stratified components resembles that of the asthenosphere and the continental and oceanic lithospheres the experiments demonstrate that under the effect of enhanced gravity the layers simulating the oceanic lithosphere detach from the front of the continental lithosphere and plunge under it pushing the more pliable asthenosphere downwards simultaneously the continental lithosphere is thrust over the downgoing slab where friction is low the continental lithosphere extends considerably so that the ductile continental lithosphere is exposed in some places the rate of thrusting of the experimental continental slab over the oceanic one as well as the amount of extension of the overriding slab and the extent of the rollback of the subduction zone that follows the initial lithospheric detachment are controlled by friction and density differences between the subducting and the overthrust slabs the analogue experiments emphasize the role of lateral density variations in incipient subduction and the effect of differential seismic friction along the subduction plane on the evolution of subduction zones their shape and the evolution of their backarc basins the morphological resemblance of the experimental results to various subduction systems seems to support their applicability to real subduction systems

theoretical analysis of shear localization in the lithosphere deformation in the earth is rarely homogeneous and often occurs in narrow regions of concentrated strain referred to as zones of shear localization mylonites found in the continental crust are the manifestation of shear localization white et al 1980 and at the largest scale shear localization is proposed to be crucial for the generation of tectonic plates from a convecting mantle bercovici 1993 1995b bercovici a 1996 1998 bercovici et al 2000 trompert and hansen 1998 tackley 1998 2000a tackley b c d shear localization is apparent in many field of physics including for example metallurgy lemonds and needleman 1986 rock mechanics poirier 1980 jin et al 1998 granular dynamics scott 1996 geminard et al 1999 e g and glaciology yuen and schubert 1979 however basic solid state rheologies such as elasticity visco elasticity viscous flow and even steady state non newtonian viscous flow are insufficient by themselves to generate shear localization this is because in all such rheologies an increase in deformation or rate of deformation results in greater resistance i e stress instead of self weakening and loss of strength shear localization tends to require dynamic feedback mechanisms wherein self weakening is controlled by a macroscopic variable such as temperature or microscopic structure grain size or microcrack density whose evolution and concentration are themselves determined by deformation in this way deformation can induce weakening which subsequently causes deformation to concentrate on the weak zone being most easily deformed causing further weakening and thus more focusing of deformation and so on one of the most fundamental manifestations of such feedback mechanisms arises from the coupling of viscous heating and temperature dependent viscosity wherein the zone of dissipative heating weakens and thus focuses deformation leading to further heating and weakening this mechanism is thought applicable to problems

evidence for shear heating musgrave block central australia the phenomenon of shear heating is generally difficult to recognise from petrologic evidence alone establishing that shear zones attain higher temperatures than the surrounding country rocks requires independent evidence for temperature gradients in the musgrave block central australia there is a clear spatial association between shear zones and interpreted elevated temperatures eclogite facies shear zones that formed at 550 ma record temperatures of 650 700 c outside the high pressure shear zones minerals with low closure temperatures such as biotite 450 c in the 40ar 39ar and rb sr systems preserve ages 800 ma suggesting that these rocks did not experience temperatures greater than about 450 c at 550 ma for any extended period thus the shear zones record temperatures that are 200 c higher than the surrounding country rocks simple calculations show that the combination of relatively high shear stresses 100 mpa and high strain rates 10 11 s 1 for short durations 1 ma can account for the observed apparent temperature variations the evidence indicates that shear heating is the dominant mechanism for localised temperature increases in the shear zones while the country rock remained at relatively lower temperatures

planforms of self consistently generated plates in 3d spherical geometry 1 in the past decade several studies have documented the effectiveness of plastic yielding in causing a basic approximation of plate tectonic behavior in mantle convection models with strongly temperature dependent viscosity strong enough to form a rigid lid in the absence of yielding the vast majority of such research to date has been in either two dimensional or three dimensional cartesian geometry in the present study mantle convection calculations are performed to investigate the planform of self consistent tectonic plates in three dimensional spherical geometry the results are compared to those of similar calculations where a three dimensional cartesian geometry is used we found that when yield stress of the lithosphere is low 20 mpa a great circle subduction zone forms at low intermediate yield stresses 100 mpa plates spreading centers and subduction zones formed and were destroyed over time at high intermediate yield stresses 200 mpa two plates form separated by a great circle boundary that is a spreading centre on one side and a subduction zone on the other side at high yield stresses 400 mpa a rigid lid was observed the great circle subduction zone and the rigid lid are stable over time while at intermediate yield stresses some episodic behavior is observed the spherical cases showed a higher more earth like toroidal poloidal ratio of the surface velocity field than the cartesian cases

a free plate surface and weak oceanic crust produce single sided subduction on earth 1 earth s lithosphere is characterized by the relative movement of almost rigid plates as part of global mantle convection subduction zones on present day earth are strongly asymmetric features composed of an overriding plate above a subducting plate that sinks into the mantle while global self consistent numerical models of mantle convection have reproduced some aspects of plate tectonics the assumptions behind these models do not allow for realistic single sided subduction here we demonstrate that the asymmetry of subduction results from two major features of terrestrial plates 1 the presence of a free deformable upper surface and 2 the presence of weak hydrated crust atop subducting slabs we show that assuming a free surface rather than the conventional free slip surface allows the dynamical behavior at convergent plate boundaries to change from double sided to single sided a weak crustal layer further improves the behavior towards steady single sided subduction by acting as lubricating layer between the sinking and the overriding plate this is a first order finding of the causes of single sided subduction which by its own produces important features like the arcuate curvature of subduction trenches citation crameri f p j tackley i meilick t v gerya and b j p kaus 2012 a free plate surface and weak oceanic crust produce single sided subduction on earth geophys res lett 39 l03306 doi 10 1029 2011gl050046

the transition from subduction to continental collision crustal structure in the north canterbury region new zealand summary the north canterbury region marks the transition from pacific plate subduction to continental collision in the south island of new zealand details of the seismicity structure and tectonics of this region have been revealed by an 11 week microearthquake survey using 24 portable digital seismographs arrival time data from a well recorded subset of microearthquakes have been combined with those from three explosions at the corners of the microearthquake network in a simultaneous inversion for both hypocentres and velocity structure the velocity structure is consistent with the crust in north canterbury being an extension of the converging chatham rise the crust is about 27 km thick and consists of an 11 km thick seismic upper crust and 7 km thick seismic lower crust with the middle part of the crust being relatively aseismic seismic velocities are consistent with the upper and middle crust being composed of greywacke and schist respectively while several lines of evidence suggest that the lower crust is the lower part of the old oceanic crust on which the overlying rocks were originally deposited the distribution of relocated earthquakes deeper than 15 km indicates that the seismic lower crust changes dip markedly near 43 s to the south west it is subhorizontal while to the north east it dips north west at about lo fault plane solutions for these earthquakes also change near 43 s for events to the south p axes trend approximately normal to the plate boundary reflecting continental collision while for events to the north t axes are aligned down the dip of the subducted plate reflecting slab pull while lithospheric subduction is continuous across the transition it is not clear whether the lower crust near 43 s is flexed or

a unified description of localization for application to large scale tectonics 1 localized regions of deformation such as faults and shear zones are ubiquitous in the earth s lithosphere however we lack a simple unified framework of localization that is independent of the mechanism or scale of localization we address this issue by introducing the effective stress exponent ne a parameter that describes how a material responds to a local perturbation of an internal variable being tested for localization the value of ne is based on micromechanics a localizing regime has a negative ne indicating a weakening behavior and localization is stronger for more negative 1 ne we present expressions for the effective stress exponent associated with several mechanisms that trigger localization at large scale brittle failure with loss of cohesion elastoplasticity rate and state dependent friction shear heating and grain size feedback in ductile rocks in most cases localization does not arise solely from the relation between stress and deformation but instead requires a positive feedback between the rheology and internal variables brittle mechanisms failure and friction are generally described by ne of the order of 100 shear heating requires an already localized forcing which could be provided by a brittle fault at shallower levels of the lithosphere grain size reduction combined with a transition from dislocation to diffusion creep leads to localization only if the grain size departs significantly from its equilibrium value because either large scale flow moves rocks through different thermodynamic environments or new grains are nucleated when shear heating or grain size feedback produce localization 1 ne can be extremely negative and can control lithospheric scale localization

numerical modelling of strain localisation during extension of the continental lithosphere dipping reflectors in the upper mantle are observed on reflection seismic data and in some cases have been interpreted to represent mantle shear zones it is not clear however how these shear zones develop and under what circumstances previous attempts to model strain localisation by strain softening in the ductile regime have failed to show the development of mantle shear zones we present here results from a numerical model of lithospheric extension the model uses an elasto visco plastic rheology dependent on temperature pressure deviatoric stress and composition strain softening is incorporated into the mechanical model via a simple ad hoc strain viscosity relationship the results demonstrate that strain localisation can dominate lithospheric deformation in an extensional regime we illustrate the effects of varying the parameters which define the strain viscosity relationship on the geometry of lithospheric scale shear zones and the rift basin we also investigate the effects on shear zone development of introducing a variety of pre extension weak zones in the crust and or mantle our results suggest that if dipping reflectors observed on deep seismic data around the world are evidence of the existence of mantle shear zones there is a need to review our conceptual models of strain strength evolution during the development of continental rifts

parameters that control lithospheric scale thermal localization on terrestrial planets 1 shear heating induced localization has been suggested as a potentially important mechanism for breaking the lithosphere yet the physical parameters that control the onset of this instability remain unclear we therefore performed systematic 2 d simulations of visco elasto plastic lithospheric deformation in which we addressed the effects of various parameters and we found that a sharp transition exists between localizing and non localizing regimes in a next step we develop a semi analytical model that combines scaling laws with a 1 d lithospheric deformation model we show that the 1 d model successfully predicts the occurrence of shear localization in 2 d models if the thickness of the plastically deforming part of the lower lithosphere is employed as characteristic length scale an application of the 1 d model to the terrestrial planets shows that this type of shear localization is expected to occur most readily on earth

modeling the behavior of the continental mantle lithosphere during plate convergence in studying orogenic processes the mechanism of viscous rayleigh taylor type removal of gravitationally unstable lithosphere is often invoked to explain the behavior of the mantle lithosphere using numerical models we consider this mechanism and explore alternate styles of deep lithospheric deformation during tectonic convergence the numerical experiments incorporate a mix of viscous and plastic rheologies to model the mechanical evolution of the lithosphere asthenosphere system our results suggest that there are a number of deformational modes of the model mantle lithosphere 1 a dripping or rayleigh taylor type instability 2 an asymmetric underthrusting or subduction 3 symmetric ablative plate consumption 4 slab breakoff the failure and detachment of the strong lithosphere and 5 mixed modes with combinations of these processes the development of the modes is controlled by the rate of convergence associated with the background tectonic regime the density field and the rheology of the mantle lithosphere it is important to determine whether these modes occur in the earth beneath collisional orogens

how unique is the udachnaya east kimberlite comparison with kimberlites from the slave craton canada and sw greenland the origin of alkali carbonates and chlorides in the groundmass of unaltered udachnaya east kimberlites in siberia is still controversial contrary to existing dogma that the udachnaya east kimberlite was either contaminated by the crustal sediments or platform brines magmatic origin of the groundmass assemblage has been proposed on the basis of melt immiscibility textures melt inclusion studies and strontium and neon isotope compositions we further tested the idea of alkali and chlorine enrichment of the kimberlite parental melt by studying olivine hosted melt inclusions and secondary serpentine in kimberlites from the slave craton canada gahcho kue jericho aaron and leslie pipes and southern west greenland majuagaa dyke host olivine phenocrysts closely resemble groundmass olivine from the udachnaya east kimberlite in morphology compositions high fo low ca complex zoning with cores of varying shapes and compositions and rims of constant fo melt inclusions in olivine consist of several translucent and opaque daughter phases and vapour bubble s the daughter crystals studied in unexposed inclusions by laser raman spectroscopy and in carefully exposed inclusions by wds eds are represented by na k chlorides calcite dolomite magnesite ca na ca na k and ca mg ba carbonates bradleyite na3mg co3 po4 k bearing nahpoite na2 hpo4 apatite phlogopite and tetraferriphlogopite unidentified sulphates fe sulphides djerfisherite pyrochlore na ca 2nb2o6 oh f monticellite cr spinel and fe ti oxides high abundances of na k e g na k ca 0 15 0 85 and incompatible trace elements in the melt inclusions are confirmed by la icpms analysis of individual inclusions heating experiments show that melting of daughter minerals starts and completes at low temperatures 100oc and 600oc respectively further reinforcing the similarity with the udachnaya east kimberlite serpentine minerals replacing olivine in some of the studied kimberlites demonstrate elevated abundances of chlorine up to 3 4 wt especially in the early generation despite heterogeneous distribution of chlorine such abundances are significantly higher than in the serpentine in abyssal and ophiolitic peridotites 0 5 wt the groundmass of most kimberlites including those studied here and altered kimberlites from the udachnaya pipe contain no alkali carbonates and chlorides and have low na2o 0 2 wt we believe that alteration disturbs original melt compositions with the alkaline elements and chlorine being mostly affected however the compositions of melt inclusions and serpentine are indicative of the chemical signature of a parental kimberlite melt it appears that enrichment in alkalies and chlorine as seen in unaltered udachnaya east kimberlites is shared by other kimberlites and thus can be assigned to deep mantle origin