plate generation in a simple model of lithosphere mantle flow with dynamic self lubrication one of the more enigmatic features of the earth s style of mantle convection is plate tectonics itself in particular the existence of strike slip or toroidal motion toroidal motion is uncharacteristic of basic thermal convection but necessarily forms through the interaction of convective flow and nonlinear rheological mechanisms recent studies have implied that the empirically determined power law rheologies of mantle silicates are not sufficient to generate the requisite toroidal motion a simple source sink model of mantle or lithospheric flow shows that dynamic self lubrication which arises through the coupling of viscous heating and temperature dependent viscosity is highly successful at generating strike slip motion in particular as the viscosity of the fluid system becomes more temperature dependent the toroidal flow field makes an abrupt transition from a state of weak unplate like motion to a state with intense and extremely focused structure in essence the fluid dynamical model develops strike slip faults

a thermodynamically self consistent damage equation for grain size evolution during dynamic recrystallization summary we employ basic non equilibrium thermodynamics to propose a general equation for the mean grain size evolution in a deforming medium under the assumption that the whole grain size distribution remains self similar we show that the grain size reduction is controlled by the rate of mechanical dissipation in agreement with recent findings our formalism is self consistent with mass and energy conservation laws and allows a mixed rheology as an example we consider the case where the grain size distribution is lognormal as is often experimentally observed this distribution can be used to compute both the kinetics of diffusion between grains and of dynamic recrystallization the experimentally deduced kinetics of grain size coarsening indicates that large grains grow faster than what is assumed in classical normal grain growth theory we discuss the implications of this model for a mineral that can be deformed under both dislocation creep and grain size sensitive diffusion creep using experimental data of olivine our predictions of the piezometric equilibrium in the dislocation creep regime are in very good agreement with the observations for this major mantle forming mineral we show that grain size reduction occurs even when the average grain size is in diffusion creep because the largest grains of the grain size distribution can still undergo recrystallization the resulting rheology that we predict for olivine is time dependent and more non linear than in dislocation creep as the deformation rate remains an increasing function of the deviatoric stress this rheology is not localizing

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

tectonic plate generation and two phase damage void growth versus grain size reduction 1 the generation of plate tectonics from mantle convection requires shear localization in order to yield narrow weak plate boundaries separating broad strong plates a plausible shear localizing mechanism involves damage e g distributed microcracking one theoretical model of which involves two phase mechanics two phase damage theory employs a nonequilibrium relation between interfacial surface energy pressure and viscous deformation thereby providing a description of void generation and microcracking and hence weakening failure and shear localization here we examine the application of this theory to the problem of generating plate like behavior from convective type divergent convergent poloidal motion through a source sink formulation we extend the previous damage theory to consider two possible damage effects 1 growth and nucleation of voids associated with dilation of the host matrix and 2 increasing fineness i e reducing coarseness of the mixture by for example grain size reduction void generating damage is found to be poor at plate generation because of the predominance of dilational motion that is adverse to the development of plate like flow fineness generating damage is found to be very efficient at generating plate like behavior if we assume that the matrix viscosity is a simple function of grain void size as is typical for diffusion creep the implied grain size reduction mechanism is different from that of dynamic recrystallization and appears to be more capable of generating the requisite shear localization for forming tectonic plates from mantle flow

mantle convection with a brittle lithosphere thoughts on the global tectonic styles of the earth and venus summary plates are an integral part of the convection system in the fluid mantle but plate boundaries are the product of brittle faulting and plate motions are strongly influenced by the existence of such faults the conditions for plate tectonics are studied by considering brittle behaviour using byerlee s law to limit the maximum stress in the lithosphere in a mantle convection model with temperature dependent viscosity when the yield stress is high convection is confined below a thick stagnant lithosphere at low yield stress brittle deformation mobilizes the lithosphere which becomes a part of the overall circulation surface deformation occurs in localized regions close to upwellings and downwellings in the system at intermediate levels of the yield stress there is a cycling between these two states thick lithosphere episodically mobilizes and collapses into the interior before reforming the mobile lid regime resembles convection of a fluid with temperature dependent viscosity and the boundary layer scalings are found to be analogous this regime has a well defined nusselt number rayleigh number relationship which is in good agreement with scaling theory the surface velocity is nearly independent of the yield stress indicating that the plate motion is resisted by viscous stresses in the mantle analysis suggests that mobilization of the earth s lithosphere can occur if the friction coeycient in the lithosphere is less than 0 03 0 13 lower than laboratory values but consistent with seismic field studies on venus the friction coeycient may be high as a result of the dry conditions and brittle mobilization of the lithosphere would then be episodic and catastrophic

a simple model of plate generation from mantle flow summary a simple model of non newtoniancreeping ow is used to evaluate classes of rheologieswhichallow viscous mantle ow to becomeplate like the model describes shallow layerlithosphericmotion driven by sources and sinks the sources represent spreading ridges while the sinks rep resent subduction zones the sources and sinks thus also prescribe the poloidal component ofthe surface ow eld the toroidal strike slip component of the ow eld is found via thesolution of the stokes equation with non newtonian rheology as a rst basic investigation ofthe model the horizontal divergence from the two dimensional rectangular velocity eld ofolson bercovici 1991 is used for the source sink eld the degree to which the induced uid ow reproducesthe rectangularplate is used to measure the success of differentrheologiesin generating plate like ows results indicate that power law rheologies even in the limit ofvery high power law index can only produce modest plate like ow for example the ratioof toroidal to poloidal kinetic energy for a source sink eld derived from a square plate is atbest 0 65 whereas a perfect square plate has a ratio of 1 0 moreover the power law rheologyappears to reach an asymptotic limit in its ability to produce plate like behavior this impliesthat plate tectonics is unlikely to arise from a power law rheology even in the limit of very high a class of rheologies that yield signi cantly more promisi ng results arise from the carreaupseudo plastic rheology with the power law index taken to be 0 one rheology in thisclass is the continuum model for stick slip earthquake behavior of whitehead gans 1974 which is essentially the carreau equation with 1 this class of rheologies referred to asthe stick slip rheologies induces a toroidal to poloidal kinetic energy ratio for a square plates ssource sink function which can be as high as0 9 the viscosity or strength distribution forthis class of rheologies also appears more plate like showing fairly uniform high viscosity re gions pseudo plates and sharply de ned low viscosity zones pseudo margins in contrast even the most nonlinear power law rheology produces spatially varying high viscosity regionsand relatively smooth low viscosity margins the greater success of the stick slip rheologiesin producing plates is attributed to a self lubricating mechanism in which the transfer of mo mentum from regions of high shear to low shear is inhibited in contrast even in the limit ofin nite power law index a power law rheology can retard but never prohibit momentum trans fer this feature is essential to the sharpening of velocity pro les into plate like pro les whichis illustrated with a simple boundary layertheory key words plate tectonics mantle convection non newtonian ow toroidal poloidal cou pling

mantle convection models featuring plate tectonic behavior an overview of methods and progress abstract arguably the presence of plate tectonic type surface motion for periods that endure over hundreds of millions of years is the primary feature a mantle convection model must possess in order to be considered earth like from the early days of mantle dynamics modeling research has been dedicated to understanding how mantle convection produces the first order observations of plate tectonics as well as how the plates and deep mantle interact fledgling studies of the effect of plates on the mantle recognized the ability of imposed plate scale surface motion to influence global temperatures and heat flux and organize convective planform later studies featuring model plates with dynamically determined velocities discovered that the interaction between convection and the plates could result in cyclic plate motion patterns and other time dependent behavior that was not manifested in systems in which dynamic plates were absent focussing on different aspects of system realism with respect to terrestrial mantle convection has spawned multiple approaches for modeling convection with dynamic integrated plates in broadest terms the two main approaches can be categorized as rheological modeling methods and methods utilizing evolving surface boundary conditions over the past dozen years studies focussing on the former approach have steadily made progress in modeling the self generation of plate tectonics from convection dynamics continual advances have been encouraging and a consensus is beginning to form regarding the necessary requirements for obtaining the primary elements of plate like surface motion however despite significant progress the generation of plates over long periods has not yet been modeled with earth like convective vigor in contrast models utilizing dynamically determined boundary conditions to achieve plate like surface motion have relatively little difficulty with emulating terrestrial convective vigor or simulations of billions of years instead their weakness is more fundamental they can only provide insight into the reciprocating dynamics of the mantle and plates once the existence of the plates is assumed and they cannot model any aspects of the dynamics responsible for the origin of the plates this paper briefly reviews the evolution of mantle convection models featuring plates and examines the progress that has been made in our understanding of the feedback between the mantle and plate tectonics through the use of both rheological and boundary condition modeling methods common findings recent advances and unbridged problems are identified and discussed

initiation of plate tectonics from post magma ocean thermochemical convection leading theories for the presence of plate tectonics on earth typically appeal to the role of present day conditions in promoting rheological weakening of the lithosphere however it is unknown whether the conditions of the early earth were favorable for plate tectonics or any form of subduction and thus how subduction begins is unclear using physical models based on grain damage a grainsize feedback mechanism capable of producing plate like mantle convection we demonstrate that subduction was possible on the hadean earth hereafter referred to as proto subduction or proto plate tectonics that proto subduction differed from modern day plate tectonics and that it could initiate rapidly scaling laws for convection with grain damage show that though either higher mantle temperatures or higher surface temperatures lead to slower plates proto subduction with plate speeds of 1 75 cm yr can still be maintained in the hadean even with a co2 rich primordial atmosphere furthermore when the mantle potential temperature is high e g above 2000 k the mode of subduction switches to a sluggish subduction style where downwellings are drip like and plate boundaries are diffuse finally numerical models of post magma ocean mantle convection demonstrate that proto plate tectonics likely initiates within 100 myr of magma ocean solidification consistent with evidence from hadean zircons after the initiation of proto subduction non plate tectonic sluggish subduction prevails giving way to modern style plate tectonics as both the mantle interior and climate cool hadean proto subduction may hasten the onset of modern plate tectonics by drawing excess co2 out of the atmosphere and cooling the climate

formation of ridges in a stable lithosphere in mantle convection models with a viscoplastic rheology numerical simulations of mantle convection with a viscoplastic rheology usually display mobile episodic or stagnant lid regimes in this study we report a new convective regime in which a ridge can form without destabilizing the surrounding lithosphere or forming subduction zones using simulations in 2 d spherical annulus geometry we show that a depth dependent yield stress is sufficient to reach this ridge only regime this regime occurs when the friction coefficient is close to the critical value between mobile lid and stagnant lid regimes maps of convective regime as a function of the parameters friction coefficients and depth dependence of viscosity are provided for both basal heating and mixed heating situations the ridge only regime appears for both pure basal heating and mixed heating mode for basal heating this regime can occur for all vertical viscosity contrasts while for mixed heating a highly viscous deep mantle is required

delamination and detachment of a lithospheric root abstract orogens can be formed by shortening of the lithosphere on time scales much shorter than that of thermal diffusion for time scales of a few ma the major part of the uplift of an orogen which may occur during the transition from crustal shortening to extension may be due to delamination of the mantle lithosphere rather than to convective thinning the negative buoyancy forces of a lithospheric root may cause lateral shortening while the lithospheric root delaminates peels off from the crust detaches and is replaced by hot upwelling asthenosphere this provides a large input of heat into the crust geological observations show that the late orogenic phase may be characterized by volcanic activity high temperature low pressure metamorphism extension high heat flow and a rapid within a few ma increase of the topography we present dynamically and thermally consistent numerical models of the evolution of an orogenic root mantle rheology is based on laboratory data of olivine while models with the rheology of olivine do not allow for delamination due to its very high viscosity the incorporation of a quasi brittle rheology is necessary for modelling delamination of the mantle lithosphere successful delamination models are always associated with a rapid change in topography we examined the parameter range of our models and found different regimes of behaviour of the orogenic root of the mantle lithosphere no delamination delamination delamination and full detachment for a fixed viscosity of the upper crust of 1023 pa s delamination occurs for a range of viscosities of 1023 pa s to 1020 pa s for the lower crust depending on the thickness of the lithospheric root but full detachment of the delaminated lithospheric slab only occurs if the viscosity of the lower crust is greater than approximately 1021 pa s hot asthenosphere is welling up into the gap opening during delamination further implications of our models are lithospheric roots or unsupported slabs of at least 100 170 km depth extent are needed to provide sufficient negative buoyancy to allow delamination and detachment in all delamination models significant amounts of lower crustal material are subducted into the mantle in applying our models to selected orogens we argue that mantle delamination may have played an important role in the variscan and the himalayan orogenies

1891 1883 ma southern bastar cuddapah mafic igneous events india a newly recognized large igneous province abstract a newly recognized remnant of a paleoproterozoic large igneous province has been identified in the southern bastar craton and nearby cuddapah basin from the adjacent dharwar craton india high precision u pb dates of 1891 1 0 9 ma baddeleyite and 1883 0 1 4 ma baddeleyite and zircon for two se trending mafic dykes from the bd2 dyke swarm southern bastar craton and 1885 4 3 1 ma baddeleyite for a mafic sill from the cuddapah basin indicate the existence of 1891 1883 ma mafic magmatism that spans an area of at least 90 000 km2 in the south indian shield this record of 1 9 ga mafic ultramafic magmatism associated with concomitant intracontinental rifting and basin development preserved along much of the south eastern margin of the south indian shield is a widespread geologic phenomenon on earth similar periods of intraplate mafic ultramafic magmatism occur along the margin of the superior craton in north america 1 88 ga molson large igneous province and in southern africa along the northern margin of the kaapvaal craton 1 88 1 87 ga dolerite sills intruding the waterberg group existing paleomagnetic data for the molson and waterberg 1 88 ga large igneous provinces indicate that the superior and kalahari cratons were at similar paleolatitudes at 1 88 ga but a paleocontinental reconstruction at this time involving these cratons is impeded by the lack of a robust geological pin such as a limpopo like 2 0 ga deformation zone in the superior province the widespread occurrence of 1 88 ga intraplate and plate margin mafic magmatism and basin development in numerous archean cratons worldwide likely reflects a period of global scale mantle upwelling or enhanced mantle plume activity at this time

a continuous kinematic model of plate tectonic motions summary one of the many problems in the study of plate mantle coupling is the disparity between the theory of mantle dynamics which involves continuum physics and the theory of plate tectonics which employs discontinuous plates this discordance causes a variety of difficulties in geodynamic models e g infinite tractions between the plates and mantle as motions of the earth s surface do not involve discontinuous plates i e intraplate deformation is significant and plate margins have finite width it is necessary to adjust the plate tectonic model to allow for continuous surface motions here we present a model of plate motions on a sphere using analytically continuous i e infinitely differentiable functions to describe both plate geometry and plate margin width we first apply this model to the idealized system of a single rectangular plate to examine the influence of plate geometry and size on kinetic energy partitioning of plate motions on a sphere the ratio of toroidal strike slip and spin kinetic energy to poloidal convergent divergent kinetic energy is affected not only by the relative lengths of strike slip and convergent divergent margins but also on plate size which controls the magnitude of plate spin for large plates spin toroidal motion contributes a major portion of the net toroidal energy basic concepts from this simple illustrative model are then expanded to derive an analytically continuous model of present day plate tectonic motions the plate boundary for any given plate is smoothed and expressed as a single valued differentiable function this function is employed to generate the analytically continuous shape function of the plate the shape function is then used to model the plate s motion about its contemporaneous euler pole this technique is carried out for all the plates and their motions are superposed to yield a complete yet simplified model of present day plate motions we use this model to examine the influence of plate margin width on energy partitioning for the earth s plates this approximately indicates the extent to which energy partitioning is influenced by intraplate deformation the calculations indicate that the introduction of finite margin width allows spin vorticity to make a larger contribution to the toroidal energy depending on margin width the partitioning of energy is possibly reversed with toroidal energy assuming a larger proportion of the net kinetic energy the model of continuous plate motions proposed here may not only ease the disparity between the theories of plate tectonics and mantle convection but is a first simple step toward incorporating intraplate deformation into plate tectonics

3 d velocity structure of the san jacinto fault zone near anza california i p waves summary seismic arrival times from microearthquakes ml 4 on the san jacinto fault near anza california are used to find spatial variations in the seismic velocity that are related to the crustal structure of the fault zone preliminary modelling of the 1 d p wave velocity structure of the upper 25 km of crust reveals that most of the variation in velocity is lateral rather than depth dependent the traveltime anomalies due to lateral structure can be partially compensated for by applying station corrections however the variance of the traveltime residuals is still 2 25 times larger than the variance of the picking error the spatially correlated residuals show that this variance is due to localized velocity anomalies and that the data require further modelling using a 3 d velocity structure because the 3 d inverse problem is non unique smoothness constraints are applied to find the model that has the minimum structure required to fit the data to the picking error where a smooth model is defined such that the gradient of the velocity perturbation from the original 1 d model is small with small non zero station corrections a 3 d velocity model can be found that fits the data well the structure is well resolved from 3 to 9 km depth where lateral perturbations of up to 7 per cent are determined independently of the trade off between station corrections and poorly resolved near surface structure the model shows a horizontal gradient with overall faster velocities in the north east side of the fault zone at 3 6 km depth the signature of the fault zone is evident in the lower velocities beneath the surface trace of the fault however at 9 km depth higher seismic velocities are found extending into the fault zone from the north east block this higher velocity region occurs where there is a distinct lack of seismicity on the fault there is also a localized feature in the south west of the modelled region that is more than 10 km from the main trace of the fault with velocities 3 per cent slower than average

effects of plate bending and fault strength at subduction zones on plate dynamics for subduction to occur plates must bend and slide past overriding plates along fault zones because the lithosphere is strong significant energy is required for this deformation to occur energy that could otherwise be spent deforming the mantle we have developed a finite element representation of a subduction zone in which we parameterize the bending plate and the fault zone using a viscous rheology by increasing the effective viscosity of either the plate or the fault zone we can increase the rates of energy dissipation within these regions and thus decrease the velocity of a plate driven by a given slab buoyancy we have developed a simple physical theory that predicts this slowing by estimating a convecting cell s total energy balance while taking into account the energy required by inelastic deformation of the bending slab and shearing of the fault zone the energy required to bend the slab is proportional to the slab s viscosity and to the cube of the ratio of its thickness to its radius of curvature the distribution of dissipation among the mantle lithosphere and fault zone causes the speed of a plate to depend on its horizontal length scale using the observation that earth s plate velocities are not correlated to plate size we can constrain the lithosphere viscosity to be between 50 and 200 times the mantle viscosity with higher values required if the fault zone can support shear tractions 50 mpa over 300 km these subduction zone strengths imply that the mantle fault zone and lithosphere dissipate about 30 10 and 60 of a descending slab s potential energy release if the slab is 100 km thick the lithospheric component is highly dependent on slab thickness it is smaller for thin plates but may be large enough to prevent bending in slabs that can grow thicker than 100 km ubduction zone strength should be more stable than mantle viscosity to changes in mantle temperature so the controlling influence of subduction zones could serve to stabilize plate velocities over time as the earth cools because the details of convergent plate boundaries are so important to the dynamics of plate motion numerical models of mantle flow should treat subduction zones in a realistic way

spherical shell models of mantle convection with tectonic plates abstract a simple three dimensional spherical model of mantle convection where plates are taken into account in the top boundary condition allows to investigate the plate tectonics mantle convection coupling in a self consistent way avoiding the strong difficulties inherent in the numerical treatment of rheology the plate condition appears efficient in reproducing the earth like features as subduction mid oceanic ridges and hotspots whereas the free slip condition leads to a classical polygonal cell pattern with cylindrical hot plumes surrounded by downwellings the plate condition favors the development of strong linear downwellings associated to passive diverging zones along plate boundaries these cold currents very similar to subductions act the main role in mantle convection they drive the whole circulation in that context hot plumes remain almost independent except if on the long term cold material spreading at the core surface induces a slight migration below a few mm yr of their surface impingement the main result is that plate tectonics appear to be more than a simple mode of organization of the surface movements it is the essence of the earth mantle dynamics

thermal convection in a cylindrical annulus with a non newtonian outer surface this study presents the results of numerical simulations of a model for lithospheremantle coupling in a terrestrial type planet to first order a geologically active terrestrial type planet may consist of a metallic core silicate mantle and lithosphere with the lithosphere being rheologically different from the mantle therefore we have developed a numerical model consisting of a thin non newtonian fluid hoop that is dynamically coupled to a thick newtonian fluid cylindrical annulus thus the rheological dichotomy between mantle and lithosphere is built into the model time dependent calculations show the existence of at least two regimes of behaviors in one regime the behavior of the hoop switches between periods characterized by low or high speeds in response to changes in convective vigor and planform this regime may apply to the planet venus where the available evidence indicates that prior to 500 myr ago the planet was resurfaced on a time scale of 100 myr since that time large scale tectonic activity on venus has been sharply curtailed in the other regime which is more like plate tectonics on earth the hoop speeds rise and fall on short time scales

grain damage hysteresis and plate tectonic states abstract shear localization in the lithosphere is an essential ingredient for understanding how and why plate tectonics is generated from mantle convection on terrestrial planets the theoretical model for grain damage and pinning in two phase polycrystalline rocks provides a frame work for understanding lithospheric shear weakening and plate generation and is consistent with laboratory and field observations of mylonites grain size evolves through the competition between coarsening which drives grain growth and damage which drives grain reduction the interface between crystalline phases controls zener pinning which impedes grain growth damage to the interface enhances the zener pinning effect which then reduces grain size forcing the rheology into the grain size dependent diffusion creep regime this process thus allows damage and rheological weakening to co exist providing a necessary positive self weakening feedback moreover because pinning inhibits grain growth it promotes shear zone longevity and plate boundary inheritance however the suppression of interface damage at low interface curvature wherein inter grain mixing is inefficient and other energy sinks of deformational work are potentially more facile causes a hysteresis effect in which three possible equilibrium grain sizes for a given stress coexist 1 a stable large grain weakly deforming state 2 a stable small grain rapidly deforming state analogous to ultramylonites and 3 an unstable intermediate grain size state perhaps comparable to protomylonites a comparison of the model to field data suggests that shear localized zones of small grain mylonites and ultra mylonites exist at a lower stress than the co existing large grain porphyroclasts rather than as predicted by paleopiezometers or paleowattmeters at a much higher stress this interpretation of field data thus allows localization to relieve instead of accumulate stress the model also predicts that a lithosphere that deforms at a given stress can acquire two stable deformation regimes indicative of plate like flows i e it permits the coexistence of both slowly deforming plate interiors and rapidly deforming plate boundaries earth seems to exist squarely inside the hysteresis loop and thus can have coexisting deformation states while venus appears to straddle the end of the loop where only the weakly deforming branch exists

plate generation and two phase damage theory in a model of mantle convection summary the formation of narrow rapidly deforming plate boundaries separating strong plate interiors are integral components of the generation of plate tectonics from mantle convection the development of narrow plate boundaries requires the interaction of a non linear rheology and convection one such non linear rheology is two phase damage theory which employs a nonequilibrium relation between interfacial surface energy pressure and viscous deformation thereby forming a theoretical model for void generation two phase damage theory was recently extended to allow for deformational work to increase the fineness reduce the grain size of the matrix phase we present results testing two phase damage theory in a 2 d convectively driven system where we allow for 1 pure void generating damage 2 pure fineness generating damage and 3 combined void and fineness generating damage pure void generating damage is found to be unsuccessful at producing plate like features finenessgenerating damage is successful at inducing plate like behaviour in certain circumstances including increasing viscosity sensitivity to fineness and certain regimes of damage input and healing rate cases with combined void and fineness generating damage produce significantly more localization than the end members due to the apparent increase of deformational work input into fineness generation the interaction of microcracks and grain size reduction in two phase damage theory suggests a rheological model for shear localization necessary for the formation of plate tectonic boundaries

controls of the structure of subducted slabs numerical simulations of subducting slabs are formulated in which the shape and dip of the slab are determined by the dynamics of the flow rather than imposed a priori the dip of slabs is a function of the time since the initiation of subduction slabs fold develop a kink in dip and thicken on entry into a high viscosity lower mantle comparison of the simulations with seismic observations suggest that the lower mantle is at least 10 30 times more viscous than the upper mantle

generation of plate tectonics with two phase grain damage and pinning source sink model and toroidal flow abstract the grain damage and pinning mechanism of bercovici and ricard 2012 for lithospheric shear localization is employed in two dimensional flow calculations to test its ability to generate toroidal strike slip motion and influence plate evolution this mechanism posits that damage to the interface between phases in a polycrystalline material like peridotite composed primarily of olivine and pyroxene increases the number of small zener pinning surfaces which then constrain mineral grains to ever smaller sizes regardless of creep mechanism this effect allows a self softening feedback in which damage and grain reduction can co exist with a grain size dependent diffusion creep rheology moreover grain growth and weak zone healing are greatly impeded by zener pinning thereby leading to long lived relic weak zones the fluid dynamical calculations employ source sink driven flow as a proxy for convective poloidal flow upwelling downwelling and divergent convergent motion and the coupling of this flow with non linear rheological mechanisms excites toroidal or strike slip motion the numerical experiments show that pure dislocation creep rheology and grain damage without zener pinning as occurs in a single phase assemblages permit only weak localization and toroidal flow however the full grain damage with pinning readily allows focussed localization and intense plate like toroidal motion and strike slip deformation rapid plate motion changes are also tested with abrupt rotations of the source sink field after a plate like configuration is developed the post rotation flow and material property fields retain memory of the original configuration for extensive periods leading to suboptimally aligned plate boundaries e g strike slip margins non parallel to plate motion oblique subduction and highly localized weak and long lived acute plate boundary junctions such as at what is observed at the aleutian kurile intersection the grain damage and pinning theory therefore readily satisfies key plate tectonic metrics of localized toroidal motion and plate boundary inheritance and thus provides a predictive theory for the generation of plate tectonics on earth and other planets

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

on the equipartition of kinetic energy in plate tectonics kinetic energy in present day plate motions is partitioned approximately equally between poloidal and toroidal parts the poloidal part is excited by buoyancy forces and is associated with cellular flow in the mantle most of the toroidal part is derived from strike slip motion at transform faults and from oblique subduction at convergent margins plate spin accounts for only a few percent of the toroidal energy of the lithosphere using a simple kinematic model we demonstrate that a square shaped plate drifting without spin has equal poloidal and toroidal energies we then show that the most probable state for an array of many rectangular plates is equipartition of poloidal and toroidal kinetic energy provided the drift directions of individual plates in the array are random our model predicts that convergent margins occupy 42 of plate boundaries while divergent and transform margins occupy 25 and 33 respectively this distribution is in good agreement with the actual distribution along the boundaries of the pacific india cocos and nazca plates which contain more than 90 of the lithosphere kinetic energy according to these calculations equipartitioning of plate kinetic energy implies a large degree of decoupling between plates and a disorganized pattern of convection in the mantle

self consistent generation of tectonic plates in time dependent three dimensional mantle convection simulations 1 presented here are self consistent three dimensional simulations of mantle convection some of which display an approximation of plate tectonic behavior that is continuous in space and time plate behavior arises through a reasonable material description of silicate deformation with a simple yield stress being sufficient to give first order plate like behavior however the required yield strength or fault frictional coefficient is much less than experimentally determined values toroidal poloidal ratios are within geologically observed limits the sensitivity of the system to yield strength and the form of strength envelope is systematically investigated optimum plate character is obtained in a narrow range of yield strength below which diffuse boundaries and above which episodic behavior and eventually a rigid lid are observed models with mobile lids develop very long wavelength horizontal structure the longest wavelength possible in the domain two dimensional models display much greater time dependence than three dimensional models

a source sink model of the generation of plate tectonics from non newtonian mantle flow a model of mantle convection which generates plate tectonics requires strain rate or stress dependent rheology in order to produce strong platelike flows with weak margins as well as strike slip deformation and plate spin i e toroidal motion here we employ a simple model of source sink driven surface flow to determine the form of such a rheology that is appropriate for earth s present day plate motions in this model lithospheric motion is treated as shallow layer flow driven by sources and sinks which correspond to spreading centers and subduction zones respectively the source sink field is derived from the horizontal divergence of plate velocities and thus directly prescribes poloidal motion the toroidal flow field is solved through the non newtonian stokes equation for shallow layer tangential flow on the surface of a sphere two plate motion models are used to derive the source sink field the first is an idealized square plate which is used to explore the basic aspects of the model the second is an analytically continuous model of earth s present day plates bercovici and wessel 1994 as originally implied in the simpler cartesian version of this model bercovici 1993 the classical power law rheologies do not generate platelike flows as well as the hypothetical whitehead gans stick slip rheology which incorporates a simple self lubrication mechanism for the idealized plate geometry the power law rheologies yield much more diffuse strike slip shear i e radial vorticity than the stick slip rheology for the present day plate geometry the power law rheologies fail to reproduce the original proportion of left and right lateral strike slip shear whereas the stick slip rheology gives almost exactly the right proportion none of the fluid rheologies examined however produce more than approximately 60 of the original maximum shear for either plate model the viscosity fields produced by the power law rheologies are diffuse and the viscosity lows over strike slip shear zones or pseudo margins are not as small as over the prescribed convergent divergent margins in contrast the stick slip rheology generates very platelike viscosity fields with sharp gradients at the plate boundaries and margins with almost uniformly low viscosity quantitative comparisons with the toroidal poloidal kinetic energy partitioning and vorticity fields of the original plate model are also examined and the stick slip rheology is generally found to yield the most favorable comparisons power law rheologies with high viscosity contrasts however lead to almost equally favorable comparisons though these also yield the least platelike viscosity fields this implies that the magnitude of toroidal flow and platelike strength distributions are not necessarily related arid thus may present independent constraints on the determination of a self consistent plate mantle rheology the results of this study however predict that if such a rheology can indeed be uniquely determined it is likely to be in the class of stick slip self lubricating rheologies

the relationship between plate velocity and trench viscosity in newtonian and power law subduction calculations convection with a newtonian temperature dependent rheology leads to little or no surface velocity unless zones of weakness are introduced plate like features are observed in calculations both with newtonian rheology employing imposed weak zones and with power law non newtonian rheology where high stresses at the trench reduce the effective viscosity since deformation at subduction zones involves faulting both of these parameterizations should be treated with some skepticism it is important to understand how the parameterizations affect the model results we study the relationship between trench viscosity and plate velocity using a newtonian rheology by varying the viscosity at the trench the plate velocity is a function of the trench viscosity for fixed rayleigh number and plate slab viscosity slab velocities for non newtonian rheology calculations are significantly different from slab velocities from newtonian rheology calculations at the same effective rayleigh number both models give reasonable strain rates for the slab when compared with estimates of seismic strain rate non newtonian rheology eliminates the need for imposed weak zones and provides a self consistent fluid dynamical mechanism for subduction in numerical convection models

role of faults nonlinear rheology and viscosity structure in generating plates from instantaneous mantle flow models concentrated strain within plate margins and a significant toroidal component in global plate motion are among the most fundamental features of plate tectonics a significant proportion of strain in plate margins is accommodated through motion on major tectonic faults the decoupling influence of faulted plate margins primarily results from history dependent lithospheric deformation rather than from instantaneous stress weakening rheologies for instantaneous mantle flow models we argue that faults should be treated as preexisting mechanical structures with models incorporating preexisting faults a power law rheology with an exponent of 3 and slab pull and ridge push forces we demonstrate that nonlinear interaction between weak faults and this power law rheology produces plate like motion our models show that in order to produce plate like motion the frictional stress on faults needs to be small and the asthenosphere viscosity should be much weaker than that of lithosphere while both plateness and the ratio of toroidal to poloidal velocities are reduced with increasing fault coupling the viscosity contrast between the lithosphere and asthenosphere only influences plateness this shows that both diagnostics plateness and the ratio of toroidal to poloidal velocities are necessary to characterize plate motion the models demonstrate that weak transform faults can guide plate motion this guiding property of transform faults and the decoupling of thrust faults result in oblique subduction where the strike of subducted slabs is oblique to transform faults subducted slabs beneath a dipping fault produce oceanic trench and fore bulge topography and principal stresses consistent with subduction zone observations

differential rotation between lithosphere and mantle a consequence of lateral mantle viscosity variations the description of plate motions in the so called hotspot reference frame introduces a global rotation of the lithosphere with respect to the mantle this rotation called toroidal field of degree 1 is roughly westward it reaches an amplitude of about 2 cm yr and has been consistently found in the different generation of plate tectonic models various authors have tried to relate this observation to the deceleration of the earth s rotation to polar wander or to tidal drag however these different physical mechanisms cannot explain the requested amplitude in this paper we compare the values of this rotation vector using different relative plate motion models expressed in the hotspot reference frame in a model earth with lateral viscosity variations a differential rotation is predicted the observed net lithospheric rotation is consistent with the dynamics of a model earth where the asthenospheric viscosity below the oceans is at least one order of magnitude lower than underneath the continents this relative westward drift of the lithosphere may account for the significant structural differences between east or west dipping subduction zones

convection in three dimensions with surface plates generation of toroidal flow this work presents numerical calculations of mantle convection that incorporate some of the basic observational constraints imposed by plate tectonics the model is three dimensional and includes surface plates it allows plate velocity to change dynamically according to the forces which result from convection we show that plates are an effective means of introducing a toroidal component into the flow field after initial transients the plate motion is nearly parallel to transform faults and in the direction that tends to minimizes the toroidal flow field the toroidal field decays with depth from its value at the surface the poloidal field is relatively constant throughout the layer but falls off slightly at the top and bottom boundaries layered viscosity increasing with depth causes the toroidal field to decay more rapidly effectively confining it to the upper low viscosity layer the effect of viscosity layering on the poloidal field is relatively small which we attribute to its generation by temperature variations distributed throughout the system the generation of toroidal flow by surface plates would seem to account for the observed nearly equal energy of toroidal and poloidal fields of plate motions on the earth a low viscosity region in the upper mantle will cause the toroidal flow to decay significantly before reaching the lower mantle the resulting concentration of toroidal flow in the upper mantle may result in more thorough mixing there and account for some of the geochemical and isotopic differences proposed to exist between the upper and lower mantles

computational approaches to studying non linear dynamics of the crust and mantle we outline a mathematical formulation for mantle convection which can deal with the viscoelastic plastic rheology of the cool parts of the lithosphere this formulation is then analyzed to expose the numerical challenges inherent in the equations and a suitable solution strategy is outlined with this strategy in place we discuss a parallel implementation explaining how we maintain computational efficiency in a tiered and modular software environment we show two examples from geodynamics which demonstrate the capability of the numerical method and its implementation c 2007 elsevier b v all rights reserved

joint modeling of lithosphere and mantle dynamics evaluation of constraints from global tomography models with the advances in technology seismological theory and data acquisition a number of high resolution seismic tomography models have been published however discrepancies between tomography models often arise from different theoretical treatments of seismic wave propagation different inversion strategies and different data sets using a fixed velocity to density scaling and a fixed radial viscosity profile we compute global mantle flow models associated with the different tomography models and test the impact of these for explaining surface geophysical observations geoid dynamic topography stress and strain rates we use the joint modeling of lithosphere and mantle dynamics approach of ghosh and holt 2012 to compute the full lithosphere stresses except that we use hc for the mantle circulation model which accounts for the primary flow coupling features associated with density driven mantle flow our results show that the seismic tomography models of s40rts and saw642an provide a better match with surface observables on a global scale than other models tested both of these tomography models have important similarities including upwellings located in pacific eastern africa iceland and mid ocean ridges in the atlantic and indian ocean and downwelling flows mainly located beneath the andes the middle east and central and southeast asia

plate like regime of a numerically modeled thermal convection in a fluid with temperature pressure and stress history dependent viscosity 1 a series of numerical models are presented for two dimensional thermal convection in a fluid with viscosity that nonlinearly depends on degree of damage as well as temperature and pressure increases and viscosity decreases with time when the convection induces strong viscous dissipation the convecting fluid recovers from the damage with a characteristic time that depends on temperature the dependence of viscosity induces a stress viscosity relationship that consists of two branches the intact branch at low stress and the damaged branch at high stress with a hysteresis between the two branches is small large and viscosity is high low on the intact damaged branch the hysteresis lets the viscosity depend on stress history the dependence of viscosity on stress history due to the hysteresis induces a regime where the numerically modeled lithosphere along the surface boundary is fragmented into smaller pieces that are on the intact branch and rigidly move the pieces of lithosphere are separated by narrow mechanically weak zones that are on the damaged branch each piece of lithosphere is further fragmented and mechanically weak zones are newly formed only when the piece is tapped by particularly strong hot uprising plumes this plate like regime is the only regime among the convective regimes searched here where each piece of lithosphere rigidly moves and still is not ruptured by the forces that drive the piece the earth s mantle is suggested to be on the plate like regime

laboratory constraints on the rheology of the upper mantle the dynamics of convection and the mechanical behavior of the lithosphere are controlled by the rheology of upper mantle rocks for this reason experimental and theoretical studies on the rheology of olivine aggregates have been fields of active research for at least the last 35 years in this short course paper i briefly review some experimental and theoretical constraints on the rheology of upper mantle rocks and minerals and then discuss the application of these data for understanding the rheology of the upper mantle in different tectonic environments there is an expansive literature on the subject of mantle rheology extensive reviews and background can be found in several recent articles and books poirier 1985 ranalli 1995 karato and wu 1993 kohlstedt et al 1995 drury and fitzgerald 1998 hirth and kohlstedt 2003 as well as numerous references made throughout this chapter i focus the discussion of this chapter on the application of experimental data for constraining the rheology of the oceanic lithosphere and mantle constraints on mantle rheology based on extrapolation of laboratory experiments to deformation conditions in the oceanic lithosphere and asthenosphere are illuminating for several reasons first the composition of the mantle is relatively well constrained by analyses of peridotites from ophiolites and mid ocean ridges as well as chemical analyses of basalts second the oceanic lithosphere is comprised of rock that cooled from high temperature conditions at high pressure and is therefore not previously fractured in this way the lithosphere is similar to the ideal rocks we use in our experiments third the temperature of the lithosphere is constrained by a number of geophysical observations fourth microstructural observations on naturally deformed mantle rocks justify applying experimental flow laws at geologic conditions finally several independent geophysical observations such as constraints on viscosity based on analysis

relating rapid plate motion variations to plate boundary forces in global coupled models of the mantle lithosphere system effects of topography and friction abstract recent high resolution models of past plate motions and their comparison with plate motion models inferred from space geodetic techniques reveal a number of short term variations in global plate velocities over the past 10 myrs such variations serve as powerful probe into the nature and magnitude of plate boundary forces because they are unlikely to originate from changes in mantle buoyancy forces which evolve on longer time scales here we explore the constraints of the velocity record using a novel coupled modeling approach of global neo tectonic simulations combined with realistic plate driving forces obtained from mantle circulation models mcms to arrive at simple global budgets of mantle lithosphere and plate boundary forces we focus on three plate boundary systems along the nazca south america plate margin the aleutian trench and the india australia plate boundary to show that gravitational spreading from high topography in the andes and tibet contributes substantially to the global plate tectonic force balance and that this contribution is sufficient to explain some 35 of recent velocity changes over the earth s surface including among others the observed 30 convergence reduction between the nazca south america plates our models make a number of specific predictions such as significant lateral variations in plate coupling forces along a given margin revealed by trench parallel gravity and bathymetry anomalies and the occurrence of large earthquakes as well as differences by as much as a factor of five from margin to margin they also support the notion of a relatively young plate boundary separating the india and australia plates which has been previously suggested based on independent observations importantly we find that the modeled nazca south america convergence reduction explains recent spreading rate variations in the south atlantic and south pacific which points to the importance of far field effects on the adjacent continents in explaining the spreading record of oceanic basins our numerical results demonstrate a that detailed budgets of forces acting upon plates can be obtained and b support the notion of strong forcing along weak plate boundaries

self consistent generation of tectonic plates in three dimensional mantle convection abstract despite the fundamental importance of plates in the earth s mantle convection plates have not generally been included in numerical convection models or analog laboratory experiments mainly because the physical properties which lead to plate tectonic behavior are not well understood strongly temperature dependent viscosity results in an immobile rigid lid so that plates where included at all in 3 d models have always been imposed by hand an important challenge is thus to develop a physically reasonable material description which allows plates to develop self consistently this paper focuses on the role of ductile shear localization in two dimensional geometry it is well established that strain rate softening non newtonian rheologies e g power law visco plastic cause weak zones and strain rate localization above up and down wellings resulting in a rudimentary approximation of plates three dimensional geometry however is fundamentally different due to the presence of transform plate boundaries with associated toroidal motion since power law and visco plastic rheologies do not have the property of producing shear localization it is not surprising that they do not produce good plate like behavior in three dimensional calculations here it is argued that a strain rate weakening rheology previously shown to produce plate like behavior in a two dimensional sheet representing the lithosphere is a reasonable generic description of various weakening processes observed in nature one and two dimensional models are used to show how this leads to shear localization and the formation of faults this rheology is then applied to the high viscosity lithosphere of 3 d mantle convection calculations and the velocity pressure viscosity solution for the entire 3 d domain lid and underlying mantle is solved self consistently it is found that the lithosphere divides into a number of very high viscosity plates separated by narrow sharply defined weak zones with a viscosity many orders of magnitude less than the plate interiors broad weak zones with dominant convergent divergent motion above up and down wellings are interconnected by a network of narrow weak zones with dominant strike slip motion passive spreading centers are formed in internally heated cases while the resulting plates are not fully realistic these results show that self consistent plate generation is a realizable goal in three dimensional mantle convection and provide a promising avenue for future research

spontaneous development of arcuate single sided subduction in global 3 d mantle convection models with a free surface we present temporally evolving 3 d global mantle convection models with single sided subduction and a free surface in both 3 d cartesian and fully spherical geometry special focus is given to the spontaneous development of three dimensional structures at the surface and in the upper mantle we find that an arcuate shape is the natural form for trenches and slabs cartesian models are used first to study the dynamic evolution of subduction zones spreading ridges and interconnected transform features these experiments highlight the strong variation of spontaneously developing arcuate slab curvature and subduction polarity along the trench strike the spontaneous development of spreading ridges leads to lateral offsets between separated segments that are characterized by normal transform motion spherical models then allow insights into the evolution of plate tectonics on a sphere investigated are the spontaneous evolution of slab geometry trench motion and subduction induced mantle flow two new dynamical features are discovered back slab spiral flow and slab tunneling

generation of plate tectonics from lithosphere mantle flow and void volatile self lubrication abstract the formation of plate tectonics from mantle convection necessarily requires nonlinear rheological behavior recent studies suggest that self lubricating rheological mechanisms are most capable of generating plate like motion out of fluid flows the basic paradigm of self lubrication is nominally derived from the feedback between viscous heating and temperature dependent viscosity here we propose a new idealized self lubrication mechanism based on void e g pore and or microcrack generation and volatile e g water ingestion we test this void volatile self lubrication mechanism in a source sink flow model this leads to a basic nonlinear system which permits the excitation of strike slip toroidal motion a necessary ingredient of plate like motion out of purely divergent i e poloidal or characteristically convective flow with relatively inviscid void filling volatiles the void volatile mechanism yields a state of highly plate like motion i e with uniformly strong plate interiors weak margins and extremely focussed strike slip shear zones moreover the void volatile model obeys a chemical diffusion time scale that is typically much longer than the thermal convection time scale the model thus complies with the observation that plate boundaries are long lived and survive even while inactive the void volatile model of self lubrication therefore predicts self focussing shear zones plate generation and plate boundary longevity through what has long been suspected to be a key ingredient for the existence of plate tectonics i e water

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

depositional history of the chhattisgarh basin central india constraints from new shrimp zircon ages a reply abstract the indian shield includes the singhbhum bastar and east and west dharwar cratons proterozoic sedimentary basins formed on these cratons have preserved rocks with a range of degrees of metamorphism and deformation in the chhattisgarh basin within the bastar craton the ca 2200 2500 m thick chhattisgarh supergroup has been preserved in nearly pristine condition previous work has shown that the sukhda tuff located about 2200 m from the base of the section was formed ca 1007 ma new u pb shrimp age determinations show that the singhora tuff located about 100 m above the base of the basin is not older than ma thus most of the chhattisgarh supergroup was deposited between 1400 and 1000 ma age data for detrital zircons from sandstones show that regardless of their stratigraphic position there is a unimodal age peak near 2500 ma the typical age of adjacent granitic and rhyolitic basement rocks indicating that these constituted the principal provenance of the sediments in the chhattisg

predicting the lithospheric stress field and plate motions by joint modeling of lithosphere and mantle dynamics the way in which basal tractions associated with mantle convection couples with the lithosphere is a fundamental problem in geodynamics a successful lithosphere mantle coupling model for the earth will satisfy observations of plate motions intraplate stresses and the plate boundary zone deformation we solve the depth integrated three dimensional force balance equations in a global finite element model that takes into account effects of both topography and shallow lithosphere structure as well as tractions originating from deeper mantle convection the contribution from topography and lithosphere structure is estimated by calculating gravitational potential energy differences the basal tractions are derived from a fully dynamic flow model with both radial and lateral viscosity variations we simultaneously fit stresses and plate motions in order to delineate a best fit lithosphere mantle coupling model we use both the world stress map and the global strain rate model to constrain the models we find that a strongly coupled model with a stiff lithosphere and 3 4 orders of lateral viscosity variations in the lithosphere are best able to match the observational constraints our predicted deviatoric stresses which are dominated by contribution from mantle tractions range between 20 70 mpa the best fitting coupled models predict strain rates that are consistent with observations that is the intraplate areas are nearly rigid whereas plate boundaries and some other continental deformation zones display high strain rates comparison of mantle tractions and surface velocities indicate that in most areas tractions are driving although in a few regions including western north america tractions are resistive citation ghosh a w e holt and l m wen 2013 predicting the lithospheric stress field and plate motions by joint modeling of lithosphere and mantle dynamics

solution of the vsp one dimensional inverse problem the acoustical impedance distribution of the substratum or equivalently the reflection coefficient sequence is determined from vsp data this nonlinear inverse problem is solved by a least squares method as the wavelet is unknown the impedance distribution and the neumann boundary condition which characterizes the excitation of the medium are simultaneously identified the inversion method is applied to synthetic and field vsp s the result is satisfactory even when strong noise corrupts the data provided that a suitable constraint on the impedance distribution is introduced in order to ensure the stability of the inverse problem the reliability of the inversion result in the case of field vsp is confirmed some ways in which this result may be used are illustrated calibration of the seismic surface data multiple identification prediction ahead of the bit

a simple global model of plate dynamics and mantle convection cooling and thickening of lithospheric plates with age and subduction result in large scale horizontal density contrasts tending to drive plate motions and mantle flow we quantify the driving forces associated with these density contrasts to determine if they can drive the observed plate motions first two dimensional models are computed to evaluate the effects of assumed rheologies and boundary conditions we are unable to obtain platelike behavior in viscous models with traction free boundary conditions the piecewise uniform velocities distinctive of plate motion can be imposed as boundary conditions and the dynamic consistency of the models evaluated by determining if the net force on each vanishes if the lithosphere has a newtonian viscous rheology the net force on any plate is a strong function of the effective grid spacing used leading to ambiguities in interpretation incorporating a rigid plastic lithosphere which fails at a critical yield stress into the otherwise viscous model removes these ambiguities the model is extended to the actual three dimensional spherical plate geometry the observed velocities of rigid plastic plates are matched to the solution of the viscous stokes equation at the lithosphere asthenosphere boundary body forces from the seismically observed slabs from the thickening of the lithosphere obtained from the actual lithospheric ages and from the differences in structure between continents and oceans are included interior density contrasts such as those resulting from upwellings from a hot bottom boundary layer are assumed to occur on a scale small compared to plate dimensions and are not included the driving forces from the density contrasts within the plates are calculated and compared to resisting forces resulting from viscous drag computed from the three dimensional global return flow and resistance to deformation at converging boundaries the rms residual torque is 30 of the driving torque the density contrasts within the plates themselves can reasonably account for plate motions body forces from convection in the interior may provide only a small net force on the plates at converging boundaries the lithosphere has a yield stress of 100 bars drag at the base of the plates is 5 bars and resists plate motion the net driving forces from subducting slabs and collisional resistance are localized and approximately balance driving forces from lithospheric thickening are distributed over the areas of the plates as is viscous drag the approximate balance of these two forces predicts plate velocities uncorrelated with plate area as observed the model represents a specific case of boundary layer convection the dynamical results are consistent with either upper mantle or mantle wide convection

role of ocean continent contrast and continental keels on plate motion net rotation of lithosphere and the geoid three dimensional spherical shell models of mantle convection have been formulated to investigate the effects of ocean continent contrast i e different viscosity for continental and oceanic lithospheres and continental keels on plate motion net rotation of lithosphere i e degree 1 toroidal plate motion and the geoid the models include relatively realistic plate rheology i e strong plate interiors and weak plate margins and continental keel structure based on seismic models the mantle flow in the models is driven by slab buoyancy the models demonstrate that the ocean continent contrast and continental keels have minor effects on the long wavelength geoid for degrees 2 5 however continental keels overriding subducted slabs for example in north america can produce large negative gravity anomalies at a regional scale this may have important implications to interpreting the gravity anomalies in north america our models show that when plates bounded by weak plate margins have the same thickness neither weak plate margins nor the ocean continent contrast efficiently excite net rotation of lithosphere although they excite toroidal motion at higher harmonic degrees however plate thickness variations like continental keels excite the net rotation in spite of their ability to excite the net rotation continental keels as thick as 300 km cannot provide the necessary coupling to the deep mantle to produce the observed net rotation of lithosphere and slow continental motion if there is a weak asthenosphere underlying them if the thermomechanic structure of north american continental upper mantle derived from seismic and heat flow studies is representative our models suggest that the temperature and pressure dependent mantle rheology may not produce sufficiently high viscosity below continental keels that is needed to explain the observed plate motion our study hints the necessity to include more realistic treatment of plate boundaries in future studies to assess possible effects of plate plate coupling on plate motion

the nature of mesoproterozoic central indian tectonic zone with exhumed and reworked older granulites abstract the ese wnw trending central indian tectonic zone citz divides the indian subcontinent into southern and northern crustal provinces its narrow northern belt consists of closed early proterozoic mahakoshal rift zone which is presently confined between two moho reaching faults that characterize the son narmada sona lineament the mesoproterozoic sausar mobile belt smb the chhotanagpur granite gneiss complex cggc and the gneissic complex of northeast india represent the wider southern belt the mahakoshal rift belt has a thick pile of mafic ultramafic rocks and possibly oceanic components the basin closed due to a south directed subduction creating a magmatic arc that was sutured to its southern boundary during 1 8 1 7 ga a south dipping ductile shear zone known as the son narmada south fault affects both its supracrustals and intrusive granitoids the son narmada south fault generally delimits the northern boundary of the gondwana basins whereas the son narmada north fault delineates the northern boundary of the mahakoshal mobile belt and the southern boundary of the meso neoproterozoic vindhyan basin the smb representing the southern belt of the citz in the central sector comprises strongly folded and metamorphosed non volcanic and mn rich sausar sediments intermixed with reworked basement gneisses migmatites and granulites representing the pre sausar assemblage the sausar orogeny closed during terminal mesoproterozoic ca 1 0 ga on the other hand metamorphism in the basement gneiss migmatites and northern and southern granulite belts pre dates the sausar orogeny the earliest structure of the smb truncates and rotates the n s oriented structures of the southward located sakoli and the dongargarh belts of neoarchaean palaeoproterozoic age the northern granulite belt of the smb and the cggc and the high grade supracrustals from the sonapahar area in ne india all indicate very high p t conditions during 1 7 1 5 ga peak metamorphism which was followed by decompressional cooling the setting resembles continental collision which was followed by tectonic exhumation and denudation on the other hand the southern granulite belt from the smb documents a late archaean 2 6 ga event and a later 1 4 ga event the dalma volcanic belt located close to the southern tectonized boundary of the cggc belt and possibly the assemblage of copious mafic enclaves within the ca 550 ma granite plutons from ne india represent back arc like setting during 1 6 1 5 ga the setting is caused due to the southward subduction of the north indian block beneath the southern block leading to continental collision the metasedimentary belt located further to the south of the dalma volcanic belt and flanking the archaean singbhum craton to the north on the other hand is palaeoproterozoic in age but has been metamorphosed during ca 1 6 ga because of the northern collision related orogeny reworking and incorporation of basement gneisses and granulites from the mid crust level to the younger sausar cover sediments denote renewed spell of thrust tectonics that remobilized the collision zone rocks of the earlier orogeny the tectonic transport was from the north to the south with north dipping thrusts thus there was a reversal in the direction of convergence from the preceding orogeny the sausar orogeny closed during ca 1 0 ga it caused anatectic event producing granitoid plutons migmatites and charnockites in the cggc belt and migmatites in the gneissic complex in ne india

influence of the zone of weakness on dip angle and shear heating of subducted slabs we study the importance of the zones of weakness and the pattern of downgoing flow in steady state models of subducting lithosphere which interacts mechanically and thermally with the ambient mantle the non linear system of governing equations consists of i the momentum equation in stream function formulation and ii the steady state heat transfer equation including conduction and advection of heat and dissipation a finite element method has been applied to this system we consider the viscosity to be a non linear function of both the temperature and the stream function in steady state two dimensional 2d flow the stream function isolines follow material trajectories they are used to follow the top of the subducting slab which because of its possible increase in water content is assumed to have a lower viscosity the zone of weakness has been thus obtained in the self consistent fashion since the stream function as well as the temperature are the output from our modeling and no a priori assumptions about the shape of the bending lithosphere are taken into account it was shown that several orders decrease of viscosity in the zone of weakness is required to obtain the dip angle of about 45 if the decrease of viscosity is not sufficient enough the subducted slab either sinks almost vertically or does not exhibit a plate like behavior we have also demonstrated that shear heating can unrealistically increase at the zone of weakness for fast subductions if decrease of viscosity is underestimated 2004 elsevier b v all rights reserved

geodynamic tomography constraining upper mantle deformation patterns from bayesian inversion of surface waves in the earth s upper mantle seismic anisotropy mainly originates from the crystallographic preferred orientation cpo of olivine due to mantle deformation large scale observation of anisotropy in surface wave tomography models provides unique constraints on present day mantle flow however surface waves are not sensitive to the 21 coefficients of the elastic tensor and therefore the complete anisotropic tensor cannot be resolved independently at every location this large number of parameters may be reduced by imposing spatial smoothness and symmetry constraints to the elastic tensor in this work we propose to regularize the tomographic problem by using constraints from geodynamic modelling to reduce the number of model parameters instead of inverting for seismic velocities we parametrize our inverse problem directly in terms of physical quantities governing mantle flow a temperature field and a temperature dependent viscosity the forward problem consists of three steps 1 calculation of mantle flow induced by thermal anomalies 2 calculation of the induced cpo and elastic properties using a micromechanical model and 3 computation of azimuthally varying surface wave dispersion curves we demonstrate how a fully nonlinear bayesian inversion of surface wave dispersion curves can retrieve the temperature and viscosity fields without having to explicitly parametrize the elastic tensor here we consider simple flow models generated by spherical temperature anomalies the results show that incorporating geodynamic constraints in surface wave inversion help to retrieve patterns of mantle deformation the solution to our inversion problem is an ensemble of models i e thermal structures representing a posterior probability therefore providing uncertainties for each model parameter

toroidal poloidal partitioning of plate motions since 120 ma changes in plate motions and plate configurations during the cenozoic and mesozoic have been investigated extensively but most geodynamical models have concentrated on present day plate motions we have investigated the recent evolution of plate tectonics by examining the history of toroidal poloidal partitioning of plate motions taking into account estimated errors our results suggest a significant increase in the ratio of toroidal to poloidal motions postdating the hawaiian emperor h e bend at 43 ma corresponding to an overall decrease in global plate motions these changes may reflect greater mantle plume activity in the mesozoic but a causal mechanism is not obvious in general observed cenozoic and mesozoic plate motions do not appear to be random which implies that they are correlated we also find perhaps three significant changes in net rotation of the lithosphere with respect to hotspots since 120 ma

a continuous plate tectonic model using geophysical data to estimate plate margin widths with a seismicity based example summary a continuous kinematic model of present day plate motions is developed which 1 provides more realistic models of plate shapes than employed in the original work of bercovici wessel 1994 and 2 provides a means whereby geophysical data on intraplate deformation is used to estimate plate margin widths for all plates a given plate s shape function which is unity within the plate and zero outside the plate can be represented by analytic functions as long as the distance from a point inside the plate to the plate s boundary can be expressed as a single valued function of azimuth i e a single valued polar function to allow su cient realism to the plate boundaries without the excessive smoothing used by bercovici wessel the plates are divided along pseudo boundaries the boundaries of plate sections are then simple enough to be modelled as single valued polar functions moreover the pseudo boundaries have little or no eiect on the nal results the plate shape function for each plate also includes a plate margin function which can be constrained by geophysical data on intraplate deformation we demonstrate how this margin function can be determined by using as an example data set the global seismicity distribution for shallow depths less than 29 km earthquakes of magnitude greater than 4 robust estimation techniques are used to determine the width of seismicity distributions along plate boundaries these widths are then turned into plate margin functions that is analytic functions of the azimuthal polar coordinate the same azimuth of which the distance to the plate boundary is a single valued function the model is used to investigate the eiects of realistic nite margin widths on the earth s present day vorticity i e strike slip shear and divergence elds as well as the kinetic energies of the toroidal strike slip and spin and poloidal divergent and convergent ow elds the divergence and vorticity elds are far more well de ned than for the standard discontinuous plate model and distinctly show the in uence of diiuse plate boundaries such as the northeast boundary of the eurasian plate the toroidal and poloidal kinetic energies of this model diier only slightly from those of the standard plate model the diierences however are systematic and indicate a greater proportion of spin kinetic energy in the continuous plate model

the purana basins of southern cratonic province of india a case for mesoproterozoic fossil rifts abstract since its cratonization in the palaeoproterozoic southern peninsular india witnessed the development of a number of large intracratonic sedimentary basins traditionally referred to as purana basins spanning in age from late palaeoproterozoic through neoproterozoic the localization of these intracratonic basins namely pranhita godavari pg chattisgarh and cuddapah basins is apparently controlled by pre existing sutures and or weak zones the pg basin and the cuddapah basin host unconformity bound thick sediment dominated successions attesting to several cycles of fluvial shallow marine to shelf slope basin sedimentation deposition was punctuated by block uplifts resulting in local hiatuses and or volcanic upheavals leading to intercalation of thin but persistent basaltic flows and acid tuffs and ignimbrites basin margin deep faults apparently played a role in the facies distribution in these basins based on these features we propose that these basins initiated as continental rifts which however never opened up into a full fledged ocean basin but links with open seaway are evident from frequent occurrence of deposits representing tidal and storm influence particularly in upper part of the chattisgarh succession spatial distribution of facies and sediment thickness in the cuddapah and pg basins suggest that an open seaway existed to the east of the south indian cratonic province during the mesoproterozoic while similar criteria point to the existence of an open seaway north of the chattisgarh basin development history including nature of inversion suggest that the southern cratonic province of india existed as a single large continental mass since the mesoproterozoic in spite of episodes of supercontinent build up and fragmentation involving india and east gondwana during the proterozoic

the potential role of non newtonian rheology in the resurfacing of venus several analyses of the impact cratering record on venus have concluded that 80 of venus was resurfaced sometime in the last 300 m y 700 m y the cratering record further indicates that the resurfacing took place over a 30 m y 100 m y interval since this period there has been little large scale tectonic activity on venus this study proposes that such behavior may result from the interaction of phase change induced avalanches with a non newtonian lithosphere the mechanism proposed here suggests that because of non newtonian rheology the venusian lithosphere becomes highly mobile during brief periods when avalanches occur afterwards due to the reduction in stress levels the lithosphere becomes rigid and large scale tectonics ceases

the effect of convection planform on the toroidal poloidal energy ratio abstract this study investigates the influence of thermal convection planform geometry on the pattern of surface deformation in a dynamic model of plate mantle coupling the lithosphere is viewed as a distinct rheological layer and is modeled as a thin non newtonian sheet that is dynamically coupled to a three dimensional convecting newtonian layer the results of numerical experiments show that planforms which possess a high degree of symmetry excite only small amounts of toroidal energy in the thin non newtonian sheet and thus have low toroidal poloidal energy ratios asymmetric planforms tend to possess toroidal poloidal energy ratios that are one to two orders of magnitude larger than symmetric cases the results of this study suggest the precipitous drop in the toroidal poloidal energy ratio for the earth s surface velocity field that occurred in the late cretaceous early cenozoic resulted from the late cretaceous superplume which organized mantle flow into a higher degree of symmetry

two dimensional convection with a self lubricating simple damage rheology summary we present 2 d simulations of convection in the earth s mantle with temperature and damagedependent viscosity in a basally heated system the equation governing the temporal evolution of damage includes a source term for damage a healing term and an advection term a systematic study of the influence of the different damage terms on the convection pattern shows that 1 at least four different convective regimes can be distinguished depending on the size of the damage source term and 2 self lubricating behaviour is possible only if the advection term in the damage equation is small enough compared with the other terms we also demonstrate that good plate like behaviour in terms of a focused low viscosity bands lvb b homogeneous surface velocities within the plates and abrupt velocity jumps across the plate boundaries and c asymmetric subduction can be obtained with this kind of rheology although an increase in subduction asymmetry tends to make convection highly time dependent

a seismodynamical model of lithosphere deformation development of continental and oceanic rift networks seismicity and lithosphere extension on the scale of a tectonic plate are investigated in two horizontal dimensions and time using a dynamical model for a thin plate overlying a viscoelastic channel the plate consists of two layers a brittle elastic plastic crust that deforms as a result of earthquakes along faults and a strong viscoelastic layer representing the aseismic creeping lower lithosphere numerical experiments of lithosphere rifting are performed for one and two layer lithosphere models using two different rupture criteria in all the calculations earthquakes and faults of various sizes may form anywhere in the numerical domain as a result of the constitutive formulation the differences between the one and two layer model results suggest a mechanical explanation for the difference between continental and oceanic rifting when the lower lithosphere is absent a small number of faults dominate the deformation and a relatively simple narrow rift zone develops corresponding to oceanic rifting when a highly viscous lower lithosphere is included a complex distributed network of faults develops similar to continental rifting the complexity of the fault system also depends on the yield criterion in the crustal layer in our simulations complexity is greater for a yield criterion with strong shear stress dependence than for one with mainly extensional stress dependence whether a result of lower lithosphere stretching crustal heterogeneity or the yield criterion higher complexity increases the timescale for fault development increases self similarity in fault system geometry and stress and strain time series and results in power law moment frequency earthquake size scaling

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

geochronology and tectonic evolution of karimnagar and bhopalpatnam granulite belts central india abstract the karimnagar granulite belt kgb and the bhopalpatnam granulite belt bgb occur along both flanks of the pranhita godavari pg rift basin we present a state of the art overview on the geochronological and tectonic aspects of these belts and surrounding geologic domains and report new age data on zircon monazite and uraninite recovered from granulite facies assemblages from kgb and bgb based on electron microprobe analyses epma zircons from kgb charnockites show core ages of up to 3 1 ga mantled by rims of 2 6 ga zircons from bgb have 1 9 ga cores mantled by 1 7 ga rims zircons with core ages of 1 6 to 1 7 ga in bgb rocks suggest new growth at this time monazites and uranitite from kgb show clear peaks with well defined ages in the narrow range between 2 42 0 08 ga and 2 47 0 03 ga rims of monazite show mean age of 2 21 0 08 ga monazites from bgb define sharp linear trend in pbo vs tho2 diagram delineating a clear isochron with age of 1 59 0 03 ga age data from kgb and bgb presented in this report negate current models linking these terrains to godavari granulite belt and considering them as single and contemporaneous entity the mid archaean to early palaeoproterozoic signature recognized from kgb is totally missing in bgb on the other hand kgb rocks do not record any evidence for major mesoproterozoic thermal regime the two granulite belts shouldering the pg rift basin have therefore evolved in different times under distinct p t conditions and thermal regimes our results have important implications in evaluating models of supercontinent assemblies particularly the older assemblies of ur columbia and rodinia while tectonothermal events in kgb broadly match with those of east dharwar we propose that bgb represents a 1 6 ga collisional mobile belt between the bastar and the dharwar cratons the 1 6 ga collisional mobile belt at the southern margin of the bastar craton was superposed by rift activity along the pg basin at 1 5 ga this sequence of events goes against the existence of a 3 0 ga old contiguous assembly of ur but closely matches with the history of accretion and break up of the columbia further parts of the pg basin located away from the influence of the eastern ghats mobile belt neither recorded any grenville ages 1 0 ga corresponding to the rodinia accretion nor late pan african ages ca 550 ma relating to the gondwana amalgamation indicating that the region did not witness any of these younger tectonic events

self lubricated mantle convection two dimensional models we present results from convection models allowing for self lubrication of downflows models impose a line source of chemically light low viscosity material at the top of a convecting layer of temperature dependent viscosity material low viscosity surface material serves as an analog to hydrated sediment crust and the high viscosity upper portion of the convecting layer as an analog to mantle lithosphere slow near surface motion in the convecting layer entrains low viscosity material into zones of downflow which has a lubricating effect once entrained lubricant is deeper than the cold high viscosity portion of the convecting layer rapid upper boundary layer overturn occurs and system properties change e g heat flux doubles this marks transition to a lubricated state before and after transition transport properties are dominantly determined by respectively the viscosity of mantle lithosphere and that of interior mantle lubricated and nonlubricated states appear as distinct regions in system output space suggesting that exchange between them is akin to a phase transition that such exchange depends on a near surface lubricant implies that the geodynamics of planets lacking such lubricants may fundamentally differ from that of planets possessing them

analytic models for the dynamics of diffuse oceanic plate boundaries summary some plates deform across zones that are many hundreds to thousands of kilometres wide much broader than traditional boundaries such as mid ocean ridges deep sea trenches and oceanic transform faults across which most deformation is concentrated in a zone just a few kilometres wide these wide zones of deformation commonly referred to as diffuse plate boundaries occur in both continental and oceanic lithosphere composite plates are composed of two or more rigid or nearly rigid component plates separated by one or more diffuse plate boundaries royer gordon 1997 such complete diffuse boundaries are terminated at both ends by triple junctions although there are other diffuse boundaries that transform into narrow boundaries here we consider the dynamics of complete diffuse oceanic plate boundaries by constructing simple analytical models on a flat earth and on a spherical earth assuming that the viscous force resisting deformation is described by either a linear newtonian law or a high exponent power law we investigate the observed tendency for the pole of relative motion between component plates separated by a diffuse plate boundary to lie within the diffuse boundary itself we show that this tendency is due to geometrical effects that make it unlikely that the total torque acting between plates at a diffuse boundary could be oriented such that relative rotation occurs between the plates about a pole lying outside the boundary this is demonstrated for both flat and spherical earth cases assuming that resistance to strain along the diffuse boundary increases linearly with stress newtonian rheology we further show that the pole of rotation is even more likely to lie in the diffuse plate boundary if the viscous force resisting deformation is described by a high exponent power law rather than a newtonian law

plate tectonics and aspherical earth structure the importance of poloidal toroidal coupling we derive poloidal flow internal loading green functions for incompressible fluid models of the mantle consisting either of a single constant viscosity spherical shell or of two adjacent spherical shells having different viscosities from the green function we obtain kernels connecting the surface divergence the geoid and the surface topography fields to the lateral density heterogeneity inferred on the basis of the application of seismic tomographic imaging techniques and with these kernels we argue that both the surface divergence and geoid fields consisting of harmonic degrees 2 5 may be reasonably fit with only a factor of 8 viscosity increase at a depth of 1200 km we point out however that the coupling from poloidal to toroidal flow which is required to understand surface velocity spectra may allow these observations to be understood in terms of a viscosity increase at depth which is smaller than required by nonhydrostatic geoid data in the context of pure poloidal models using the observed kinetic energy in the surface plate motions as a constraint allows us to infer a value for the steady state upper mantle viscosity of 2 0 0 5 1021 pa s we comment on the implication of the difference between this number and the somewhat lower value 1 1021 pa s which has been derived on the basis of analyses of signatures of the glacial isostatic adjustment process

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

on the effect of temperature and strain rate dependent viscosity on global mantle flow net rotation and plate driving forces summary global circulation models are analysed using a temperature and strain rate dependent rheology in order to refine previous estimates of the nature of mantle flow and plate driving forces based on temperature inferred from a tectonic model and seismic tomography the suboceanic viscosity is lower than underneath continents by one order of magnitude if net rotations of the lithosphere with respect to a stable lower mantle reference frame are accounted for the patterns of flow in the upper mantle are similar between models with layered and those with laterally varying viscosity the excited net rotations scale with the viscosity contrast of continental roots to the ambient mantle this contrast is dynamically limited by the power law rheology surface net rotations match the orientation of hotspot reference frame euler poles well and amplitudes are of the right order of magnitude i compare prescribed surface velocity models with free slip computations with imposed weak zones at the plate boundaries velocity fields are generally consistent models based on laboratory creep laws for dry olivine are shown to be compatible with average radial viscosity profiles plate velocities in terms of orientation and amplitudes plateness of surface velocities toroidal poloidal partitioning and fabric anisotropy formation under dislocation creep in the upper mantle including temperature dependent variations increases the relative speeds of oceanic versus continental lithosphere makes surface velocities more plate like and improves the general fit to observed plate motions these findings imply that plate driving force studies which are based on simpler mantle rheologies may need to be revisited

self consistent generation of tectonic plates in time dependent three dimensional mantle convection simulations 2 strain weakening and asthenosphere 1 in a previous paper tackley 2000b it was shown that a combination of temperature dependent viscosity and viscoplastic yielding is sufficient to give rudimentary plate tectonic like behavior in three dimensional models of mantle convection here the calculations are extended to include two complexities that have been suggested as being important in localizing deformation at plate boundaries strain weakening and the presence of a low viscosity asthenosphere introducing an asthenosphere by reducing the viscosity by a factor of 10 where material reaches a solidus 1 dramatically improves plate quality even if the asthenosphere is restricted to regions around spreading centers 2 gives good smoothly evolving platelike behavior over a wide range of yield stress values spanning an order of magnitude and 3 gives bimodal stable solutions over a range of yield stresses either immobile lid or plate behavior may be obtained depending on initial condition by contrast introducing an asthenosphere by using depth dependent viscosity has a much smaller effect on system behavior increasing strain weakening 1 improves localization at spreading centers but leads to an increasingly complex network of spreading centers fragmenting the plates 2 weakens convergent zones and can make downwellings highly episodic and 3 does not lead to pure transform boundaries in these calculations time dependent damage evolution and instantaneous strain rate weakening give very similar results all cases that display platelike behavior have very long wavelength mantle heterogeneity consistent with earth s

variations in planetary convection via the effect of climate on damage abstract a new model for the generation of plate tectonics suggests an important interaction between a planet s climate and its lithospheric damage behavior and thus provides a simple explanation for the tectonic difference between earth and venus we propose that high surface temperatures will lead to higher healing rates e g grain growth in the lithosphere that will act to suppress localization plate boundary formation and subduction this leads to episodic or stagnant lid convection on venus because of its hotter climate in contrast earth s cooler climate promotes damage and plate boundary formation the damage rheology presented in this paper attempts to describe the evolution of grain size by allowing for grain reduction via deformational work input and grain growth via surface tension driven coarsening we explore the interaction of damage and healing in two dimensional numerical convection simulations we also develop a simple drip instability model to test the hypothesis that the competition between damage and healing controls convective and plate tectonic style by modulating episodicity at subduction zones at small values of damage f a or large values of healing k a the lithosphere remains strong enough to resist subduction on time scales of billions of years at intermediate values of f a and k a the lithosphere may become mobilized and allow for short bursts of tectonic behavior followed by periods of quiescence at large small values of f a k a the fineness is increased so that the viscosity of the plate boundary is reduced to allow for continuous unimpeded subduction of lithosphere and plate like deformation the results suggest the feasibility of our proposed hypothesis that the interplay of climate and damage control the mode of tectonics on a planet