crustal structure of a transform plate boundary san francisco bay and the central california continental margin wide angle seismic data collected during the bay area seismic imaging experiment provide new glimpses of the deep structure of the san francisco bay area block and across the offshore continental margin san francisco bay is underlain by a veneer 300 m of sediments beneath which p wave velocities increase rapidly from 5 2 km s to 6 0 km s at 7 km depth consistent with rocks of the franciscan subduction assemblage the base of the franciscan at 15 18 km depth is marked by a strong wide angle reflector beneath which lies an 8 to 10 km thick lower crust with an average velocity of 6 75 0 15 km s the lower crust of the bay area block may be oceanic in origin but its structure and reflectivity indicate that it has been modified by shearing and or magmatic intrusion wide angle reflections define two layers within the lower crust with velocities of 6 4 6 6 km s and 6 9 7 3 km s prominent subhorizontal reflectivity observed at near vertical incidence resides principally in the lowermost layer the top of which corresponds to the 6 s reflector of brocher et al 1994 rheological modeling suggests that the lower crust beneath the 6 s reflector is the weakest part of the lithosphere the horizontal shear zone suggested by furlong et al 1989 to link the san andreas and hayward calaveras fault systems may actually be a broad zone of shear deformation occupying the lowermost crust a transect across the continental margin from the paleotrench to the hayward fault shows a deep crustal structure that is more complex than previously realized strong lateral variability in seismic velocity and wide angle reflectivity suggests that crustal composition changes across major transcurrent fault systems pacific oceanic crust extends 40 50 km landward of the paleotrench but contrary to prior models probably does not continue beneath the salinian block a cretaceous arc complex that lies west of the san andreas fault in the bay area the thickness 10 km and high lower crustal velocity of pacific oceanic crust suggest that it was underplated by magmatism associated with the nearby pioneer seamount the salinian block consists of a 15 km thick layer of velocity 6 0 6 2 km s overlying a 5 km thick high velocity 7 0 km s lower crust that may be oceanic crust cretaceous arc derived lower crust or a magmatically underplated layer the strong structural variability across the margin attests to the activity of strike slip faulting prior to and during development of the transcurrent pacific north american plate boundary around 29 ma

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

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

generation of long wavelength heterogeneity in the mantle by the dynamic interaction between plates and convection lateral variations in seismic velocity through its dependence on temperature can easily be generated at the gravest harmonics including degrees one and two by the dynamic interaction between plates and convection models of thermal convection with a single non subducting plate have been formulated in a cylindrical geometry plates of width one to four times times the thickness of the convecting region strongly modulate the flow by being pushed over cold downwellings and inhibiting cooling of the fluid beneath during rapid motion off of hot regions a large scale pattern of shear is developed causing small uprising limbs to be swept into the largest upwellings both insulation and plume plume collisions pump energy into the lower wavenumber harmonics

plume capture by divergent plate motions implications for the distribution of hotspots geochemistry of mid ocean ridge basalts and estimates of the heat flux at the core mantle boundary abstract the coexistence of stationary mantle plumes with plate scale flow is problematic in geodynamics we present results from laboratory experiments aimed at understanding the effects of an imposed large scale circulation on thermal convection at high rayleigh number 106 ra 109 in a fluid with a temperature dependent viscosity in a large tank a layer of corn syrup is heated from below while being stirred by large scale flow due to the opposing motions of a pair of conveyor belts immersed in the syrup at the top of the tank three regimes are observed depending on the ratio v of the imposed horizontal flow velocity to the rise velocity of plumes ascending from the hot boundary and on the ratio of the viscosity of the interior fluid to the viscosity of the hottest fluid in contact with the bottom boundary when v 1 and 1 large scale circulation has a negligible effect on convection and the heat flux is due to the formation and rise of randomly spaced plumes when v 10 and 100 plume formation is suppressed entirely and the heat flux is carried by a sheet like upwelling located in the center of the tank at intermediate v and depending on established plume conduits are advected along the bottom boundary and ascending plumes are focused towards the central upwelling heat transfer across the layer occurs through a combination of ascending plumes and large scale flow scaling analyses show that the bottom boundary layer thickness and in turn the basal heat flux q depend on the peclet number pe and when 10 q pe1 2 and when 1 q pe 1 3 consistent with classical scalings when applied to the earth our results suggest that plate driven mantle flow focuses ascending plumes towards upwellings in the central pacific and africa as well as into mid ocean ridges furthermore plumes may be captured by strong upwelling flow beneath fast spreading ridges this behavior may explain why hotspots are more abundant near slow spreading ridges than fast spreading ridges and may also explain some observed variations of mid ocean ridge basalt morb geochemistry with spreading rate moreover our results suggest that a potentially significant fraction of the core heat flux is due to plumes that are drawn into upwelling flows beneath ridges and not observed as hotspots

the influence of plate like surface motion on upwelling dynamics in numerical mantle convection models abstract tectonic plate geometry organises the planform of convection in the earth s mantle and is therefore expected to strongly influence mantle upwelling dynamics we present the findings from two and three dimensional mantle convection simulations with plate like surface motion and analyse how convective patterns and time dependence change as surface plate geometry is transformed from a simple configuration permitted in 2d experiments allowing only divergent and convergent plate boundaries into arrangements requiring three dimensional modelling our experiments model vigorous convection ra 107 based on the upper mantle viscosity in a stratified viscosity system featuring both internal and basal heating we first consider a suite of two dimensional experiments and determine an estimate for a uniform surface velocity that is comparable in magnitude to the mean transit time for the upwellings associated with the system we argue that a surface velocity that neither forces nor resists the convectively driven flow meets this requirement but show that temporally varying and constant plate velocities can both satisfy this condition over a given period of time with different results for the partially internally heated aspect ratio 4 cases considered here we choose a fixed velocity boundary condition and find this velocity is about 23 lower than the mean velocity obtained with a free slip surface condition in an otherwise identical model the plate velocity obtained from our two dimensional experiments is then adopted for our three dimensional calculations that include plates as plate geometry is systematically varied for the parameters specified in our study which result in a basal heat flux of approximately 50 the surface value and a viscosity contrast of a factor of 30 between the upper and lower mantle steady plume like upwellings are present in both free slip and rigid surface calculations however a surface boundary condition featuring a pair of congruent plates moving in opposing directions with a velocity comparable to the plume transit time forces the convective planform into a roll like pattern featuring essentially sheet like upwellings positioned below the divergent plate boundary when plate geometries are specified in a way that produces offset segments of convergent and divergent boundary joined by boundaries characterised by strike slip motion the planform of the underlying convection organises into patterns featuring columnar plume like upwellings using calculations of upwelling advective heat flux to determine plume locations we track plume motion in the upper and lower mantle over periods of several plume rise times we show that long lived nearly stationary plumes appear in calculations featuring surface velocities comparable to the mean vertical velocity of the upwellings and that the associated plume heads remain positioned below intraplate positions for periods that can exceed tens of millions of years

hotspots mantle plumes and core heat loss abstract the heat flux at the core mantle boundary cmb is a key parameter for core dynamics since it controls its cooling however it is poorly known and estimates range from 2 tw to 10 tw the lowest bound comes from estimates of buoyancy fluxes of hotspots under two assumptions that they are surface expression of mantle plumes originating from the base of the mantle and that they are responsible for the totality of the heat flux at the cmb using a new procedure to detect plumes in a numerical model of rayleigh benard convection convection between isothermal horizontal planes with internal heating it is shown that many hot plumes that start from the bottom boundary do not reach the top surface and that the bottom heat flux is primarily controlled by the arrival of cold plumes hot plumes easily form at the bottom boundary but they are mostly due to the spreading of cold plume heads that allow the concentration of hot matter these plumes are generally not buoyant enough to cross the whole system and the hot plumes that reach the top surface result from an interaction between several hot plumes according to this simple dynamical behavior the heat flux at the bottom boundary is shown to be strongly correlated with the advection due to cold plumes and not with advection by hot plumes that arrive at the surface it is then inferred that the heat flux out of hotspots can only give a lower bound to the heat flow at the cmb and that knowing the advection by subducted plates would give a better estimate

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

the geoid constraint in global geodynamics viscosity structure mantle heterogeneity models and boundary conditions summary the earth s non hydrostatic gravity field or geoid provides a first order constraint on mantle density structure and dynamics geodynamic models for the geoid have proliferated since the advent of seismic mapping of mantle heterogeneity structure tomography because the geoid offers perhaps the best measured independent constraint on mantle density heterogeneity however dynamic geoid models involve a number of questionable physical assumptions and uncertainties whose effects need to be evaluated before geodynamic inferences based upon the geoid can be considered sound troubling issues include the appropriate surface boundary conditions free slip no slip plates and parametrization of radial viscosity variations how many layers can be resolved in addition to lateral viscosity variations possible chemical layering of the mantle phase transitions etc there are also uncertainties in the density heterogeneity models used as input to dynamic geoid models most of which are derived from seismic tomography and require weakly constrained empirical conversion factors to go from seismic velocity variations to density variations here we address several of the most straightforward problems inherent in geoid modelling namely the issues of viscosity structure resolution uncertainties in appropriate boundary conditions and differences among mantle heterogeneity models a robust feature of all models is a lower mantle viscosity at least a factor of 30 greater than that of the upper mantle but there is little resolution with regard to finer details such as lithospheric or uppermost mantle low viscosity zone viscosity ironically free slip boundary conditions result in the best fits to the geoid in all cases but all boundary conditions exhibit predictable trade offs with the uppermost mantle viscosity models with a single viscosity layer representing the lower mantle yield similar dynamic topography estimates of the order of 700 1000 m in amplitude regardless of the finer details of upper mantle viscosity structure boundary conditions or input heterogeneity models comparing mantle heterogeneity models based on two independent seismological determinations harvard and berkeley models and on the history of subduction we find that these models are virtually indistinguishable regarding inferences of mantle viscosity structure and amplitude of dynamic topography and in terms of the effects of different boundary conditions uncertainties concerning which type of boundary condition is appropriate are much more important than which mantle heterogeneity model is chosen given other uncertainties in modelling the geoid particularly the strong effects due to lateral viscosity variations for intermediate 10 000 km wavelengths we conclude that the class of dynamic geoid models explored so far cannot reliably elucidate the details of upper mantle viscosity structure

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

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

multiple scales in mantle convection abstract the multiple scales structure of mantle convection remains largely unknown a 3d model of convection is used to investigate the effect of a viscosity step on the multiple scales pattern of an infinite prandtl number convection for rayleigh numbers ra from 10 5 to 1 75 10 7 the planform of the large scale convection is polygonal and the ascending plumes are quite steady even for a rayleigh number of 1 75 10 7 when the rayleigh number exceeds a value of 3 10 5 the upper thermal boundary layer becomes unstable small scale instabilities appear away from the plume and they are advected by the large scale flow the pattern of these small scale flows evolves with the rayleigh number they form circular like waves centered on the axis of the plume for ra 10 6 an increase of the rayleigh number above ra 5 10 6 leads to the generation of cold drops inside the circular waves finally for ra 1 75 10 7 the circular waves disappear at some distance from the plume axis then the small scale flow consists of cold drops as they are advected by the large scale flow the cold drops mature inside cold radial gutters this superimposition of small scale instabilities on the large scale flow clearly results from the viscosity jump the implications of these models appear more straightforward in the case of venus than of the earth due to the absence of moving plates in the model the existence of small scale convection around the plumes could explain the presence of volcanoes in the plains around the equatorial highlands of venus

turbulent 3 d thermal convection in an infinite prandtl number volumetrically heated fluid implications for mantle dynamics summary the structure and time dependence of 3 d thermal convection in a volumetrically heated infinite prandtl number fluid is examined for high values of the rayleigh number the methods employed allow the numerical experiments to proceed for long enough times to derive good estimates of mean and fluctuating parts of the structure an iterative multirigid method to solve for the buoyant incompressible viscous flow at each time step of the energy equation is a novel aspect of the methodology a simple explicit time step of the energy equation is utilized that vectorizes well on serial computers and which is ideally suited to massively parallel computers numerical experiments were carried out for rayleigh numbers from 3 106 to 3 107 in a cartesian region with a prescribed temperature at the top boundary and an adiabatic bottom boundary over this complete range of rayleigh number the flow structure consists dominantly of cold nearly axisymmetric plumes that migrate horizontally sweeping off the cold thermal boundary layer that forms at the top of the convecting fluid plumes disappear by coalescing with other plumes new plumes are created by thermal boundary layer instability sheet plumes form only occasionally and do not penetrate to significant depths in the fluid plumes have sizes comparable to the thickness of the thermal boundary layer and an average spacing comparable to the fluid depth no persistent large scale motion in the fluid can be identified its absence may reflect the large subadiabatic stratification that develops beneath the thermal boundary layer as cold plumes penetrate to the bottom boundary without thermally equilibrating with surrounding fluid we consider the possible implications for convection in planetary mantles and for the existence of plate tectonics

dynamic feedback between a continentlike raft and thermal convection seismic observations of the mantle which include long wavelength structure a k 1 dependence of heterogeneity on harmonic k and a heterogeneous upper boundary layer and supercontinent kinematics may be explained by the dynamic interaction between a continent like raft and thermal convection we have formulated finite element models of convection with rafts simulating continental plates in a cylindrical geometry the azimuthal interconnectivity of this geometry is vital to resolve the two way dynamics between rafts and convection computations show that 1 raft motion is periodic 2 long wavelength thermal structure is significant within both thermal boundary layers and the fluid interior and 3 the large scale thermal structure with a wavelength longer than the width of raft is responsible for raft motion these three results which are observed for a range of rayleigh numbers internal heating rates and raft sizes are a direct consequence of the dynamic interaction between the raft and convection the physical processes for a model with a rayleigh number of 10 5 are representative when the raft is stationary due to the less efficient heat transfer through the raft and instabilities from the bottom boundary layer heat accumulates beneath the raft and results in long wavelength thermal anomalies the long wavelength thermal anomalies enhance raft motion accompanying the enhanced raft movement the long wavelength thermal anomalies diminish and the raft velocity decreases or the raft comes to rest since convection models without rafts generate less long wavelength heterogeneity compared to the models with rafts or continental plates we suspect that continental plates may play a crucial role in mantle dynamics interestingly raft motion with a period of about 10 transit times is usually significant 10 transit times is about 600 m y if scaled to the earth this is close to the observed 300 500 m y period of supercontinent aggregation and dispersal

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

mantle convection experiments with evolving plates we have performed numerical mantle convection experiments in an annulus with plates whose geometries evolve with time a thermally activated rheology results in a high viscosity surface boundary layer which is mobilized by weak zones small regions of low viscosity these weak zones are advected with the flow leading to evolving plates surface plates organize the mantle flow system resulting in large scale structures and a thermal angular power spectrum dominated by low angular degrees plate size and plate velocity distributions are used to characterize the system of surface plates these statistics are sensitive to the radial flow structure and provide a new way of evaluating convection models using reconstructions of earth s plate tectonic record a direct comparison of the results from our two dimensional 2d experiments to the plate tectonic record for the past 120 ma indicates that models with a 30 fold viscosity increase in the lower mantle are most consistent with these observational constraints while calculations with a strong endothermic phase change that leads to intermittently layered convection are least consistent with the plate tectonic record

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

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

the dependence of convection planform on mode of heating a fundamental property of a convecting fluid is its planform the distribution in the horizontal plane of hot rising regions and cold sinking regions for the earth s mantle the planform might he visualized as a map of subduction zones hotspots and possibly ocean ridges here i report numerical experiments of convection at high rayleigh number which show a strong dependence of planform on heating mode when heat generation is distributed uniformly through the box the preferred planform consists of an ensemble of time dependent cold axial sinkers distributed in a hot diffuse upward flow when half of the heat is generated within the box and the other half is input through the base the preferred planform consists of an array of hot axial plumes and elongated cold sheets in the former case the mean horizontal wavelength is about equal to the layer depth for the latter it is about twice the layer depth

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

geothermal heat flux from hydrothermal plumes on the juan de fuca ridge thesis m s massachusetts institute of technology dept of ocean engineering and woods hole oceanographic institution 1991

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

modulation of mantle plumes and heat flow at the core mantle boundary by plate scale flow results from laboratory experiments we report results from analog laboratory experiments in which a large scale flow is imposed upon natural convection from a hot boundary layer at the base of a large tank of corn syrup the experiments show that the subdivision of the convective flow into four regions provides a reasonable conceptual framework for interpreting the effects of large scale flow on plumes region i includes the area of the hot thermal boundary layer tbl that is thinned by the large scale flow thereby suppressing plumes region ii encompasses the critically unstable boundary layer where plumes form region iii is the area above the boundary layer that is devoid of plumes region iv comprises the area of hot upwelling and plume conduits quantitative analysis of our experiments results in a scaling law for heat flux from the hot boundary and for the spatial extent of plume suppression when applied to the earth s core mantle boundary cmb our results suggest that large scale mantle flow due to sinking lithospheric plates can locally thin the tbl and suppress plume formation over large fractions of the cmb approximately 30 of heat flow from the core may be due to increased heat flux from plate scale flow furthermore cmb heat flux is non uniformly distributed along the cmb with large areas where heat flux is increased on average by a factor of 2 as a consequence the convective flow pattern in the outer core may be affected by cmb heat flux heterogeneity and sensitive to changes in plate scale mantle flow becauseofplumesuppressionanddfocusingtofhotmantlefromthecmbintozonesofupwellingflow plumeconduits hotspots