the thermal structure of mantle plumes axisymmetric or triple junction summary a mantle plume is probably a complex 3 d thermal structure that possesses approximate axisymmetry as it approaches the base of the lithosphere from below but followed down towards the base of the layer probably consists of a triple junction or quadruple junction of connected hot sheets a relatively weak hot sheet rising only part way through the layer probably connects two neighbouring mantle plumes these conclusions are suggested by numerical experiments on a 3 d constant viscosity plane layer with stress free boundaries which detail the gradational change in the planform of a convecting layer from the top of the layer to its base the planform of a convecting layer is a map in the horizontal plane of the principal thermal anomalies in the layer these anomalies are the main sources of positive for hot fluid or negative for cold fluid buoyancy and therefore they drive the convective flow they may appear in cross section as structures with either axial symmetry columns planar symmetry sheets or some complex asymmetric form when convection is driven at least partially by basal heating the planform near the top of the layer may be described as a network of cold sinking sheets and isolated hot columns while near the base of the layer it appears as a network of hot rising sheets and isolated cold columns the hot columns near the upper surface arise from the vertices or nodes of the network of hot sheets on the lower surface and similarly the cold columns at the base of the layer form below the vertices of the network of cold sheets near the upper surface near the upper surface the apparent planform of this experiment is analogous to that of mantle convection the cold sheets compared to subduction zones and the hot columns compared to mantle plumes the hot plumes impinging on the upper surface produce approximately axisymmetric temperature anomalies surface uplift and extensional stress fields however the relatively minor deviations from axisymmetry of surface observables reflect the deep structure of the mantle plume formed by the junction of three or four hot sheets on the base of the layer it seems likely that the commonly occurring triple junction form of continental rifts may reflect an underlying structure that is implicit in the convective circulation of the mantle beneath

a geodynamic model of mantle density heterogeneity using cenozoic and mesozoic plate motion reconstructions we derive a model of present day mantle density heterogeneity under the assumption that subducted slabs sink vertically into the mantle the thermal buoyancy of these slabs is estimated from the observed thermal subsidence cooling of oceanic lithosphere slab velocities in the upper mantle are computed from the local convergence rate we assume that slabs cross the upper lower mantle interface and continue sinking into the lower mantle with a reduced velocity for a velocity reduction factor between 2 and 5 our slab heterogeneity model is as correlated with current tomographic models as these models are correlated with each other we have also computed a synthetic geoid from our density model for a viscosity increase of about a factor of 40 from the upper to lower mantle our model predicts the first 8 spherical harmonic degrees of the geoid with statistical confidence larger than 95 and explains 84 of the observed geoid assuming that the model c21 and s21 terms are absent due to a long relaxation time for earth s rotational bulge otherwise 73 of the geoid variance is explained the viscosity increase is consistent with our velocity reduction factor for slabs entering the lower mantle since downwelling velocities are expected to scale roughly as the logarithm of viscosity loge 40 3 7 these results show that the history of plate tectonics can explain the main features of the present day structure of the mantle the dynamic topography induced by this heterogeneity structure consists mainly of about 1 km amplitude lows concentrated along the active continental margins of the pacific basin our model can also be used to predict the time variation of mantle heterogeneity and the gravity field we find that the age of the geoid defined as the time in the past before which the geoid becomes uncorrelated with the present geoid is about 50 m y our model for the history of the degree 2 geoid which is equivalent to the history of the inertia tensor should give us a tool to study the variations in earth s rotation pole indicated in paleomagiietic studies

a mantle flow mechanism for the late paleozoic subsidence of the parana basin the carboniferous permian stage in the evolution of the parana basin is characterized by the long wavelength deposition of up to 2 5 km of sediment in the continental interior the tectonics of the region during this time were dominated by convergence and active subduction along the nearby panthalassan margin of gondwana while subsidence in the basin is clearly related to the major tectonic events at the plate margin there is a distinct delay between the onset of subduction and the initiation of basin deposition this and the nature of basin stratigraphy suggests that the large scale subsidence may have been the dynamic response of the lithosphere to mantle flow associated with the penetration of accumulated slab material through the phase change at 660 km depth we present numerical experiments of mantle convection which show that subducting slabs can stagnate at the 660 km depth phase change and intermittently penetrate through the associated negative dynamic topography remains at relatively low amplitudes as the subducting material pools and then increases rapidly to a maximum during the phase of penetrative flow we find that the predicted delay time between initial descent of the slab and the maximum surface topography corresponds with evidence from the geological record several models of sedimentation based on the evolving dynamic topography are presented and a simulation generated using infill rates independently estimated for the basin provides a close fit to the amplitude and horizontal length scale of material accumulation in the parana basin

transitions in thermal convection with strongly variable viscosity one of the most important material properties influencing the style of convection in the mantles of terrestrial planets is the extreme temperature dependence of viscosity three dimensional numerical convection calculations in a wide 8 8 1 cartesian box and in a spherical shell ratio of inner to outer radius of 0 55 characteristic of terrestrial planets both display two fundamental transitions as the viscosity contrast is progressively increased from unity to a factor of 105 these transitions not only mark changes in the style of deformation in the upper boundary layer from mobile lid to sluggish lid to stagnant lid but also have dramatic effects on the style planform and horizontal length scales of convection in the entire domain vertical variations of viscosity are the most important for determining the horizontal length scales of the convective patterns while lateral viscosity variations play a role in shaping the relative structures of the upwelling and downwelling flows convection in venus appears to be represented most closely by the sluggish lid regime of convection whereas the earth with plate tectonics more closely resembles the mobile lid style of convection forcing plate like characteristics onto the convective flows in the form of imposed weak zones and prescribed surface velocities results in flow patterns dominated entirely by the form used to enforce the plate like behavior and tells us little about why the mantle exhibits long wavelength heterogeneity

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

plume heat flow in a numerical model of mantle convection with moving plates abstract self consistent numerical models are presented for a two dimensional thermal convection with moving plates to estimate the heat flow transported by hot upwelling plumes in both internally and basally heated mantle the plume heat flow depends on the internal heating rate and convective regimes but does not exceed 30 of basal heat flow when the plates rigidly move as observed on the earth the fraction of plume heat flow to basal heat flow becomes higher when the lithosphere behaves as a stagnant lid or as a mechanically not so strong plate when estimated from the dynamic topography of plume swells above hot upwelling plumes the plume heat flow appears to be only a small fraction of the real plume heat flow as a whole the apparent plume heat flow estimated from dynamic topography remains only a few percent of the total heat flow on the surface boundary the value observed for the earth even when the basal heating rate exceeds 50 of the total heating rate such a high fraction of basal heating rate is necessary for the amplitude of topography above hot upwelling plumes to become comparable to the value observed for the earth too it is necessary to reexamine the earlier inference that the heat released from the core manifests itself as plume heat flow in the earth

role of the lithosphere in mantle convection plate geometry and kinematics generally reflect the mechanical properties of the solid lithosphere rather than those of the fluid mantle underneath and plate formation and subduction account for most of the heat transport from the earth s interior correspondingly mantle convection models must incorporate a stiff but mobile boundary layer like the lithosphere before they can reproduce the main features of mantle convection a relatively easy way to accomplish this in numerical models is to combine a temperature dependent viscosity with an imposed piecewise constant surface velocity boundary condition it is shown how surface heat flux topography gravity and geoid but not plate velocities or stresses can then be derived numerical models confirm that a lithosphere has a first order effect on the underlying flow structure for internally heated models approx imating the case of whole mantle convection the calculated surface signatures are in first order agreement with observations a level of empirical success which hitherto has not been approached by models of mantle convection companion papers exploit the observations more fully to constrain the main features of mantle convection

mantle plumes and continental tectonics abstract it is now recognised that plumes originate from a thermal boundary layer deep in the mantle a new plume consists of a large head with a diameter of approximately 800 to 1200 km and it is followed by a smaller tail which has a diameter of 100 to 200 km at the top of its ascent the head flattens to form a disk 2000 to 2500 km in diameter that may melt to produce a continental flood basalt or oceanic plateau the tail melts to produce chains of volcanic activity such as the hawaiian emperor chain the ascent of a new plume leads to surface uplift of 500 to 1000 m over a length scale of 2000 km this places the lithosphere under tension but the horizontal forces produced do not result in runaway extension unless the continental lithosphere is already anomalously hot and therefore weak if the lithosphere is cold and strong slow extension leading to a new spreading ridge may postdate plume arrival by 10 to 40 m y the time difference being the time taken to conduct heat from the plume to the overlying lithosphere plume heads may control the timing and position of new ocean ridges but are not the fundamental force that drives plate tectonics the heat from plume tails may weaken the overlying plate and pin the position of spreading the ascent of a mantle plume can also have an important influence on subduction large oceanic plateaus such as the ontong java plateau are more buoyant than normal oceanic crust because they have a thicker basaltic layer and because they are underlain by a 200 km thick layer of hot material from a mantle plume head as a consequence oceanic plateaus are more difficult to subduct than normal oceanic crust this can lead to jamming of plates at subduction zones resulting in a flip in the sense of subduction as appears to have happened in the caribbean region or to obduction of the plateau finally when a plume head is emplaced beneath continental crust heat released from the plume may lead to melting of the overlying crust the granites associated with many greenstone belts and intercontinental magmatic provinces such as the paleozoic lachlan fold belt of eastern australia and the middle proterozoic anorogenic granites of the central and southwestern united states may have formed in this way

the empirical age depth relation and depth anomalies in the pacific ocean basin this paper presents a new age depth relation and a comprehensive depth anomaly map for the pacific ocean age depth and sediment thickness were averaged for each 1 1 area bathymetry was corrected for isostatic effects due to sediment and water load and for the variation of sound velocity in water seafloor existing at extreme distance from hot spot tracks is found to be anomalously deep hot spots were treated as thermal anomalies and data within 800 km of them were eliminated from further analysis an age depth equation was determined by fitting a least squares line to the remaining data the resulting depth versus age distribution confirms the linear dependence of depth on age up to 80 ma all older seafloor is within 800 km of hot spots or hot spot tracks and is shallower than predicted this flattening of the age depth distribution requires that a separate function be fit to data older than 80 ma as a result data representing the deepest seafloor older than 80 ma were selected for curve fitting and the age depth distribution was approximated by an exponential function it is impossible to distinguish between the infinite half space and cooling plate models of the lithopshere using the age depth data from the pacific ocean a depth anomaly map prepared by comparing observed depth with the depth predicted by the new age depth formula shows several newly recognized features including swells over the louisville ridge in the south pacific and in the gulf of alaska seamounts

subducted slabs and the geoid 1 numerical experiments with temperature dependent viscosity one of the most powerful constraints on mantle viscosity comes from the correlation of the long wavelength degree 4 9 geoid with that predicted by a density model for subducted slabs the effect of lateral variations of viscosity should be most pronounced at subduction zones due to the strong effect of temperature on viscosity an idealized slab model with temperature dependent viscosity is considered with various lateral and vertical viscosity structures using a two dimensional finite element formulation the viscosity parameterization affects the amplitude of the long wavelength geoid anomaly but not the sign of the correlation between the geoid and density anomalies depth dependent viscosity models with a high viscosity lithospheric layer do not completely match the temperature dependent laterally varying results suggesting that the rheology of the slab does have an effect on the long wavelength surface topography and geoid however this affect is minor suggesting that the radial models of mantle viscosity inferred from surface observables are correct to first order in contrast the short wavelength features are dramatically affected by the rheology of the region surrounding the downwelling further study of the shorter wavelength geoid over subduction zones may provide better insight into subduction zone processes

numerical modelling of lithosphere asthenosphere interaction in a subduction zone we developed a new 2 d numerical approach to study solid fluid coupling applied to subduction zones the lithosphere is characterised by an elastic or elastoplastic behaviour and the asthenosphere by a homogeneous isoviscous fluid the temperature effects are ignored and viscosity and density are constant in time the solid and the fluid problem are discretised by the finite elements method fem the same solid code used in hassani et al hassani r jongmans d chery j study of plate deformation and stress in subduction processes using two dimensional numerical models j geophys res 1997 102 17951 17965 has been used to compute the solution of the solid problem the stokes problem is solved by a direct solver with a stabilisation procedure we used a very simple staggered coupling method where the fluid domain is regularly re meshing we observed numerical instabilities when the time step is not sufficiently small especially when strong coupling between the solid and the fluid occurs we have tested different configurations where the lithosphere is elastic or elastoplastic and show how the slab geometry the topography and the stress regime in the plates are affected by the viscous resistance of the mantle we observed that the asthenosphere viscosity is a fundamental parameter in the subduction process for subduction with an extensional regime in the upper plate we observe a linear decrease of the extensional stress as a function of the asthenospheric viscosity

ridge spreading subduction and sea level fluctuations a numerical model of mantle convection shows that sea level fluctuations are not simply associated with temporal changes in ocean c plate spreading in the dynamic model sea level rises rapidly and then falls toward a steady value but one still higher than the initial following increased ridge spreading this time dependence results from profound changes in the deep thermal structure under ocean and continent the use of past variations in oceanic spreading to infer sea level fluctuations is called into question with more realistic models and better continental stratigraphy constraints may be placed on the viscosity structure of the mantle

towards a realistic simulation of plate margins in mantle convection we have incorporated faults as plate margins into time dependent mantle convection models by using a mixed eulerian and lagrangian finite element formulation plate margins in our models can migrate dynamically in response to variations in mantle buoyancy and this enables us to study the dynamics of mantle and plates including changes in plate size convection models in a cylindrical geometry with such a faulted converging margin non newtonian rheology and continents indicate that the converging margin tends to migrate oceanward the oceanward trench migration leads to an increase in the size of the overriding continental plate

evidence for a 20 tilting of the earth s rotation axis 110 million years ago true polar wander tpw the shift of the earth s rotation axis with respect to the entire globe is most probably due to mass redistribution in the earth s mantle as a result of convection using a new rigorously selected palaeomagnetic database gathering only directions obtained from magmatic rocks we find that tpw has been clearly intermittent over the last 200 ma with two long periods of strict standstill from the present to 80 ma and from approximately 150 to 200 ma a single period of shifting is observed between 80 and about 150 ma ago this period culminates around 110 ma ago in an 20 abrupt tilting during which an angular speed exceeding 5 ma 0 5m yr may have been reached assuming that the time averaged geomagnetic field is axial our results indicate that the changes in the position of the rotation axis and therefore in the inertia tensor of the earth are intermittent we suggest that a major reorganization of the mass distribution in the earth s mantle occurred in the lower cretaceous this event concomitant with plume hyperactivity at the earth s surface and probable drastic changes at the core mantle boundary attested by the inhibition of geomagnetic reversals suggests unmixing of upper and lower mantle by avalanching of upper mantle material down to the core mantle boundary the astonishingly strict stability of the time averaged position of the rotation axis before and after this episode of shifting implies the existence of some steady convection which does not modify the large scale distribution of mass within the mantle given the intermittence of mantle avalanching we suggest that these long periods of stability correspond to the temporary reestablishment of a basically two layered convection system within the mantle

the deep structure of ocean ridges in a convecting mantle abstract plate tectonic models have frequently assumed that mid ocean ridges are the surface expression of the hot rising limb of a convection cell measured half spreading rates show that in any reference frame the horizontal transverse velocity of some ridges is comparable to the individual plate velocities if the above assumption is correct this observation implies that the thermal structure beneath the ridge can adjust rapidly to the changing surface configuration of the plates numerical experiments in a two dimensional convecting layer of constant viscosity fluid show that such a rapid adjustment is probably unrealistic a symmetrically spreading ridge moving horizontally is simulated by specifying a velocity boundary condition on the upper surface of the layer the other boundary conditions are uncertain so several different combinations are used in the experiments including periodic or reflecting lateral boundaries and stress free or no slip lower boundary in all the experiments the rising sheets of the convection cells are anchored firmly in the mean horizontal flow of the layer unless the mean flow coincides approximately with the ridge velocity the ridge quickly moves away from a rising sheet which is initially beneath it if the aspect ratio width depth of the convection cells is significantly greater than one this conclusion is even more evident in the earth it seems unlikely that there is a systematic deep of the order of the convecting layer thickness structure beneath the worldwide network of ocean ridges

evidence for extraneous origin of a magnesiowustite metal fremdling from the vigarano cv3 chondrite a calcium aluminum rich inclusion cai from the vigarano cv3 chondrite 477b contains three types of fremdlinge and pt rich phases 1 feni blebs 2 sub micron pt rich fe bearing nuggets and 3 pt rich fe bearing veins many of the feni fremdlinge contain grains of mgfe oxide periclase wustite series ion microprobe measurements of an unusually large 5 m per70 wu30 grain reveal isotopically light mg 4 3 amu in contrast to heavy mg 4 7 amu in adjacent spinel and melilite the oxygen isotopic composition of the periclase wustite is 17osmow 9 1 18osmow 12 5 distinct from isotopically normal oxygen in the surrounding melilite and the large 16o enrichments 16oexcess 52 in adjacent spinel the petrographic mineral chemical and isotopic properties of the magnesiowustite grain argue against in situ formation in the cai and indicate an extraneous origin from a reservoir depleted in silicon this reservoir probably had normal oxygen in contrast to the 16o rich reservoir from which the cai formed and isotopically light magnesium

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

the effects of chemical density differences on convective mixing in the earth s mantle subducted lithosphere and crust are chemically distinct from ambient mantle and some have hypothesized that the resulting anomalous buoyancy may affect mixing and in particular may cause chemical heterogeneity to persist to explore this effect two dimensional convective mixing calculations have been carried out boundary conditions mimicking features of plate kinematics have been imposed and negatively buoyant tracers placed beneath converging plate margins to simulate subduction the principal parameter of interest is the density anomaly ratio o t the ratio of the chemical to the thermal buoyancy for a density anomaly ratio appropriate to complete separation of the oceanic crust from the rest of the lithosphere it is marginally possible for the tracers to segregate into the warm region near the bottom and neutralize the thermal buoyancy there for internally heated flows and to segregate to the base of the uprising limbs of convection for bottom heated flows however for the more likely scenario of oceanic crust and lithosphere maintaining their layering after subduction there is neither segregation nor neutralization of thermal buoyancy the average residence time is the average time tracers remain in the box from subduction to sampling beneath ridges and could be increased by 4 from the passive case at the very most if the crust and lithosphere remain layered even in the more extreme case of separation of crust from lithosphere the residence times are only increased by 15 from the passive case

compressible convection with constant and variable viscosity the effect on slab formation geoid and topography two dimensional cartesian finite difference models of compressible convection with constant and variable viscosity and fixed bottom temperature are presented density variations according to the adams williamson equation of state are included in the case of constant viscosity convection viscous and adiabatic heating damp the flow compressible density variations hardly influence geoid undulations however the lower thermal boundary layer becomes thinner and the mean cell temperature increases in the case of variable viscosity the nonlinear coupling between compression adiabatic and viscous heating and a temperature pressure and stress dependent rheology leads to important consequences the upwelling flow broadens and plumes are retarded the flow strongly concentrates toward the downwelling region and becomes mechanically decoupled from the interior of the cell by a low viscosity region this mechanism seems to be important for the formation of subducting slabs extrapolated to mantle conditions two low viscosity regions are predicted flanking the slab on either side and inhibiting an early dispersal and mixing of slab material into the mantle this process might be aided by an increase of negative buoyancy forces with depth as observed in the models further results are as follows increasing the dissipation number in variable viscosity convection may either damp or speed up convection depending on the rheology models with internal heating and a fixed bottom temperature show that the threshold to time dependent variable viscosity convection is drastically reduced if the anelastic liquid approximation is applied instead of the extended boussinesq approximation

the influence of second scale convection on the thickness of continental lithosphere and crust abstract the effect of sublithospheric convection on the thickness and structure of the continental lithosphere is studied in numerical models assuming different rheologies newtonian non newtonian and temperature and pressure dependent heat fluxes and heating modes bottom versus internal heating the stagnant regions near the top of the models are identified with the lithosphere we distinguish a seismic and thermal lithosphere controlled by temperature an elastic lithosphere controlled by viscosity and a mechanical lithosphere controlled by strain rate strong lateral thickness undulations with a thick lithosphere above the downwelling regions and a thin lithosphere above the upwelling regions develop the thickness of the elastic lithosphere is about two thirds of the mechanical lithosphere while the ratio of the elastic to the thermal lithosphere varies between 0 4 and 0 8 the time dependence of some models with internal heating and a surface heat flow of 20 mw m 2 is characterized by long periods of the order of 1 ga close to steady state and short periods 100 ma of changing cell patterns and lithospheric thicknesses models showing thick lithospheric roots suggest that the mantle beneath some old shields may be associated with cold slowly downwelling convective flow rather than being firmly attached to the lithosphere the missing gravity and topography signals from such regions can be explained by elastic bending of the lithosphere and by dynamic adjustment of the moho observed lithospheric thickness variations in europe and their minimum to maximum spacing agree well with the models suggesting sublithospheric convection to be the cause compared to other observed features thickness undulations of the lithosphere seem to provide the strongest indications for sublithospherical convection relatively low viscosities in the lower crust may lead to a long term decoupling of surface topography from moho topography and mantle dynamics the moho depth is capable of adjusting to mantle stresses within relaxation times of the order of 100 ma while surface topography may flatten out such a mechanism may be important in regions with a deep moho such as fennoscandia or with a shallow moho such as the pannonian basin neither region showing a pronounced surface topography

global distribution and characteristics of coronae and related features on venus implications for origin and relation to mantle processes coronae on venus range from 60 to over 2000 km across and are characterized by a complex range of morphologies the annuli around coronae range from about 10 to 150 km across and have tectonic features ranging from extensional to compressional to a combination of both topographically coronae are domes plateaus plateaus with interior lows and rimmed depressions a subset of features classified here as coronae corresponds to depressions and is interpreted to consist of large scale calderas a number of features have been identified with many of the basic characteristics of coronae similar interior deformation associations with volcanism high topography but lacking a distinct tectonic annulus these features tend to be somewhat smaller than coronae and may represent failed coronae or coronae in an early stage of evolution the size distribution of coronae and coronalike features with maximum widths greater than about 250 km is well represented by a power law of the form n d kd where n is the number of coronae with maximum widths greater than d km and 3 05 the spatial distribution of coronae is not random the features are concentrated in a few groups and along several chains coronae are similar in many morphologic characteristics to major volcanic shield structures and volcanic rises such as western eistla regio the largest corona artemis is actually larger than several volcanic rises on venus coronae and volcanic rises appear to be surface manifestations of mantle plumes there is no evidence of any systematic variation in age along chains of coronae as occurs in hotspot chains on earth instead a number of multiple and overlapping coronae may indicate limited movement of the surface above a hotspot or mantle plume the morphology and size distribution of coronae highlands and major shields suggest that mantle upwelling on venus operates either on several spatial scales with coronae representing smaller scale upflows and major volcanic rises representing larger convective upwellings or on several temporal scales with coronae representing shorter duration upflows and major volcanic rises representing long term upwellings

on the existence of a second scale of convection in the upper mantle summary this paper is concerned with an examination of the possibility that there might exist a small scale of convective circulation beneath the oceanic lithosphere recent suggestions that this might be the case have been made in an effort to understand why the bathymetry of the sea floor deviates from the prediction of boundary layer theory for ages in excess of about 100 ma the energy source which sustains the secondary motion is supposed to be found in the steep temperature gradient near the planetary surface which is itself presumably maintained by the large scale convective circulation associated with plate creation and destruction here we investigate the extent to which the temperature dependence of viscosity may act so as to stabilize the upper boundary layer against disruption by such secondary instability if the viscosity profile is monotonie and the asymptotic upper mantle viscosity is about 1022poise as suggested by post glacial rebound data then the existence of the second scale is extremely unlikely on the other hand if a sufficiently pronounced low viscosity zone does exist under old sea floor then the development of such a second scale cannot be ruled out completely some recently obtained geophysical evidence is reviewed which suggests that this is unlikely to be the case

mantle convection model with a dynamic plate topography heat flow and gravity anomalies summary surface observables have been calculated for a numerical convection model that includes a dynamic plate that is a stiff but mobile section of the upper boundary layer that is driven entirely by internal buoyancy forces the results for heat flux and topography are virtually identical to those obtained from a partially kinematic model in which plate mobility results from an imposed horizontal velocity on the top surface these results confirm the validity of the partially kinematic approach which has been used previously the partially kinematic approach is more efficient computationally

dynamic models of downgoing plate buoyancy driven subduction subduction motions and energy dissipation abstract it is much debated whether the forces associated with the downgoing plate the overriding plate passive or active mantle flow are dominant in controlling the paths of plates into the mantle we investigate the dynamics and energetics for a free subduction system driven solely by downgoing plate buoyancy using a finite element model of a viscoelastic plate with a free surface sinking into a passive unbounded mantle represented by drag forces parameters are varied to study effects of an asthenosphere ridge push and a passive overriding plate for a range of subducting plate viscosities and densities such a single free plate achieves subduction mainly through trench retreat most of the energy dissipation occurs in driving the passive mantle response as a result the slab s sinking velocity is its stokes velocity determined by lithospheric buoyancy and mantle viscosity the total subduction velocity and dip adjust to minimize bending dissipation in the lithosphere and are affected by slab rheology as well as buoyancy a low viscosity asthenosphere and ridge push facilitate plate advance increasing plate dips and lowering subduction velocity while suction and buoyancy of a work free passive overriding plate decreases plate dips thus increasing subduction and rollback velocities however the geometrical relation between the different parameters is the same in all model cases because the slabs sink according to their stokes velocity the free subduction models thus provide a reference that can be used to distinguish the signature of downgoing plate buoyancy from that of other driving forces in global compilations of subduction parameters

free surface formulation of mantle convection i basic theory and application to plumes in mantle convection models the top surface is traditionally approximated as a free slip boundary and the dynamic topography is obtained by assuming that the normal stress on the free slip boundary is compensated instantaneously through surface deformation it has already been shown that this approximation is valid for long wavelength topography based on both viscous and viscoelastic models with a free surface we have found that the characteristic time for topographic growth is comparable to the timescales of mantle convection 10 6 year for short and intermediate wavelengths 10 3 km or less and or a high effective lithospheric viscosity 10 24 pa s this suggests that the topography is history dependent under these conditions and that a free surface formulation is required to study the topography at these wavelengths we have developed a new eulerian finite element technique to model a free surface since the technique is based upon an undeformable eulerian grid this enables us to study long term free surface dynamics in the presence of evolving buoyancy we have compared numerical with analytic solutions of viscous relaxation for fixed buoyancy problems as long as the magnitude of topography is much smaller than the wavelength we find that the finite element method is very accurate with relative errors of less than 1 per cent this numerical technique can be applied to a variety of geophysical problems with free surfaces in applying this technique to dynamic models of mantle plumes we find that surface relaxation retards the topography at intermediate and short wavelengths and produces a smoother topography compared with topography from free slip calculations this reduced topography has a significant influence on the geoid at the corresponding wavelengths moreover free surface models by allowing vertical motion on the free surface yield a hotter lithosphere over ascending plumes than models with free slip boundaries

effects of lithospheric rigidity on ocean floor bathymetry and heat flow the observed quasi rigid behaviour of surface plates in the course of their relative motion is a consequence of the high viscosity which obtains in the cold near surface region by assigning a particular constant velocity as the upper boundary condition in a numerical model of mantle convection we have investigated the effect of lithospheric rigidity on the variation of oceanic bathymetry and heat flow as a function of ocean floor age predicted variations of both bathymetry and heat flow at the surface of mantle wide convection cells which are partially heated from within exhibit the same qualitative behaviour as data compiled for the major ocean basins the bathymetry varies with distance x from the spreading centre initially as x sup 1 2 but subsequently flattens with respect to an x sup 1 2 reference curve whereas the heat flow closely follows an x sup 1 2 decay over most of the convection cell consequently the viability of the mechanism for sea floor flattening proposed by jarvis and peltier 1980 is increased when a constant surface velocity characteristic of rigid plates is incorporated in the model this model successfully predicts both that the bathymetry should flatten and that the heat flow should not

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

geoid anomalies from cenozoic subduction in semi dynamical flow models including a phase boundary in order to investigate the relationship between the geoid and plate subduction we develop a 3 d spherical shell model in which the circulation is driven by both buoyancy forces and an imposed surface velocity taken from plate reconstruction for the past 65 ma to avoid numerical resolution problems we use an enhanced value of thermal diffusivity which leads to an overly thick lithosphere the correct amount of buoyancy is re established by using a reduced value of thermal expansion coefficient first we calculate the present temperature field in the mantle due to the cenozoic plate motions for models with and without a phase transition at 660 km depth which is approximated by a locally modified effective thermal expansion coefficient in a second step the geoid anomalies are determined subject to a stress free upper boundary condition when the thermodynamic parameters of the boundary at 660 km allow slab penetration into the lower mantle the medium wavelength l 4 11 geoid agrees well with the observed geoid if there is a moderate increase of viscosity from the upper to the lower mantle when the clapeyron slope is sufficiently negative to prevent slab penetration the agreement is poor

petrology and k ar ages of dredged samples from laysan island and northampton bank volcanoes hawaiian ridge and evolution of the hawaiian emperor chain summary the hawaiian emperor volcanic chain is made up of at least 107 indentifiable shield volcanoes chase and others 1970 bargar and jackson 1974 clague and others 1980 and is the longest linear island and seamount chain in the pacific fig 1 beginning at the active volcanoes kilauea and mauna loa on the island of hawaii this chain of volcanoes extends west northwestward along the hawaiian ridge for a distance of 3 500 km where it turns northward and continues another 2 300 km as the emperor seamounts ending near the intersection of the aleutian and kurile trenches it is now thought that the hawaiian emperor chain was formed as the pacific lithospheric plate moved first northward and then northwestward relative to the hawaiian hot spot a more or less stable melting anomaly in the asthenosphere and that the bend in the chain reflects a major change in pacific plate motion several mechanisms have been proposed to explain the hawaiian and other hot spots including a propagating fracture betz and hess 1942 jackson and wright 1970 diapiric upwelling along a line of structural weakness green 1971 mcdougall 1971 thermal morgan 1972a 1972b or chemical anderson 1975 plumes of gravitationally unstable material rising from the deep mantle shear melting coupled with thermal feedback shaw 1973 and geographically stabilized by gravitational sinking of refractory residua shaw and jackson 1973 and extrusion induced by lateral motion along plate boundaries handschumacher 1973 despite the variety of dynamic models proposed there has yet to be devised a definitive experiment to test any of them all these mechanisms are however encompassed by the general or kinematic hot spot hypothesis which when used in the broadest sense implies neither mechanism nor excess heat

a comparison of heat flow from the gondwana continents with velocities of gondwana plates geodynamic implications abstract the velocities of the lithospheric plates generally differ from each other and the cause of the super mobility of the indian subcontinent is an unresolved problem as the lithospheric plates and the sub lithospheric mantle form the two key elements of plate tectonic movement the thermal characteristics of the three constituent plates of gondwanaland i e the indian african and australian landmasses have been compared in this study it has been clearly shown that the mean surface heat flow values q s in those gondwana terrains of india which remained unaffected by tectonic and igneous activity during the last 150 m y i e after the break up of gondwanaland are either equal to or mostly lower by 5 22 mw m 2 than those in similar terrains of australia and even the immobile african continent and that q s values for the terrains of these landmasses which were affected by such activity during the last 150 m y are uniformly equal it is inferred that the indian lithosphere is neither hotter nor thinner than that beneath the above mentioned continents and that the sub lithospheric upper mantle beneath the indian peninsula is not hotter or less viscous than that beneath the african and australian shields these results and inferences evidently imply that the thermal regime and the other related parameters of the continental lithosphere do not contribute to the mobility of the plates to which it is attached that the rapid movement of the indian landmass is not coupled with the thermal characteristics of its lithosphere and that the drag force which the present studies have shown to be insignificant would not have been lower on the base of the indian lithosphere than beneath the african and australian landmasses accordingly the earlier reported postulate that the high velocity of the indian landmass is due to its thin and hot continental lithosphere and less viscous upper mantle is not valid the paleo reconstruction indicates the existence of the reunion and kerguelen plumes one on each side of the indian landmass it is likely that these plumes created in the sub lithospheric mantle favourable conditions which worked together with forces that resulted from slab pull and ridge push to give a high velocity to the indian landmass

mantle convection plates and hotspots abstract more than 20 years after their discovery plates and hotspots are still awaiting a consistent dynamic model both imply large viscosity variations in the mantle sustained efforts have been targeted on modeling on computer as well as in the laboratory convection in fluids with temperature and pressure dependent viscosity the main results of these studies are reviewed and summarized in a few simple rules several properties of plates such as ridge push or heat flow distribution are well accounted for by convection models with temperature dependent viscosity however the process of subduction is not properly explained by these models one of the simple rules deduced from the study of convection and temperature dependent viscosity states that the viscosity drop across the lower boundary layer adjusts to a low value less than 10 this constrasts strongly with the viscosity variations required by current hotspot formation models which are typically 100 times larger it is suggested that this paradox can be solved if subduction is properly included in the convection models

archean komatiites and geotherms solution to an apparent contradiction the high liquidus temperatures of archean komatiites and the low geothermal gradients in archean continents appear to give contradictory indications of temperatures in the archean mantle we resolve this contradiction in terms of an idealized model of convection in the archean mantle we suggest that temperatures in the archean mantle were no more than 100 c higher than at present that komatiites originate from the hot lower boundary layer of a non steady convection cell and that archean continents were formed near subduction zones where near surface temperature gradients were lower than elsewhere in the convecting mantle

mantle convection with strong subduction zones because mantle viscosity is temperature dependent cold subducting lithosphere should be strong which implies that the rapid localized deformation associated with subduction should strongly resist plate motions due to computational constraints the deformation of a subducting plate cannot be accurately resolved in mantle scale convection models so its effect on convection is difficult to investigate we have developed a new method for implementing subduction that parametrizes the deformation of the oceanic lithosphere within a small region of a finite element grid by imposing velocity boundary conditions in the vicinity of the subduction zone we enforce a geometry for subduction producing a slab with a realistic thermal structure to make the model dynamically consistent we specify a rate for subduction that balances the energy budget for convection which includes an expression for the energy needed to deform the oceanic lithosphere as it subducts this expression is determined here from a local model of bending for a strong viscous lithosphere by implementing subduction in this way we have demonstrated convection with plates and slabs that resemble those observed on earth but in which up to 40 per cent of the mantle s total convective resistance is associated with deformation occurring within the subduction zone this additional resistance slows plate velocities by nearly a factor of two compared to models with a weak slab for sufficiently strong lithosphere the bending deformation slows surface plates sufficiently that they no longer actively participate in global scale convection which occurs instead beneath a sluggish lid by introducing a low viscosity asthenosphere beneath the oceanic plate we demonstrate that small scale convection at the base of oceanic lithosphere may limit plate thickness and thus the resistance to bending and cause plate velocities to depend on the strength of the bending lithosphere rather than on the viscosity of the underlying mantle for a cooling earth the effective lithosphere viscosity should be nearly constant but the mantle viscosity should increase with time thus subduction resisted convection should produce nearly constant plate velocities and heat flow over time which has implications for the earth s thermal evolution we estimate that this style of convection should apply if the effective viscosity of the bending lithosphere is greater than about 10 23 pa s but only if some mechanism such as small scale convection prevents the bending resistance from stopping plates altogether such a mechanism could be fundamental to plate tectonics and earth s thermal history

distribution of mantle up welling determined from plate motions a case for large scale benard convection the number and geometric distribution of putative mantle up welling centers and the associated convection cell boundaries are determined from the lithospheric plate motions as given by the 14 euler poles of the observational nuvel model for an assumed distribution of up welling centers called cell cores the corresponding cell boundaries are constructed by a voronoi division of the spherical surface the resulting polygons are called benard cells by assuming the flow kinematics within a cell the viscous coupling between the flow and the plates is estimated and the euler poles for the plates are computed under the assumption of zero net torque the positions of the cell cores are optimized for the hs2 nuvel1 euler poles by a method of successive approximation subplex convergence to one of many local minima occurred typically after 20 000 iterations cell cores associated with the fourteen hs2 nuvel1 euler poles converge to a relatively small number of locations 8 to 10 depending on interpretation irrespective of the number of convection cells submitted for optimized distribution from 6 to 50 these locations are correlated with low seismic propagation velocities in tomography uniformly occur within hotspot provinces and may specifically be associated with the hawaiian iceland reunion kerguelen indian ocean easter island melanesia society islands south pacific azores cape verde canary islands tristan da cunha south atlantic balleny islands and possibly yellowstone hotspots it is shown that arbitrary euler poles cannot occur in association with mantle benard convection irrespective of the number and the distribution of convection cells nevertheless eight of the observational euler poles including the five that are accurately determined in hs2 nuvel1 australia cocos juan de fuca pacific and philippine are benard valid i e can be explained by our benard model five of the remaining six observational poles must be relocated within their error ellipses to become benard valid the eurasia pole alone appears to be in error by 115 and may actually lie near 40 n 154 e the collective results strongly suggest benard like mantle convection cells and that basal shear tractions are the primary factor in determining the directions of the plate motions as given by the euler poles the magnitudes of the computed euler vectors show however that basal shear cannot be the exclusive driving force of plate tectonics and suggest force contributions of comparable magnitude for perhaps half of the plates from the lithosphere itself specifically subducting slab pull and continental collision drag which are provisionally evaluated the relationship of the putative mantle benard polygons to dynamic chaos and turbulent flow is discussed

the effect of depth dependent viscosity on convective mixing in the mantle and the possible survival of primitive mantle the effect depth dependent viscosity has on convective mixing and sampling or degassing of primitive mantle beneath ridges is explored in two dimensional models higher relative viscosities in the deep mantle decrease convection velocities and strain rates and prolong the residence time of material in the deep mantle if the average viscosity of the lower mantle is at least 100 times the viscosity of the upper mantle then some mantle material could have survived from very early in the earth s history if in addition the depth of degassing under ridges has been less than 75 km on average over earth history then helium isotopic systematics are qualitatively consistent with whole mantle convection

effect of a low viscosity layer on long wavelength topography upper mantle case numerical models of upper mantle convection incorporating both plates and a substantial low viscosity layer show that long wavelength topography is only moderately reduced compared with a model without the low viscosity layer in particular topography due to hot upwelling from a putative hot boundary layer at 670 km depth is still large in the case of a migrating spreading center the symmetry and square root of age dependence of seafloor topography would be destroyed these results strengthen the case against mantle models in which heat transport across the 670 km seismic discontinuity is predominantly by conduction a substantial mass flux through 670 km is implied

the origin of large scale structure in mantle convection effects of plate motions and viscosity stratification convection in earth close quote s mantle is dominated by long wavelength structure as evidenced by the very open quote open quote red close quote close quote spectra of both seismic velocity heterogeneity in the deep mantle and the non hydrostatic gravity field or geoid here we show that this large scale structure may be a consequence of two factors that influence the scale of mantle convection first the existence of surface plates which tend to organize the flow second a substantial increase in lower mantle viscosity for which there is considerable independent geophysical evidence combining these two factors in 3 d spherical mantle convection models explains rather well the observed seismic spectrum of mantle heterogeneity copyright american geophysical union 1996

on the separation of relatively buoyant components from subducted lithosphere subducted oceanic lithosphere consists of a sandwich of component layers morb underlain by depleted parent mantle these layers give rise to intrinsic density contrasts within the slab which have been hypothesized to cause component separation after subduction we explore this process through numerical models of simple layered slabs and through convection models which incorporate large local chemical density contrasts we show that the components of positive and negative buoyancy density contrast component volume must be almost equal in order to cause significant component separation or to selectively block deep penetration of buoyant slab components in the transition zone published petrological constraints on component densities and relative volumes indicate that such buoyancy neutralization is not achieved in subducted slabs therefore component separation should not occur on the timescale associated with the sinking of slabs through the upper mantle and transition zone

steady plumes produced by downwellings in earth like vigor spherical whole mantle convection models if mantle thermal upwellings plumes are the cause of volcanic hot spots then observations suggest that plumes are relatively fixed with nonuniform distribution and limited lifetimes to date fixity of upwellings has only been shown in models of convection at either low vigor or with layering though studies where the lower mantle has high viscosity do frequently show upwellings with much lower drift velocities than the surface velocity since more vigorous convection traditionally shows more time dependence fixity of upwellings has not been expected for nonlayered convection at earth like vigor rather we might expect slow but increasing drift velocities i have undertaken numerical models of whole mantle convection in three dimensional spherical geometry at approaching earth like vigor surprisingly these simulations show prominent steady virtually fixed plumes arising from self organization controlled by the smaller but numerous cold downwellings if downwelling subduction dominates earth s interior dynamics then this work suggests that plume fixity need not require layering the regular spacing and permanence of model upwellings contrast with observations of hot spots though in these models which do not simulate plates the fixity and regular spacing result from the freedom of downwellings to occur everywhere except where plumes reach the surface i suggest that on earth this feedback is weakened by the presence of plates but that whole mantle thermal convection can still produce relatively fixed plumes though we might expect them to be weaker more mobile and transient

dynamical and thermal structure of a subduction zone influence of slab geometry on the convective state of the earth s upper mantle preliminary results received 29 march 1996 accepted 3 july 1996 abstract the aim of this study is to investigate the influences of plate kinematics and of the downgoing slab s geometry on internal dynamics and thermal structure in the vicinity of a subduction zone a systematic study depending on these parameters has been carried out based on a two dimensional finite differences code in a convective domain representing the upper mantle plate displacements are prescribed by kinematic boundary conditions in particular the subducting plate moves and dips at a constant velocity under the slower overriding one typical subduction dips 30 45 and 70 have been studied for a realistic rayleigh number of about l05 and for plate velocities around a coupling velocity of 2 3 cm year 1 this limit value was inferred from the balance between surface forces and buoyancy forces for any subduction dip and plate velocities lower than this coupling velocity plate kinematics variations induce significant effects on thermal and mineralogical patterns at greater plate velocities these patterns stabilize for plate velocities of the order of the coupling velocity a subduction dip decrease of 40 involves a heating of the downgoing plate of 100degrees and a depth increase of 20 km of the olivine spinel phase transition in this plate in the particular case of a non moving overriding plate the balance between this plate and underlying internal dynamics requires a moving plate velocity lower than 2 3 cm year j for a lower dip moreover a shallow subduction enhances a lateral large scale convection under the upper plate even if this plate is motionless in contrast to the case of a steep subduction this is consistent with observed back arc extension at the surface which is often associated with steep subductions our model suggests a spreading zone of between 500 and 1000km in the upper plate for a subduction velocity lower than 2 3 cm year i and a rayleigh number of about l05 1 introduction the earth s mantle undergoes a rayleigh benard thermal convection coupled to oceanic lithospheric plate movements rigid and moving lithospheric corresponding author plates form the thermal and mechanical limit bound aries of the earth s mantle convection cells one of the concerns of numerical modelling is to account for a real dynamic convection model coupled to plate tectonics to force the movement of rigid plates one may either model a dynamic plate by prescribing a lower viscosity at plate margins or impose the horizontal surface velocity davies 1989 0031 9201 97 17 00 copyright 1997 elsevier science b v all rights reserved ph s0031 9201 96 03209 8

effects of multiple phase transitions in a three dimensional spherical model of convection in earth s mantle numerical models of mantle convection that incorporate the major mantle phase changes of the transition zone reveal an inherently three dimensional flow pattern with cylindrical features and linear features that behave differently in their ability to penetrate the 670 km discontinuity the dynamics are dominated by accumulation of cold linear downwellings into rounded pools above the endothermic phase change at 670 km depth resulting in frequent avalanches of upper mantle material into the lower mantle the effect of the exothermic phase transition at 400 km depth is to reduce the overall degree of layering by pushing material through the 670 km phase change resulting in smaller and more frequent avalanches and a wider range of morphologies large quantities of avalanched cold material accumulate above the coremantle boundary cmb resulting in a region of strongly depressed mean temperature at the base of the mantle the 670 km phase change has a strong effect on the temperature field with three distinct regions being visible 1 the upper mantle containing linear downwellings and pools of cold material in the transition zone and characterized by a high amplitude long wavelength spectrum 2 the midmantle containing quasi cylindrical avalanche conduits and characterized by a low amplitude broad spectrum and 3 the deep mantle containing large pools of cold avalanched material and characterized by a high amplitude ultra red i e long wavelength spectrum the effect on the velocity field is very different flow penetration across the 670 km phase change is strongly wavelength dependent with easy penetration at long wavelengths but strong inhibition at short wavelengths thus when comparing numerical models with long wavelength seismic tomography diagnostics based on the density field such as the radial correlation function are much more sensitive to the effects of phase transitions than those based on the velocity field the amplitude of the geoid is not significantly affected by the partial layering because the contribution from the strong heterogeneity in the transition zone is almost perfectly balanced by the contribution from deflection of the 670 km discontinuity avalanches are associated with geoid lows however a more complex viscosity structure is required to correctly match the sign of the geoid over slabs in earth

mantle convection as a boundary layer phenomenon summary the boundary layer nature of vigorous thermal convection is explored using high resolution numerical solutions to the governing hydrodynamic equations these solutions are obtained for a series of idealized models of the earth s mantle in which the viscosity is assumed to be constant a detailed analysis of the local energy balance within the horizontal and vertical thermal boundary layers is presented in terms of which a test of the fundamental assumptions of boundary layer theory is provided the results of this test have important geophysical consequences since the asymptotic predictions of boundary layer theory have been employed extensively in the context of thermal history modelling although boundary layer theory closely predicts the correct power law behaviour of various quantities it does not determine their absolute values accurately vertical advection is shown to play an important role in the energy balance within horizontal boundary layers at all rayleigh numbers horizontal and vertical advection dominate the energy balance within vertical plumes while horizontal diffusion plays a very minor role when heating is partially from within the fluid vertical advection into the upper thermal boundary layer can produce significant departures in the thermal structure from that found when heating is entirely from below for a free upper boundary this results in a relative flattening of the variations of surface topography and heat flow across the convection cells for a constant velocity upper boundary similar to plate motion the bathymetry flattens but the heat flow does not this result agrees with marine observations rigidity of the thermal boundary layer below the upper surface is not included explicitly in the model and it is not known whether the inclusion of this feature in future models would significantly alter the topographic expression if not the observed departure of the oceanic bathymetry from a 6 dependence at old ocean floor ages could be attributed to a small amount of internal heating in a mantle wide convective circulation

thermal origin of the hawaiian swell heat flow evidence and thermal models the lithospheric reheating hypothesis for the origin of the hawaiian swell has been tested by heat flow measurements along the swell between hawaii and midway ninety five measurements at eight carefully selected sites show that the heat flux on the swell increases systematically from near normal values 52 2 mw m 2 near hawaii to values near midway 59 2 mw m 2 about 20 25 higher than normal for lithosphere of that age 110 m y this heat flow pattern is qualitatively consistent with a deep seated thermal anomaly created in a lithospheric plate moving across a fixed heat source modeling of the heat flow and bathymetry data on the hawaiian swell strongly suggest that the swell is caused by a rapid heating within 40 to 50 km depth of normal 90 m y old lithosphere over a relatively broad 500 1000 km region near hawaii this model is also consistent with gravity and geoid anomalies associated with the swell which require a low density region in the lower lithosphere and with flexure studies of seamounts in the hawaiian chain which indicate that the rigidity of the lithosphere is not significantly reduced by the reheating appendices a c are available with entire article on microfiche order from american geophysical union 2000 florida avenue n w washington d c 20009 document j82 005 1 00 payment must accompany order

stirring and mixing in the mantle by plate scale flow large persistent blobs and long tendrils coexist the stirring of a small passive heterogeneity in an unsteady circulation is investigated by following the boundary of the heterogeneity the circulation mimics features of plate scale flow after initial release the heterogeneity is stirred and subsequently consists of at least one large blob connected to long but thin tendrils tendrils exponentially lengthen and exponentially thin with time as predicted by a turbulent mixing law but the width of blobs decays about 100 times more slowly the blobs mix slowly because they are smaller than the scale of flow and are sheared and occasionally unmixed by the laminar flow within the interiors of convection cells the decay time of 1 to 100 km sized heterogeneities is on the order of billions of years for whole mantle convection and thus is in accord with isotopic observations which indicate the mantle has chemical heterogeneities persisting for billions of years

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

convection beneath young oceanic lithosphere implications for thermal structure and gravity small scale convection under the oceanic lithosphere which begins in the first 5 m y of cooling can produce a gravity signal with the amplitude and wavelength observed for large areas of the central pacific and southern indian oceans using seasat altimeter data the trend of the observed anomalies is parallel to the direction of plate motion as might be expected if they were produced by small scale convection models predict that the wavelengths of gravity anomalies increase more rapidly with age than is observed the persistence of short relatively uniform wavelength anomalies 200 km to crustal ages of 50 ma may indicate that they were produced when the lithosphere was very young and thin and were frozen in as cooling thickened the elastic lithosphere small scale convection which begins under very young lithosphere does not violate other geophysical data such as the rate of seafloor subsidence and variations of geoid height with age after convection has begun the subsidence due to thermal contraction within the lithosphere varies linearly with age in the absence of mantle heat sources although the rate of change of these quantities is affected by convection much of the variation of the geoid height across fracture zones can be fit by a model which includes small scale convection

an independent test of thermal subsidence and asthenosphere flow beneath the argentine basin abstract we have used primary precision depth recorder and single channel seismic data from three cruises of the r v conrad to test thermal subsidence and asthenosphere flow models for seafloor depth versus age in the argentine basin in the western south atlantic we found a region in the west central part of the basin where anomalously shallow depths that can not be explained by any simple thermal or dynamic model are associated with a local free air gravity anomaly elsewhere over ages ranging from 1 to 104 ma there is no evidence of the flattening of the depth age trend that is characteristic of the plate cooling model for the thermal subsidence of the oceanic lithosphere the halfspace thermal subsidence model accounts for nearly 98 of the variance of seafloor depth but the slope b 425 10 m ma 1 2 implies improbably high mantle temperatures and or low mantle densities moreover there is some systematic misfit between the data and the halfspace model a thermal subsidence model in which initial conditions vary with age accounts for the misfit but also requires an implausible variation of mantle temperature and or density alternatively a model that includes the effect of induced flow in the asthenosphere eliminates the misfit and yields a reasonable rate of thermal subsidence b 330 20 m ma 1 2 that the mantle temperature t m 1150 70 c implied by the subsidence rate is slightly lower than normal is consistent with the hypothesis that this region has not been affected by hot spots or mantle plumes the viscosity of the asthenosphere derived from the model 3 4 10 19 pa s is high but consistent with viscosities estimated from plate dynamics models when the low mantle temperature is taken into account finally the pms flow model is consistent with measured heat flow in the region these results lend weight to the hypothesis that the bathymetry of the argentine basin is influenced by induced flow in the asthenosphere as well as by halfspace cooling of the upper mantle

flattening of the oceanic topography and geoid thermal versus dynamic origin summary the origin of the flattening of the seafloor bathymetry and geoid at old ages is still a matter of debate is this departure from the square root of age law induced by dynamic uplift of the lithosphere linked to the flow in the mantle or by cooling of the lithosphere different from that predicted for an infinite half space the amplitude of the dynamic uplift should strongly decrease at short wavelengths and should not be correlated with the seafloor age on a local scale therefore in order to eliminate the dynamic signal the cooling of the lithosphere is studied here by means of depth age and geoid age relationships computed from high pass filtered bathymetric geoid and age fields or from local dtopography d and dgeoid dage slopes the geoid age and depth age relationships obtained here are in good agreement with those previously deduced from global non filtered data at all observation scales a significant departure from the half space solution is found however the data are not sufficiently accurate to discriminate between the plate and chablis constant heat flow at the base of the lithospheric isotherm models our results support the existence of small scale convection supplying heat at the base of the old oceanic lithosphere

ocean bathymetry and mantle convection 2 small scale flow numerical models demonstrate that a boundary layer instability of the lower lithosphere does not stop the lithosphere from subsiding and so it cannot explain the so called flattening of old seafloor the slower subsidence of the old seafloor is in any case better seen as a perturbation probably due to plumes furthermore if a boundary layer instability or any mode of upper mantle convection transported most of the heat emerging from old seafloor there would be pervasive large amplitude local bathymetrie gravity and geoid anomalies such anomalies have never been convincingly differentiated from the effects of the cooling lithosphere and hotspot tracks except for some low amplitude linear geoid anomalies near spreading centers the only modes of mantle convection with horizontal scales less than those of plates for which there is reasonably clear evidence are hotspot plumes and some possible near ridge boundary layer instabilities hotspots transport less than about 10 of the earth s heat flux and other small scale modes are probably less important

seasat gravity undulations in the central indian ocean abstract in the southeast indian ocean geoid and gravity maps derived from the geos3 and seasat satellites data show clear evidence of a lineated pattern located between the southeast indian ridge and the southern branch of the ninetyeast ridge we have carried out two dimensional spectral analyses of the gravity data over four regions each of 10 sx 10 dimension three being located over the indo australian plate one over the antarctica plate we have also analysed 13 seasat geoid height profiles roughly parallel to the southeast indian ridge covering both sides of the ridge power spectra of the gravity and geoid data over the indo australian plate confirm the existence of undulations oriented n40 e of 200 km wavelength and of 10 mgal and 40 ma the wavelength remains constant with increasing plate age such undulations are not seen west of the southeast indian ridge i e over the antarctica plate where observed the geoid undulations have a sinusoidal signature quite different from the typical step like signature of fracture zones the lineations observed in the southeast indian ocean have characteristics comparable to those reported by haxby and weissel in the central pacific and interpreted as evidence of small scale convection occurring in a low viscosity layer just beneath the lithosphere

subducted slabs and the geoid constraints on mantle rheology and flow geoid anomalies are primarily the result of the density contrasts driving mantle convection and plate motion the total geoid anomaly resulting from a given density contrast in a convecting earth is affected by the mass anomalies associated with the flow induced deformation of the upper surface and internal compositional boundaries as well as by the density contrast itself these boundary deformations and hence the total gravity field depend on the radial distribution of effective viscosity if the internal density contrasts can be estimated as is the case for subducted slabs useful constraints can be placed on the depth and on the variation of viscosity with depth of the convecting system the degree 4 9 components of the observed long wavelength geoid are highly correlated with those predicted by a density model for seismically active subducted slabs the positive sign of the correlation requires that the effective viscosity increases with depth by a factor of 30 or more the amplitude of the correlation cannot be explained by the density contrasts associated with just the seismically active parts of subducted slabs however the amplitude can be explained if the density contrasts associated with subduction extend into the lower mantle or if old lithosphere is piled up at the base of the upper mantle beneath subduction zones to a thickness in excess of 350 km over horizontal distances of thousands of kilometers mantlewide convection in a mantle that has a viscosity increasing with depth provides a simple explanation of the long wavelength geoid anomalies over subduction zones

degree one mantle convection dependence on internal heating and temperature dependent rheology 1 geophysical and geological observations suggest that a degree one mantle flow pattern consisting of one upwelling and one downwelling may have existed at some time in the mantles of mars the moon and perhaps even for the earth during times of supercontinent formation simple fluid experiments utilizing isoviscous rheologies predict shorter wavelength flow patterns and it is therefore important to determine fluid dynamical parameter sets which lead to larger wavelength flow patterns consistent with observations we perform a series of numerical fluid dynamics calculations in a spherical 3 d geometry in which we vary rayleigh number rheological activation parameter and the degree of internal heating in order to define which parameter choices can lead to degree one mantle convection we find that increasing the degree of internal heating increases the interior temperature of the mantle which leads to a larger viscosity contrast across the top thermal boundary layer and that degree one mantle flow occurs only in cases which exhibit internal heating utilize activation coefficients which lead to 103 or higher viscosity contrasts across the mantle and have viscosity contrasts across the top thermal boundary layer within the range of 200 3000

comment on mixing by time dependent convection by u christensen commentaire et reponse concernant l article de u christensen earth planet sci lett 95 382 394 1989

evidence for small scale mantle convection from seasat altimeter data evidence for the early development of convective instability in the thermal boundary layer associated with cooling plates has been found from gravity anomalies and residual sea surface heights derived from seasat altimeter data subtle lineated patterns trending in the direction of plate motion in the hot spot reference frame are observed over the younger portions of the fast moving pacific and indo australian plates in particular for the east central pacific ocean the seasat derived data sets reveal lineations with 1 wavelengths in the range 150 500 km perhaps increasing with plate age and 2 peak to trough amplitudes of 5 20 mgal for gravity anomalies the lineated pattern over the pacific plate which first becomes discernable over seafloor 5 to 10 m y old west of the east pacific rise is clearly oblique to the trends of the prominent pacific farallon fracture zones onset of convective instability at such early ages can be understood if young oceanic lithosphere is underlain by a layer having a viscosity of about 1018 pa s 1019 p which is about 3 orders of magnitude less than mantle viscosity inferred from postglacial rebound studies recent numerical studies of convection in fluids with a temperature and pressuredependent viscosity support an early onset time for convective instability and low viscosity zones in the upper mantle beneath young lithosphere such low viscosity zones may correspond to similarly located regions of low shear wave velocities resolved through studies of surface waves

tomography the geoid and plate motions the dynamics of the earth s mantle and its relationship to mantle structure as revealed by seismic tomography the geoid and plate motions are discussed in a critical review of u s research from the period 1987 1990 sections are devoted to plates and mantle convection seismic anomalies flow and the geoid subducted slabs and the 670 km discontinuity the physical properties of the mantle plumes and computational and experimental modeling efforts also included is a comprehensive bibliography for the period 248 refs

continental collisions in wide aspect ratio and high rayleigh number two dimensional mantle convection models distinct rigidly moving oceanic and continental plates of finite thickness are incorporated into a two dimensional numerical model of mantle convection we investigate upper mantle convection in models having aspect ratios as great as 24 and compare our findings with the results of earlier studies which were limited to aspect ratio 4 models in addition we implement models of whole mantle flow by specifying high rayleigh number convection and thinner nondimensional plates we are thus able to compare the results of continental collision models which include similarly sized continents in the cases of upper and whole mantle convection for each case considered we model a pair of identical continents being carried toward a site of plate convergence by underlying counterrotating mantle convection cells upon collision the continents form a motionless rigid model supercontinent while oceanic plate material continues to recycle through the mantle following the continental collision our models of upper mantle convection exhibit a reorganization of the convective planform below the model supercontinent into a smaller wavelength mode which is unable to generate the net stress needed to break apart the continent alternating compressive and tensile deviatoric stress associated with the small scale flow results in a low integrated stress in contrast the large scale of whole mantle convection enables flow reversals to produce shear stresses acting in a common direction over extensive areas of the base of a continent the integrated effect of which is capable of causing continental rifting the conventional view of the role of thermal blanketing in continental rifting does not apply in the whole mantle convection scenario

how valid are dynamic models of subduction and convection when plate motions are prescribed a detailed comparison between fully dynamic and kinematic plate formulations has been made in models of mantle convection plate velocity is computed self consistently from fully dynamic plate models with temperature and stress dependent viscosity and preexisting mobile faults in fully dynamic models the flow is driven solely by internal buoyancy while in kinematic models the flow is driven by a combination of the prescribed surface velocity and internal buoyancy only a temperature dependent viscosity close to the effective viscosity determined from the fully dynamic models is used in the kinematic models the two types of models give very similar temperature structures and slab evolutionary histories when the effective viscosity and surface velocity are nearly identical in kinematic plate models the additional work introduced by the prescribed velocity boundary condition is apparently dissipated within the lithosphere and has little influence on the convection under the lithosphere in models with periodic lateral boundary conditions slabs sink into the lower mantle at an oblique angle and this contrasts with the vertical sinking which occurs with reflecting boundary conditions models show that we can simulate fully dynamic models with kinematic models under either periodic boundary conditions or reflecting boundary conditions

sand transport under combined current and wave conditions a semi unsteady practical model for the general purposes of morphodynamic computations in coastal zones simple formula based models are usually employed to evaluate sediment transport sediment transport rates are computed as a function of the bottom shear stress or the near bed flow velocity and it is generally assumed that the sediment particles react immediately to changes in flow conditions it has been recognized through recent laboratory experiments in both rippled and plane bed sheet flow conditions that sediment reacts to the flow in a complex manner involving non steady processes resulting from memory and settling entrainment delay effects these processes may be important in the cross shore direction where sediment transport is mainly caused by the oscillatory motions induced by surface short gravity waves the aim of the present work is to develop a semi unsteady practical model to predict the total bed load and suspended load sediment transport rates in wave or combined wave current flow conditions that are characteristic of the coastal zone the unsteady effects are reproduced indirectly by taking into account the delayed settling of sediment particles the net sediment transport rates are computed from the total bottom shear stress and the model takes into account the velocity and acceleration asymmetries of the waves as they propagate towards the shore a comparison has been carried out between the computed net sediment transport rates with a large data set of experimental results for different flow conditions wave current flows purely oscillatory flow skewed waves and steady currents in different regimes plane bed and rippled bed with fine medium and coarse uniform sand the numerical results obtained are reasonably accurate within a factor of 2 based on this analysis the limits and validity of the present formulation are discussed

large aspect ratio convection cells in the upper mantle summary numerical experiments which model a possible large scale flow in the upper mantle are described the lithospheric plates are represented by a constant velocity boundary condition on the upper surface of a twodimensional convecting layer the transition from small scale multiple cell flow to single cell flow is described in terms of the rayleigh number and the peclet number the mean flow field is successfully compared with a simple parameterized model in which flow is driven by the moving upper boundary and by a mean horizontal temperature gradient which must be present in any large aspect ratio cell bathymetry and gravity profiles are calculated for the long cells and it is shown that in the absence of a low viscosity zone a realistic variation of bathymetry and gravity is only obtained if the flow in the cell is being driven predominantly by the horizontal temperature gradient rather than the moving plate mean horizontal temperature gradients in the upper mantle of 0 025 c km are suggested beneath a fast moving plate such as the pacific transverse boundary layer instabilities in the large cells are shown to be governed by a critical boundary layer rayleigh number which linearly increases with the boundary layer pcclet number

mantle convection under simulated plates effects of heating modes and ridge and trench migration and implications for the core mantle boundary bathymetry the geoid and benioff zones summary numerical convection models are presented in which plates are simulated by imposing piecewise constant horizontal velocities on the upper boundary a 4 1 box of constant viscosity fluid and two dimensional 2 d flow is assumed four heating modes are compared the four combinations of internal or bottom heating and prescribed bottom temperature or heat flux the case with internal heating and an isothermal base is relevant to lower mantle or whole mantle convection and it yields a lower thermal boundary layer which is laterally variable and can be locally reversed corresponding to heat flowing back into the core locally when scaled to the whole mantle the surface deflections and gravity and geoid perturbations calculated from the models are comparable to those observed at the earth s surface for models with migrating ridges and trenches the flow structure lags well behind the changing surface plate configurations this may help to explain the poor correlation between the main geoid features and plate boundaries trench migration substantially affects the dip of the cool descending fluid because of induced horizontal shear in the vicinity of the trench such shear is small for whole mantle convection but is large for upper mantle convection and would probably result in the tonga benioff zone dipping to the se opposite to the observed dip for the case of upper mantle convection

lagging mantle convection the geoid and mantle structure abstract in numerical models of convection incorporating migration of a simulated subduction zone the main descending flow lags far behind the migrating trench and a geoid low is associated with the main descending flow this provides physical plausibility for the suggestion by chase and sprowl that present very long wavelength degree 2 4 geoid lows are associated with mesozoic trench locations and suggests further that the present long wavelength geoid deep mantle structure and hotspot distribution may be straightforward consequences of plate evolution since the upper paleozoic

residual geoid anomalies in atlantic ocean basin relationship to mantle plumes the relations of geoid data from radar altimeter measurements geos 3 to water depth and geochemical variations along the mid atlantic ridge are investigated eight geophysical lines across the ridge in the atlantic ocean were constructed approximately normal to the local ridge trend slopes of geoid per kilometer of topographic relief show an asymmetry between the two sides of the ridge that generally is not matched by topography which has better symmetry between the two flanks subtracting a regional field based on previous work produces residual geoid anomalies whose source must be in the earth s outer 600 km the residual geoid anomalies of the north atlantic show striking correlation with the axis of the mid atlantic ridge but those in the south atlantic do not instead major positive residual geoid anomalies appear over the rio grande and walvis ridges determination of slope s residual geoid per million years crustal age reveals that s increases with greater residual geoid anomaly and with higher shallower crestal ridge topography the slope of 22 cm m y west of the azores high near 38 n suggests that the anomalously high crestal residual geoid and depth anomalies may not be entirely of thermal origin which may normally produce slopes only of about 8 cm m y as found near 28 n away from shallow ridge topography to account for this difference in slopes simply by a variation in mantle temperature would require a difference of about 940 c between the two sites which appears excessive also the decrease in topographic height with crustal age away from the azores high is much greater than predicted by theoretical cooling curves correlation of residual geoid anomalies with depth geochemical variations along the length of the mid atlantic ridge and the chemistry of the rio grande rise and walvis ridge suggest that many regions of anomalous residual geoid and crestal depth values may be in large part a function of crustal thickness and density variations induced by plume intrusion and volcanism in addition to their transient thermal effects

the role of water in the deformation of dunite specimens of two natural dunites anita bay of 100 m grain size and aheirn of 900 m grain size have been deformed in experiments at temperatures between 1200 and 1400 c and constant strain rates between 10 4 and 10 6 s 1 in a gas medium deformation apparatus at 300 mpa confining pressure prior to these experiments the specimens were given a heat treatment in a controlled oxygen fugacity furnace at 1200 c for 60 hours to dehydrate the trace layer silicate minerals present and drive off adsorbed water the predried specimens are much stronger than specimens tested under wet conditions in an earlier study the predried specimens also do not show the apparent grain size dependence seen under wet conditions infrared absorption measurements on the present specimens and those of the earlier study indicate that for a given rock flow stress can be correlated with the intensity of a residual water related broad absorption the addition of water to a predried specimen results in both a mechanical reweakening and an intensifying of the broadband infrared component the weakening of the dunites under wet conditions is probably strongly influenced by the presence of small amounts of a water related species in the grain boundaries but intragranular weakening may also be contributing it is suggested that the concentration of the water related species in the grain boundaries is governed by its concentration in the small melt fraction present the amounts of water that have been found to be of importance for the strength of these dunites are of the order of 0 01 wt amounts much less than most estimates of the water content of the earth s undepleted upper mantle such water may have an important role in determining upper mantle flow behavior stress strain curves for all experiments are available with entire manuscript on microfiche order from american geophysical union 2000 florida avenue n w washington dc 20009 document b84 008 2 50 payment must accompany order

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

effects of plate and slab viscosities on the geoid abstract the effects of plate rheology strong plate interiors and weak plate margins and stiff subducted lithosphere slabs on the geoid and plate motions considered jointly are examined with three dimensional spherical models of mantle flow buoyancy forces are based on the internal distribution of subducted lithosphere estimated from the last 160 ma of subduction history while the ratio of the lower mantle upper mantle viscosity has a strong effect on the long wavelength geoid as has been shown before we find that plate rheology is also significant and that its inclusion yields a better geoid model while simultaneously reproducing basic features of observed plate motion slab viscosity can strongly affect the geoid depending on whether a slab is coupled to the surface in particular deep high viscosity slabs beneath the northern pacific that are disconnected from the surface as a result of subduction history produce significant long wavelength geoid highs that differ from the observation this suggests that slabs in the lower mantle may be not as stiff as predicted from a simple thermally activated rheology if the slab model is accurate

geoid anomalies in a dynamic earth in order to obtain a dynamically consistent relationship between the geoid and the earth s response to internal buoyancy forces we have calculated potential and surface deformation love numbers for internal loading these quantities depend on the depth and harmonic degree of loading they can be integrated as green functions to obtain the dynamic response due to an arbitrary distribution of internal density contrasts spherically symmetric self gravitating flow models are constructed for a variety of radial newtonian viscosity variations and flow configurations including both whole mantle and layered convection we demonstrate that boundary deformation due to internal loading reaches its equilibrium value on the same time scale as postglacial rebound much less than the time scale for significant change in the convective flow pattern by calculating relaxation times for a series of spherically symmetric viscous earth models for uniform mantle viscosity the geoid signature due to boundary deformations is larger than that due to internal loads resulting in net negative geoid anomalies for positive density contrasts geoid anomalies from intermediate wavelength density contrasts are amplified by up to an order of magnitude geoid anomalies are primarily the result of density contrasts in the interior of convecting layers density contrasts near layer boundaries are almost completely compensated layered mantle convection results in smaller geoid anomalies than mantle wide flow for a given density contrast viscosity stratification leads to more complicated spectral signatures because of the sensitivity of the dynamic response functions to model parameters forward models for the geoid can be used to combine several sources of geophysical data e g subducted slab locations seismic velocity anomalies surface topography to constrain better the structure and viscosity of the mantle

convection with internal heat sources and thermal turbulence in the earth s mantle summary the influence of internal heat sources on mantle convection is investigated using numerical calculations of 2 d thermal convection in an infinite prandtl number incompressible fluid the geometry is a cylindrical annulus with inner and outer radii in proportion to the whole mantle time dependent calculations are made starting from random initial conditions with rayleigh numbers rat based on boundary temperature difference and ra based on internal heat production in the range 1dsrats lo7 and osra 524rat at fixed rat increasing ra results in transitions in flow structure from steady cells to a pattern of stationary cells with time variable amplitude and finally to thermally turbulent convection with a non stationary cell count for rat 10 and ra rat approximately the travelling plumes disrupt the large scale circulation producing turbulent convection at ra lo7 the flow is fully developed thermal turbulence and for ra 0 consists of a rapidly fluctuating irregular flow driven by transient rising and sinking sheets of buoyant fluid large fluctuations in total kinetic energy occur in this regime with periodicities ranging from 40 to 1400myr the transition to thermal turbulence occurs in these calculations at rayleigh numbers well below the value estimated for subsolidus convection in the mantle suggesting thermally turbulent convection may occur in the mantle a consequence of internal heat sources thermal turbulence offers an explanation for long term fluctuations in the rate of subduction sea floor spreading and global volcanic activity