toward a boot strap hypothesis of plate tectonics feedbacks between plates the asthenosphere and the wavelength of mantle convection abstract the solid earth system is characterized by plate tectonics a low viscosity zone beneath plates the asthenosphere and long wavelength flow in the convecting mantle we use suites of numerical experiments to show 1 how long wavelength flow and the operation of plate tectonics can generate and maintain an asthenosphere and 2 how an asthenosphere can maintain long wavelength flow and plate tectonics plate subduction generates a sub adiabatic temperature gradient in the mantle which together with temperature dependent viscosity leads to a viscosity increase from the upper to the lower mantle this allows mantle flow to channelize in a low viscosity region beneath plates an asthenosphere forms dynamically flow channelization in turn stabilizes long wavelength convection the degree of dynamic viscosity variations from the upper to the lower mantle increases with the wavelength of convection and drops toward zero if the system transitions from plate tectonics to a single plate planet the plate margin strength needed to initiate that transition increases for long wavelength cells long wavelength flow allows plate tectonics to exist over a wider range of plate margin strength the coupled feedbacks allow for a linked causality between plates the asthenosphere and the wavelength of mantle flow with none being more fundamental than the others and the existence of each depending on the others under this hypothesis the asthenosphere is defined by an active process plate tectonics which maintains it and is maintained by it and plate tectonics is part of an emergent self sustaining flow system that bootstraps itself into existence

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

inferring the viscosity and the 3 d density structure of the mantle from geoid topography and plate velocities summary in a dynamic earth mantle mass heterogeneities induce gravity anomalies surface velocities and surface topography these lateral density heterogeneities can be estimated on the basis of seismic tomographic models recent papers have described a realistic circulation model that takes into account the observed plate geometry and is able to predict the rotation vectors of the present plates the relationship between the surface observables and the heterogeneities is sensitive to the viscosity stratification of the mantle here we use this model combined with a generalized least squares method in order to infer the viscosity profile of the earth from the surface observations and to get some new insight into the 3 d density structure of the mantle the computed radial viscosity profile presents a continuous increase of more than two orders of magnitude the asthenosphere has a viscosity close to 2 x lo2 pa s no sharp discontinuity is requested at the upper lower mantle interface the largest viscosity 7 x 10 pas is reached in the middle of the lower mantle at greater depth approaching the core mantle boundary the viscosity decreases by one order of magnitude the model suggests that the well known degree 2 and order 2 anomaly in the transition zone of the upper mantle is merely the signature of the slabs it also slightly increases the degree 2 and order 0 in the lower mantle and decreases it in the upper mantle in other words the inversion requests a hotter lower mantle beneath the equator and a colder upper mantle at the same latitudes

role of a low viscosity zone in stabilizing plate tectonics implications for comparative terrestrial planetology 1 earth s near surface layer its lithosphere is broken into quasi rigid plates that form the upper thermal boundary layer for mantle convection since the discovery of plate tectonics it has been widely conjectured but only recently demonstrated that this peculiar style of convection may be facilitated by an upper mantle low viscosity zone lvz over which the plates glide easily the lvz or asthenosphere concept dates from 19th century investigations of isostatic support of mountain belts and is supported by modern evidence for a seismic low velocity zone and by studies of postglacial rebound and dynamic compensation of the earth s gravity field here we show in both two dimensional 2 d cartesian and 3 d spherical earth models that combining a pronounced lvz and a plastic yield stress to allow localized weakening of the cold thermal boundary layer results in a distinctly plate tectonic style of convection with 30 toroidal surface motion for the 3 d case recycling of water into the upper mantle at subduction zones is a plausible cause of earth s lvz whereas venus is dry and lacks both an lvz and plate tectonics

mantle convection with reversing mobile plates a benchmark study 1 recent investigations of mantle convection with mobile plates have documented a mode of convection with periodic and or aperiodic plate reversals 2 d or reorganizations 3 d we show that it is possible to calibrate plate formulations so that three different modeling methods reproduce the global flow diagnostics to within 3 in 2 d calculations plate reversals are independent of the method of plate generation once the calculations are tuned to reproduce the same physical characteristics e g nusselt number and plate velocity the periods of oscillation of the flow reversals from three different plate methods agree to within 4

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

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

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

inferences of mantle viscosity from tectonic plate velocities the present day velocities of the earth s tectonic plates provide direct constraints on the absolute value of the mantle viscosity we present the results of a formal inversion of plate motion data and demonstrate its utility in constraining the depth variation of absolute viscosity

constraints on plate tectonics initiation from scaling laws for single cell convection abstract the earth is the only planet known to have plate tectonics while other planets are covered with a stagnant lid on the earth the initiation of subduction which is thought to be the fundamental process for plate tectonics initiation is caused not only by the negative buoyancy of the lithosphere but also by the forces from plate motions however for planets which do not have plate tectonics the very first episode of lithospheric failure has to be caused by forces other than plate motions sublithospheric convection has been proposed as a possible mechanism that provides lithospheric instability through inducing stresses in the lithosphere and lithospheric failure can occur when the yield stress is below a critical value we test the applicability of scaling laws for the critical yield stress obtained in single cell convection simulations to strongly time dependent multi cell systems we show that with an appropriate choice of characteristic aspect ratio for the convective system the scaling laws from single cell simulations can be used to evaluate the conditions on the terrestrial planets in the inner solar system for plate tectonics to exist in agreement with previous studies the estimated values for critical yield stress and coefficient of friction are much lower than the expected values for the earth s lithosphere

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

radial profile of mantle viscosity results from the joint inversion of convection and postglacial rebound observables we present new inferences of the radial profile of mantle viscosity that simultaneously fit long wavelength free air gravity harmonics associated with mantle convection and a large set of decay times estimated from the postglacial uplift of sites within previously glaciated regions hudson bay arctic canada and fennoscandia the relative sea level variation at these latter sites is constrained by age height pairs obtained by geological survey rather than the subjective trends which are commonly used in glacial isostatic adjustment gia studies our viscosity inferences are generated using two approaches first we adopt a relative viscosity profile which is known to provide a good fit to the free air gravity harmonics and determine an absolute scaling which yields a best fit to the gia decay time constraints second we perform an iterative nonlinear joint inversion of the two data sets in both cases our inferred profiles are characterized by a significant increase of viscosity 2 orders of magnitude with depth to values of 1022 pa s in the bottom half of the lower mantle the new viscosity profiles are shown to satisfy constraints based on the postglacial uplift of both fennoscandia the classic haskell 1935 number and hudson bay which have commonly been invoked to argue for an isoviscous mantle furthermore the models are used to predict a set of long wavelength signatures of the gia process these include predictions of gia induced variations in 1 the length of day over the late holocene period 2 the earth s precession constant and obliquity over the last 2 6 myr and 3 the present day zonal harmonics of the geopotential jl l 7 the predictions 1 and 3 bound the late holocene and ongoing mass flux between the large polar ice sheets greenland and antarctic and the global oceans to small values 0 4 mm yr equivalent eustatic sea level rise

arrhenius rheology versus frank kamenetskii rheology implications for mantle dynamics 1 the viscosity of planetary mantle material is strongly temperature dependent this dependence is described by an arrhenius law but for the realistic viscosity contrast that appears over the depth of the mantle strong gradients in the upper thermal boundary layer occur these strong gradients are not realizable in numerical models therefore the frank kamenetskii approximation leading to a linearized exponential viscosity function is commonly used much research on the plate mantle system has been done applying the frank kamenetskii rheology the question though still arises if these results can be reproduced when using the arrhenius law here it has to be kept in mind that in numerical models the realistic viscosity contrast appearing over the mantle can neither be coped with by the arrhenius nor the frank kamenetskii approach thus the computational aspects to date only allow for viscosity contrasts being moderate as compared to realistic values and extrapolations to planet like values have to be made for both rheologies comparing results obtained by the commonly used forms of the arrhenius and the frank kamenetskii approach we observe the same change in flow behavior from mobile lid to stagnant lid convection the differences are only of quantitative nature in the stagnant lid regime some arrhenius formulations lead to a thinner top boundary layer which results in values of lithospheric thicknesses being more realistic here it has to be noted that different forms of the arrhenius law have been used which differ among themselves when properly scaled the differences between the frank kamenetskii and arrhenius rheology can however be strongly diminished to understand general features in the plate tectonics mantle convection system an additional stress dependence of the viscosity has to be considered the discrepancies between the various viscosity formulations are then of even less importance because for an earth like convection regime the top viscosity is more strongly influenced by the stress dependence rather than by the temperature dependence

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

interaction of weak faults and non newtonian rheology produces plate tectonics in a 3d model of mantle flow according to the theory of plate tectonics relatively rigid plates are bounded by large faults plate motion has negligible internal strain with significant toroidal component to the velocity by contrast models of mantle flow with viscous rheology in an intact medium predict little toroidal component and substantial internal strain in surface motion it has been suggested5 that the observed characteristics of plate motion are related to faulted plate margins which are observed to be weak here we confirm this suggestion using three dimensional models of mantle flow that incorporate faults and the forces exerted on plates by subducting slabs slab pull and mid ocean ridges ridge push our models show that plate like motion results from the interaction between weak faults and a strain weakening power law rheology weak transform faults tend to guide plate motion this guiding effect and the decoupling that occurs at thrust faults may result in oblique subduction convergent margins are associated with realistic trench and fore bulge topography by simultaneously predicting surface kinematics topography and gravity the models achieve a useful degree of tectonic realism

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

an inversion for radial viscosity structure using seismic tomography using a uniform velocity density scaling we have inverted the seismically inferred 3 dimensional structure of the whole manfie for the radial viscosity structure which best fits the geoid we are able to obtain 60 72 variance reductions for three different s wave tomographic models the resulting viscosity structures are remarkably similar showing a high viscosity lid a low viscosity zone in the transition region and a high viscosity lower manfie a resolution analysis indcates that the viscosity structure in the upper manfie is well resolved by the data however the resolution in the lower manfie is poorer our models axe in general agreement with previous studies except that our inversions prefer a low viscosity layer at 400 670 km as opposed to 100 400 kin

the viscosity structure of the mantle during 1991 1994 the four year period covered by this report there has been a shift in emphasis away from one dimensional radial mantle viscosity models and toward an understanding of the three dimensional radial and lateral structure of mantle viscosity our understanding of mantle viscosity comes primarily from two sources studying the creep properties of mantle minerals under appropriate pressures and temperatures and using theoretical flow models to predict surface observables such as plate velocities gravity geoid and heat flow laboratory measurements of deformation indicate that the rheology of upper mantle minerals such as olivine mg fe 2sio4 is a strong function of temperatue grain size and stress cf karato and wu 1993 the deformation of minerals under mantle conditions generally follows a flow law of the form e a nd mexp q qrt 1 where is the deformation rate is the deviatoric stress is the shear modulus d is the grain size of the rock q is the activation energy for the deformation mechanism t is the temperature in kelvin r is the gas constant and a is a constant viscosity is defined as e 2 therefore deformation is directly related to viscosity substituting equation 1 into equation 2 an effective viscosity eff a n 1dmexp qrt 3 can be defined for temperature changes of 100 degrees k the viscosity changes by an order of magnitude at constant stress cf karato and wu 1993 changes of deviatoric stress by a factor of 2 change the viscosity by an order of magnitude cf karato and wu 1993 other factors such as partial pressure of oxygen and water content may also have important effects

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

upper mantle shear structure beneath the northwest atlantic ocean we have modeled the sh motion from earthquakes in the northwest atlantic ocean to derive an oceanic upper mantle shear velocity model the signals were recorded on long period wwssn and canadian network stations on the east coast of north america the travel times and waveforms of seismograms in the distance range 11 16 were used to constrain the lid structure these data indicate a fast 4 75 km s lid of about 100 km thickness in the older western atlantic from 16 to 28 the s waves pass through triplications due to velocity jumps near 400 and 660 km the branches from both discontinuities are visible in the s wave data these arrivals were modeled using synthetic seismograms to obtain accurate travel times the two triplications are also apparent in ss data from 30 to 50 the triplication curves derived from the s waves agree with the ss data given the lid structure the waveforms and travel times from the more distant data put tight constraints on the shear velocities at greater depths we find shear velocities from 200 to 400 km to be slow in relation to a shear model of the canadian shield derived by a similar technique indicating continent ocean heterogeneity to about 400 km

modeling temperature inversion in southeastern yellow sea during winter 2016 a significant temperature inversion with temperature differences larger than 3 c was observed in the southeastern yellow sea ys during february 2016 by analyzing in situ hydrographic profiles and results from a regional ocean model for the ys this study examines the spatiotemporal evolution of the temperature inversion and its connection with wind induced currents in winter observations reveal that in winter when the northwesterly wind prevails over the ys the temperature inversion occurs largely at the frontal zone southwest of korea where warm saline water of a kuroshio origin meets cold fresh coastal water our model successfully captures the temperature inversion observed in the winter of 2016 and suggests a close relation between northwesterly wind bursts and the occurrence of the large inversion in this respect the strong northwesterly wind drove cold coastal water southward in the upper layer via ekman transport which pushed the water mass southward and increased the sea level slope in the frontal zone in southeastern ys the intensified sea level slope propagated northward away from the frontal zone as a shelf wave causing a northward upwind flow response along the ys trough in the lower layer thereby resulting in the large temperature inversion diagnostic analysis of the momentum balance shows that the westward pressure gradient which developed with shelf wave propagation along the ys trough was balanced with the coriolis force in accordance with the northward upwind current in and around the inversion area

a low viscosity wedge in subduction zones geochemical petrologic and seismological observations indicate that there may be high concentrations of water in the region above a subducting slab the mantle wedge which could decrease the viscosity of the mantle locally by several orders of magnitude using numerical models we demonstrate that a low viscosity wedge has a dramatic influence on the force balance in a subduction zone and leads to an observable signal in the topography gravity and geoid a regional dynamic model of the tonga kermadec subduction zone shows that the viscosity of the wedge is at least a factor of 10 smaller than surrounding mantle lithosphere and asthenosphere consistent with estimates from seismic dissipation and deformation experiments

the manson impact structure 40ar 39ar age and its distal impact ejecta in the pierre shale in southeastern south dakota the 40 ar 39 ar ages of a sanidine clast from a melt matrix breccia of the manson iowa impact structure mis indicate that the mis formed 73 8 0 3 million years ago ma and is not coincident with the cretaceous tertiary boundary 64 43 0 05 ma the mis sanidine is 9 million years older than 40 ar 39 ar age spectra of mis shock metamorphosed microcline and melt matrix breccia interpreted earlier to be 64 to 65 ma grains of shock metamorphosed quartz feldspar and zircon were found in the crow creek member upper campanian at a biostratigraphic level constrained by radiometric ages in the pierre shale of south dakota that are consistent with the 40 ar 39 ar age of 73 8 0 3 ma for mis reported herein

mantle viscosity and ice age ice sheet topography ice age paleotopography and mantle viscosity can both be inferred from observations of earth s response to the most recent deglaciation event of the current ice age this procedure requires iterative application of a theoretical model of the global process of glacial isostatic adjustment results demonstrate that the iterative inversion procedure converges to a paleotopography that is extremely close to that from the ice 4g model the accompanying mantle viscosity profile is furthermore shown to reconcile the requirements of aspherical geoid anomalies related to the mantle convection process thus resolving a fundamental issue concerning mantle rheology the combined model also explains postglacial sea level histories for the east coast of the united states

effect of lower mantle viscosity on the time dependence of plate velocities in three dimensional mantle convection models 1 earth s evolution has featured stages of relatively steady plate motion interrupted by brief periods of rapid change in plate direction previous studies have shown that vigorously convecting internally heated systems featuring dynamically determined plate like surface motion can also be characterized by predominantly steady periods punctuated by comparatively short reorganization events here we investigate time dependence in two mantle convection models featuring significantly contrasting viscosity profiles and assess the influence of lower mantle viscosity on plate velocity time dependence we model a system featuring nine finite thickness viscous plates at the top of a 6 6 1 cartesian geometry solution domain we find that plate reorganization events involving between 1 and 3 plates occur with geologically relevant frequency in a calculation featuring a factor of 36 increase in lower mantle viscosity relative to the upper mantle specifying a mantle viscosity at a depth of 2000 km that is 3000 times greater than the upper mantle viscosity suppresses this time dependence

high strain rate zone in central honshu resulting from the viscosity heterogeneities in the crust and mantle abstract a linear zone with high strain rates along the backarc side of central honshu the so called niigata kobe tectonic zone has been revealed by the dense gps array geonet operated by the geographical survey institute of japan in order to explore the origin of this zone we examine rheological heterogeneities in the crust or mantle above a subducting slab which possibly contribute to the high strain rates we calculate velocity profiles at the surface of the upper plate due to loading and unloading of the subducting philippine sea plate using a 2 dimensional finite element method from the numerical experiments we find that the high strain rates can be reproduced by viscosity heterogeneities either in the crust or the mantle if viscosity heterogeneity in the crust is an origin the conditions to be satisfied are i an effective elastic thickness of 5 km for short term loading 10 2 10 3 yr ii a low viscosity 19 pa s in the lower crust beneath the zone with a normal viscosity 10 21 pa s in the ambient lower crust and iii a uniform viscosity of 10 19 pa s in the upper mantle on the other hand if viscosity heterogeneity in the mantle is an origin the conditions to be satisfied are i an effective elastic thickness of 30 km for short term loading ii a low viscosity 10 18 pa s at least down to a depth of 60 km in the zone and to a depth of 10 km further seaward below the moho depth and iii a viscosity of 10 20 pa s in the ambient mantle the crust heterogeneity model contradicts the 15 km cut off depth of intraplate seismicity and the 20 km effective elastic thickness previously inferred from gravity and topography in central honshu the fact that quaternary active faults and intraplate earthquakes are not particularly concentrated in the zone also favours the mantle viscosity heterogeneity model thus we prefer the mantle heterogeneity model we suggest that upward movement of water dehydrated from the subducting philippine sea and pacific plates partial melting of the mantle above the pacific plate and serpentinization in the wedge mantle above the philippine sea plate are possible origins of the low viscous upper mantle possible low viscosities in the upper mantle wedge presented in this study seem to provide important constraints for subduction processes of oceanic plates and strain accumulation processes in the upper plate

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

the influence of tectonic plates on mantle convection patterns temperature and heat flow summary the dynamic coupling between plate motion and mantle convection is investigated in a suite of cartesian models by systematically varying aspect ratios and plate geometries the aim of the study presented here is to determine to what extent plates affect mantle flow patterns temperature and surface heat flux to this end we compare numerical convection models with free slip boundary conditions to models that incorporate between one and six plates where the geometries of the plates remain fixed while the plate velocities evolve dynamically with the flow we also vary the widths of the plates and the computational domain in order to determine what constraint these parameters place on the mean temperature heat flux and plate velocity of mantle convection models we have investigated the influence of plates for three whole mantle convection cases that differ in their heating modes internally heated and basally heated and rheologies isoviscous and depth dependent viscosity we present a systematic investigation of over 30 models that exhibit increasingly complex behaviour in order to understand highly time dependent systems using the insight gained from simpler models in models with aspect ratios from 0 5 to 12 we find that for the same heating mode variations in temperature can be as much as 40 per cent when comparing calculations with unit width plates to models incorporating plates with widths equal to five times the model depth mean surface heat flux may decrease by 60 per cent over the same range of plate widths we also find that internally heated mantle convection models incorporating plates exhibit novel behaviour that we believe has not been described previously in mantle convection studies specifically in internally heated models plate motion is characterized by episodic reversals in direction driven by changes in the mantle circulation from clockwise to counterclockwise and vice versa these flow reversals occur in internally heated convection and are caused by a build up of heat in the interiors of wide convection cells close to mantle downwellings we find that flow reversals occur rapidly and are present in both single plate and multiple plate models that include internal heating this behaviour offers a possible explanation for why the pacific plate suddenly changed its direction some 43 ma

models of convection driven tectonic plates a comparison of methods and results summary recent numerical studies of convection in the earth s mantle have included various features of plate tectonics a number of different methods for modelling plate like behaviour have been used the differences in the methods of modelling plates may assume or predict significantly different plate deformation we describe three methods of modelling plates through material properties force balance and a thin power law sheet approximation we compare the results obtained using each method on a series of simple calculations from these results we are able to develop scaling relations between the different parametrizations while each method produces different degrees of deformation within the surface plate the surface heat flux and average plate velocity agree to within a few per cent the main results are not dependent upon the plate modelling method and therefore are representative of the physical system we set out to model

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

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

the sensitivity of glacial isostatic adjustment predictions to a low viscosity layer at the base of the upper mantle abstract recent inferences of mantle viscosity based on convection related observables long wavelength nonhydrostatic geoid and free air gravity harmonics indicate the presence of a relatively thin low viscosity region at the base of the upper mantle we explore the sensitivity of observables associated with glacial isostatic adjustment gia to the viscosity and thickness of this region these observables include post glacial relative sea level rsl variations within previously glaciated areas and in the far field of the late pleistocene ice sheets as well as anomalies associated with the rotational state of the planet the latter include present day secular variations in the geopotential harmonic j 2 or equivalently variations in the rotation rate and polar wander speed we find in contrast to previous suggestions that the gia observables with the exception of polar wander speed are sensitive to fine scale low viscosity structure at the base of the upper mantle for example j 2 predictions can be altered by as much as 2 10 11 yr 1 by the inclusion of a low viscosity zone this signal is sufficient to significantly affect both inferences of mantle viscosity and constraints on the present day melting of large polar ice sheets antarctic greenland that are derived using this observable indeed if a low viscosity region exists then models that do not include it can overestimate recent polar melting events by as much as 0 5 mm yr of equivalent eustatic sea level rise