a comparison of mantle convection models featuring plates oceanic plates are an integral part of the earth s mantle and thus play an important role in its dynamics and evolution to allow plate behavior to arise naturally in numerical mantle convection models self consistent plate generation methods apply a fully rheological approach featuring a temperature pressure and stress dependent viscosity however due to the extreme local viscosity changes that the self generation of model plates entails their computational requirements are demanding alternative plate modeling methods specify the existence of plates explicitly but can also obtain dynamically determined velocities e g by employing a force balance method here we present modifications to a force balance model by utilizing a rheology dependent viscosity profile accordingly plate viscosity and plate thickness are no longer prescribed by the modeler but now follow as a dynamic consequence of the temperature and stress dependence of the viscosity and the model s evolution we describe the new method and present benchmark results for a rheologically self consistent mantle convection model and the modified force balance plate model our results show that both plate modeling methods lead to the same system behavior for a wide range of system parameters making the new method a powerful tool to also achieve plate like surface motion naturally

generation of plate like behavior and mantle heterogeneity from a spherical viscoplastic convection model 1 how plate tectonics arises from mantle convection is a question that has only very recently become feasible to address with spherical viscoplastic computations we present mainly internally heated convection results with temperature dependent viscosity and explore parts of the rayleigh number ra yield stress y phase space as well as the effects of depth dependent y bottom heating and a low viscosity asthenosphere convective planform and toroidal poloidal velocity field ratio tpr are affected by near surface viscosity variations and tpr values are close to observed values for our most plate like models at the relatively low convective vigor that is accessible at present most models favor spherical harmonic degree one convection though models with a weaker surface viscosity form degree two patterns and reproduce tomographically observed power spectra an asthenospheric viscosity reduction improves plate like nature as expected for our incompressible computations pure bottom heating produces strong plumes that tend to destroy plates at the surface this implies that significant internal heating may be required both to reduce the role of active upwellings and to form a low viscosity zone beneath the upper boundary layer

neoproterozoic glacial deposits from the aracuai orogen brazil age provenance and correlations with the sao francisco craton and west congo belt article i nfo glacigenic diamictite successions of the macaubas group are widespread in the western domain of the aracuai orogen east of the sao francisco craton brazil diamictites also occur on this craton and in the african counterpart of the aracuai orogen the west congo belt detrital zircon grains from the matrix of diamictites and sandstones from the macaubas group were dated by the u pb shrimp technique the geochronological study sets the maximum depositional age of the glacial diamictites at 900 ma and indicates multiple sources for the macaubas basin with ages ranging from 900 to 2800 ma sm nd tdm model ages determined on whole rock samples range from 1 8 ga to 2 5 ga and get older up section comparison of our data with those from the cratonic area suggest that these glacial deposits can be correlated to the jequitai and carrancas diamictites in the sao francisco craton and to the lower mixtite formation of the west congolian group exposed in africa the 900 1000 ma source is most probably represented by the zadinian mayumbian volcanic rocks and related granites from the west congo belt however one of the most voluminous sources with ages in the 1 1 1 3 ga interval has not been detected in the sao francisco congo craton possible sources for these grains could occur elsewhere in africa or possibly from within the brasilia belt in western central brazil

plate motions and the viscosity structure of the mantle insights from numerical modelling abstract the viscosity structure of the earth s mantle is likely to play an important role with respect to the motion of the lithospheric plates a zone of low viscosity in the upper mantle as postulated by seismological studies and also by investigations of postglacial uplift has been proposed to facilitate plate motion another inferred feature of the viscosity profile in the mantle is a significant increase at greater depth we have employed a three dimensional mantle convection model to explore the relation between the appearance of plate motion and the viscosity structure of the mantle beneath the model allows for a complex fluid rheology strong temperature pressure and stress dependence of the viscosity and can so account for the self consistent formation of plates at the surface of the convecting mantle plate like motion appears only in a limited parameter range and we demonstrate that this appearance is closely linked to a specific viscosity structure the viscosity is characterized by a local minimum at shallow depth low viscosity zone and by a local maximum at greater depth self consistent plate motion is only observed if such a viscosity structure exists in order to determine the functional relationship between the viscosity structure and plate motion we also employ an approach in which a certain viscosity profile is prescribed these studies again reveal the importance of the local extrema in the viscosity profile taking into account an increased interior viscosity also obtained by the pressure dependence we find stable plate motion as a general result we observe that the balance of the temperature and stress dependence of the viscosity is necessary to obtain plate motion at the same time we find a viscosity profile showing a minimum at shallow depth and a maximum at greater depth

implementation and application of adaptive mesh refinement for thermochemical mantle convection studies numerical modeling of mantle convection is challenging owing to the multiscale nature of mantle dynamics high resolution is often required in localized regions with coarser resolution being sufficient elsewhere when investigating thermochemical mantle convection high resolution is required to resolve sharp and often discontinuous boundaries between distinct chemical components in this paper we present a 2 d finite element code with adaptive mesh refinement techniques for simulating compressible thermochemical mantle convection by comparing model predictions with a range of analytical and previously published benchmark solutions we demonstrate the accuracy of our code by refining and coarsening the mesh according to certain criteria and dynamically adjusting the number of particles in each element our code can simulate such problems efficiently dramatically reducing the computational requirements in terms of memory and cpu time when compared to a fixed uniform mesh simulation the resolving capabilities of the technique are further highlighted by examining plume induced entrainment in a thermochemical mantle convection simulation

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 comparison of numerical surface topography calculations in geodynamic modelling an evaluation of the sticky air method summary calculating surface topography in geodynamic models is a common numerical problem besides other approaches the so called sticky air approach has gained interest as a free surface proxy at the top boundary the often used free slip condition is thereby vertically extended by introducing a low density low viscosityfluid layer this allows the air crust interface to behave in a similar manner to a true free surface we present here a theoretical analysis that provides the physical conditions under which the sticky air approach is a valid approximation of a true free surface two cases are evaluated that characterize the evolution of topography on different timescales 1 isostatic relaxation of a cosine perturbation and 2 topography changes above a rising plume we quantitatively compare topographies calculated by six different numerical codes using finite difference and finite element techniques using three different topography calculation methods i direct calculation of topography from normal stress ii body fitting methods allowing for meshing the topography and iii lagrangian tracking of the topography on an eulerian grid it is found that the sticky air approach works well as long as the term st ch hst l 3 is sufficiently small where st and hst are the viscosity and thickness of the sticky air layer and ch and l are the characteristic viscosity and length scale of the model respectively spurious lateral fluctuations of topography as observed in some marker based sticky air approaches may effectively be damped by an anisotropic distribution of markers with a higher number of markers per element in the vertical than in the horizontal direction

the effect of rheological parameters on plate behaviour in a self consistent model of mantle convection abstract in a three dimensional numerical model of mantle convection we have explored the self consistent formation and evolution of plates this was done by investigating the influence of temperature stress and pressure dependence of the viscosity on plate like behaviour further the role of a depth dependent thermal expansivity and of internal heating was examined first order self consistent plate tectonics can be obtained for temperature and stress dependent viscosity we observe virtually undeformed moving plates and the phenomenon of trench migration however plate motion only appears during short intervals which are interrupted by long phases characterised by an immobile lid an improvement is achieved by adding pressure dependence of the viscosity and of the thermal expansivity to the model this leads to extended plates with continuous plate motion and the appearance of a low viscosity zone internal heating accelerates subduction and gives an increase in plate velocity the plates are otherwise left intact we find that the surface velocity is largely determined by subduction rather than by upwellings plate like behaviour is restricted to a narrow parameter window the window is bordered by an episodic or a stagnant lid type of flow on the one side and by a domain in which convection is akin to constant viscosity flow on the other side with these different convective regimes the behaviour of various terrestrial planets can be described self consistently occasionally even a change from the plate regime to the stagnant lid regime occurs such a type of transition has possibly changed the style of tectonics on some terrestrial planets such as mars

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

a community benchmark for 2 d cartesian compressible convection in the earth s mantle benchmark comparisons are an essential tool to verify the accuracy and validity of computational approaches to mantle convection six 2 d cartesian compressible convection codes are compared for steady state constant and temperature dependent viscosity cases as well as time dependent constant viscosity cases in general we find good agreement between all codes when comparing average flow characteristics such as nusselt number and rms velocity at rayleigh numbers near 106 and dissipation numbers between 0 and 2 the results differ by approximately 1 per cent differences in discretization and use of finite volumes versus finite elements dominate the differences there is a small systematic difference between the use of the anelastic liquid approximation ala compared to that of the truncated ala in determining the onset of time dependence there was less agreement between the codes with a spread in the rayleigh number where the first bifurcation occurs ranging from 7 79 10 5 to 1 05 10 6

time domain parallelization for computational geodynamics 1 i present a time domain parallelization approach for geodynamic modeling this algorithm named parareal is based on the use of coarse sequential and fine parallel propagators to predict and to iteratively correct the solution of the governing equations over a given time interal although the method has been successfully used to solve differential equations in various scientific areas it has not been applied to model solid state convective motions relevant to the earth and other planetary mantles in that case the time dependence of the velocity is only implicit which requires modifications to the original algorithm the performances of this adapted version of the parareal algorithm were investigated using theoretical model predictions in good agreement with numerical experiments i show that under optimum conditions the parallel speedup increases linearly with the number of processors and speedups close to 10 were measured using only few tens of cpus this parareal approach can be used alone or combined with any spatial parallel algorithm allowing significant additional increase in speedup with increasing number of processors

rejuvenation of kar systems for minerals in the taiwan mountain belt the late mesozoic amphibolites and granitic rocks in the basement complex of the taiwan mountain belt are overprinted by late tertiary greenschist facies metamorphism the kar isotope systems of late mesozoic horn blende muscovite biotite and microcline have been reset by this metamorphic event as reflected in three systematic variations 1 a regional decrease in40ar 39ar dates with increasing metamorphic overprinting 2 a unique sequence of decreasing dates among minerals i e hornblende muscovite biotite microcline in the same sample or within closely spaced samples and 3 a positive correlation between the grain size fractions and their40ar 39ar dates e g smaller grain size fractions of a given mineral yield younger dates in the lower greenschist facies area hornblendes and coarse grained muscovites still retain most of their radiogenic argon and display fairly flat40ar 39ar age spectra with plateau dates of 82 95 ma which record a rapid cooling during the nanao orogeny a late mesozoic tectonothermal event in contrast all microclines are completely reset and yield young plateau dates of 1 6 and 1 7 ma reflecting the rapid uplift associated with the penglai orogeny most of the partially reset minerals e g muscovites from the upper greenschist facies area and biotites from the lower greenschist facies area yield geologically meaningless40ar 39ar integrated dates that fall between the ages of the two tectonothermal events and exhibit disturbed age spectra which are caused mainly by mixing of argon released from two generations of phases excess argon and partial argon loss after isolating possible recrystallization and mixing effects the regional variation in the40ar 39ar dates for the earlier generation phases could be simulated by a volume diffusion model coupled with a thermal model for the taiwan mountain belt

a community benchmark for subduction zone modeling we have developed a suite of benchmarks to facilitate the comparison of numerical models for the dynamics and thermal structure of subduction zones the benchmark cases are based on a thermomechanical approach in which the slab is prescribed kinematically and the wedge flow is computed dynamically we propose various cases to investigate the influence of boundary conditions and rheology on wedge flow and resulting thermal structure a comparison between the codes suggest that accurate modeling of the thermal field requires a good implementation of the velocity discontinuity along the seismogenic zone and high resolution in the thermal boundary layers a minor modification to the boundary conditions of the wedge flow is also necessary to avoid a pressure singularity that exists in analytical solutions of the cornerflow model

a benchmark comparison for mantle convection codes summary we have carried out a comparison study for a set of benchmark problems which are relevant for convection in the earth s mantle the cases comprise steady isoviscous convection variable viscosity convection and time dependent convection with internal heating we compare nusselt numbers velocity temperature heat flow topography and geoid data among the applied codes are finite difference finite element and spectral methods in a synthesis we give best estimates of the true solutions and ranges of uncertainty we recommend these data for the validation of convection codes in the future

the spiral grid a new approach to discretize the sphere and its application to mantle convection 1 this paper presents a new method to generate a three dimensional spherical grid using natural neighbor voronoi cells distributed by spiral functions a unique property of this grid is the complete removal of symmetries with arbitrary selectable lateral and radial resolution which are not restricted to discrete radial levels or geometrical constraints as compared to the commonly used grids based on projected triangulated platonic solids such as a cube a rhomboid or an icosahedron the spiral grid can be refined in certain areas of interest and makes it possible to have a very small inner radius to outer radius ratio cell volumes can be made almost constant throughout the computational domain analysis statistics and computation methods are described in detail as well as a possible domain decomposition suitable for parallel computing conductive temperature profiles were numerically calculated in the spherical shell and directly compared with the analytic solution as verification the grid is applied to numerical simulations of mantle convection using a finite volume scheme the model is validated by a comparison of steady state cubic and tetrahedral convection patterns with other published models

dynamical consequences in the lower mantle with the post perovskite phase change and strongly depth dependent thermodynamic and transport properties article i nfo we have carried out numerical simulations of large aspect ratio 2 d mantle convection with the deep phase change from perovskite pv to post perovskite ppv using the extended boussinesq approximation for a fluid with temperature and pressure dependent viscosity we have investigated the effects of various ppv phase parameters on the convective planform heat transport and mean temperature and viscosity profiles since ppv is expected to have a relatively weak rheology with respect to pv and a large thermal conductivity we have assumed that the transition from pv to ppv is accompanied by both a reduction in viscosity by 1 to 2 orders of magnitude and by an increase in thermal conductivity by a factor of 2 furthermore we have analyzed the combined effects of a strongly decreasing thermal expansivity in pv and steeply increasing thermal conductivity according to recent evidence from high pressure experiments and first principle calculations as long as the thermal expansivity and conductivity are constant ppv exerts a small but noticeable effect on mantle convection it destabilizes the d layer causes focusing of the heat flux peaks and an increase of the average mantle temperature and of the temporal and spatial frequency of upwellings when the latest depth dependent thermal expansivity and conductivity models are introduced the effects of ppv are dramatic on the one hand without ppv we obtain a very sluggish convective regime characterized by a relatively cool mantle dominated by large downwellings that tend to stagnate beneath the transition zone with ppv on the other hand we observe an extremely significant increase of the average mantle temperature due to the formation of large sized and vigorous upwellings that in some cases tend to cluster thus forming superplumes if a very large thermal conductivity at the core mantle boundary is assumed k 20 wk 1 m 1 we obtain a quasi steady state regime characterized by large and stable plumes with long lifetimes the combination of strongly depth dependent expansivity and conductivity is a viable mechanism for the formation of long wavelength long lived thermal anomalies in the deep mantle even if a low viscosity ppv atop the core mantle boundary is included

a systematic 2 d investigation into the mantle wedge s transient flow regime and thermal structure complexities arising from a hydrated rheology and thermal buoyancy 1 arc volcanism at subduction zones is likely regulated by the mantle wedge s flow regime and thermal structure and hence numerous studies have attempted to quantify the principal controls on mantle wedge conditions in this paper we build on these previous studies by undertaking a systematic 2 d numerical investigation into how a hydrated rheology and thermal buoyancy influence the wedge s flow regime and associated thermal structure we quantify the role of a range of plausible i water contents 0 5000 h 106si ii subduction velocities 2 10 cm yr and iii upper plate ages 50 120 myr finding that small scale convection ssc resulting from rayleigh taylor instabilities or drips off the base of the overriding lithosphere is a typical occurrence the morphology of ssc varies with viscosity and subduction parameters with drips at their most prominent when subduction velocities and wedge viscosities are low our results confirm that high subduction velocities and wedge viscosities promote a dominantly corner flow regime and strong upper plate erosion below the arc region by contrast we find that back arc upper plate erosion by ssc is largely controlled by wedge viscosity occurring when i viscosities are 5 1018 pa s and ii the length of the upper plate available for destabilization exceeds the characteristic wavelength of instabilities thus if hydrous weakening of wedge rheology extends at least 100 150 km from the trench our 2 d models predict an unstable flow regime resulting in temperature fluctuations of 50 100 k which are sufficient to influence melting and the stability of hydrous minerals

a community benchmark for viscoplastic thermal convection in a 2 d square box numerical simulations of thermal convection in the earth s mantle often employ a pseudoplastic rheology in order to mimic the plate like behavior of the lithosphere yet the benchmark tests available in the literature are largely based on simple linear rheologies in which the viscosity is either assumed to be constant or weakly dependent on temperature here we present a suite of simple tests based on nonlinear rheologies featuring temperature pressure and strain rate dependent viscosity eleven different codes based on the finite volume finite element or spectral methods have been used to run five benchmark cases leading to stagnant lid mobile lid and periodic convection in a 2 d square box for two of these cases we also show resolution tests from all contributing codes in addition we present a bifurcation analysis describing the transition from a mobile lid regime to a periodic regime and from a periodic regime to a stagnant lid regime as a function of the yield stress at a resolution of around 100 cells or elements in both vertical and horizontal directions all codes reproduce the required diagnostic quantities with a discrepancy of at most 3 in the presence of both linear and nonlinear rheologies furthermore they consistently predict the critical value of the yield stress at which the transition between different regimes occurs as the most recent mantle convection codes can handle a number of different geometries within a single solution framework this benchmark will also prove useful when validating viscoplastic thermal convection simula tions in such geometries

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

effects of strongly temperature dependent viscosity on time dependent three dimensional models of mantle convection numerical simulations of thermal convection in a wide 8 8 1 cartesian box heated from below with temperature dependent viscosity contrasts of 1000 and rayleigh number 105 show that boundary conditions and aspect ratio have an enormous effect on the preferred flow pattern with rigid upper and lower boundaries spoke pattern flow with small diameter 1 5 cells is obtained consistent with laboratory experiments and previous numerical results however with the arguably more realistic stress free boundaries the flow chooses the largest possible wavelength forming a single square cell of aspect ratio 8 with one huge cylindrical downwelling surrounded by upwelling sheets the addition of stress dependence to the rheology weakens the stiff upper boundary layer resulting in smaller cells though still with upwelling sheets and downwelling plumes

fluidity a fully unstructured anisotropic adaptive mesh computational modeling framework for geodynamics we present a new computational modeling framework fluidity for application to a range of two and three dimensional geodynamic problems with the focus here on mantle convection the approach centers upon a finite element discretization on unstructured simplex meshes which represent complex geometries in a straightforward manner throughout a simulation the mesh is dynamically adapted to optimize the representation of evolving solution structures the adaptive algorithm makes use of anisotropic measures of solution complexity to vary resolution and allow long thin elements to align with features such as boundary layers the modeling framework presented differs from the majority of current mantle convection codes which are typically based upon fixed structured grids this necessitates a thorough and detailed validation which is a focus of this paper benchmark comparisons are undertaken with a range of two and three dimensional isoviscous and variable viscosity cases in addition model predictions are compared to experimental results such comparisons highlight not only the robustness and accuracy of fluidity but also the advantages of anisotropic adaptive unstructured meshes significantly reducing computational requirements when compared to a fixed mesh simulation

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