incorporating self consistently calculated mineral physics into thermochemical mantle convection simulations in a 3 d spherical shell and its influence on seismic anomalies in earth s mantle 1 phase assemblages of mantle rocks calculated from the ratios of five oxides cao feo mgo al2o3 sio2 by free energy minimization were used to calculate the material properties density thermal expansivity specific heat capacity and seismic velocity as a function of temperature pressure and composition which were incorporated into a numerical thermochemical mantle convection model in a 3 d spherical shell the advantage of using such an approach is that thermodynamic parameters are included implicitly and self consistently obviating the need for ad hoc parameterizations of phase transitions which can be complex in regions such as the transition zone particularly if compositional variations are taken into account convective planforms for isochemical and thermochemical cases are however not much different from those computed using our previous simple parameterized reference state which means that our previous results are robust in this respect the spectrum and amplitude of seismic velocity anomalies obtained using the self consistently calculated material properties are more realistic than those obtained when seismic velocity is linearly dependent on temperature and composition because elastic properties are dependent on phase relationship of mantle minerals in other words pressure and temperature in all cases the spectra are dominated by long wavelengths spherical harmonic degree 1 to 2 similar or even longer wavelength than seismic tomographic models of earth which is probably due to self consistent plate tectonics and depth dependent viscosity in conclusion this combined approach of mantle convection and self consistently calculated mineral physics is a powerful and useful technique for predicting thermal chemical phase structures in earth s mantle however because of uncertainties in various parameters there are still some shortcomings in the treatment of the postperovskite phase transition additionally transport properties such as thermal conductivity and viscosity are not calculated by this treatment and are thus subject to the usual uncertainties

risk perception and volcanic hazard mitigation individual and social perspectives this paper discusses how people s interpretation of their experience of volcanic hazards and public volcanic hazard education programs influences their risk perception and whether or not they adopt measures that can mitigate their risk drawing on four studies of volcanic risk perception and preparedness the paper first examines why experiencing volcanic hazards need not necessarily motivate people to prepare for future volcanic crises this work introduces how effective risk communication requires communities and civic agencies to play complementary roles in the risk management process next the findings of a study evaluating the effectiveness of a public volcanic hazard education program introduce the important role that social interaction amongst community members plays in risk management building on the conclusions of these studies a model that depicts preparing as a social process is developed and tested the model predicts that it is the quality of the relationships between people communities and civic agencies that determines whether people adopt measures that can reduce their risk from volcanic hazard consequences the implications of the model for conceptualizing and delivering volcanic hazard public education programs in ways that accommodate these relationships is discussed

the combined effects of continents and the 660 km depth endothermic phase boundary on the thermal regime in the mantle abstract we explore a wide range of parameter space to investigate the dynamical interaction between effects due to surface boundary conditions representing continental and oceanic lithosphere and the endothermic phase boundary at 660 km depth in simple two dimensional convection calculations phase boundary induced mantle layering is strongly affected by the wavelength of convective flows and mixed surface boundary conditions strongly increase the horizontal wavelength of convection our study shows that for mixed cases the effects of the surface boundary conditions dominate the effects of the phase boundary we show that the calculations with complete continental coverage have the most significantly decoupled lower and upper mantle flows and substantial thermal and mechanical layering unlike the free slip case where the surface heat flow decreases substantially with increasing magnitude of the clapeyron slope surface heat flow is shown to be almost independent of the clapeyron slope for mixed boundary condition cases although very different when not layered models with free and mixed surfaces have very similar planforms with very large aspect ratio flows when run with large magnitudes of the clapeyron slope we also calculate the critical boundary layer rayleigh number as a measure of the thermal resistance of the surface boundary layer our results show that the thermal resistance in the oceanic and the continental regions of the mixed cases are similar to fully free and no slip cases respectively we find that even for purely basally heated models the mantle becomes significantly subadiabatic in the presence of partial continental coverage this is due to the significant horizontal advection of heat that occurs with very large aspect ratio convection cells

convection under a lid of finite conductivity in wide aspect ratio models effect of continents on the wavelength of mantle flow 1 mantle convection in the earth and mars are dominated by large scale flow and this can be due at least in part to the effect of thermally insulating continent like heterogeneities indeed the presence of a finitely conducting lid on top of a convective isoviscous fluid at infinite prandtl number induces the formation of a zone of hot upwelling centered beneath the lid and a large horizontal cellular circulation on each side of the lid in a previous paper this lateral cellular circulation was limited in size by the dimensions of the model we now use very large aspect ratio models in order for this circulation to be unhampered the large scale circulation consists of the constructive superposition of hot and cold plumes attracted to and expelled from respectively the conductive lid the width of the cellular circulation increases with the rayleigh number of the fluid and we propose a scaling law to explain this expansion scaling laws for the velocity of the plumes and heat transfer by this large scale circulation are also developed although the model used is much simpler than actual planetary mantles the driving mechanism for the large scale circulation must operate in a similar fashion important implications in terms of heat transfer can therefore be predicted

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

true polar wander in mantle convection models with multiple mobile continents a b s t r a c t a r t i c l e i n f o the geologic record supports numerous instances during which continents apparently moved at speeds signi cantly faster than any of today s tectonic plates while the time dependence of convective driving forces likely explains some such observations rapid motions of large continents in particular are often attributed to true polar wander tpw in order to gauge the potential for connections between continents mantle temperature anomalies and polar motion we present the rst calculations of tpw derived from models that couple mantle convection with multiple mobile continents we nd that the aggregation and dispersal of supercontinents can lead to two types of tpw driven either by a well developed hot upwelling axis that creates a stable maximum moment of inertia or by the homogenization of mantle thermal structure following continent dispersal that leads to destabilization of the principal axis and possible large magnitude polar wander these supercontinent modulated thermal heterogeneities drive model tpw events as large as 90 at rates of up to 2 5 ma 1 such magnitudes and speeds are greater than those attained in similar models lacking continents but comparable to those for episodes inferred from paleomagnetic data for some large continents in the past published by elsevier b v on behalf of international association for gondwana research

convective heat transfer as a function of wavelength implications for the cooling of the earth 1 attempting to reconstruct the thermal history of the earth from a geophysical point of view has for a long time been in disagreement with geochemical data the geophysical approach uses parameterized models of mantle cooling the rate of cooling of the earth at the beginning of its history obtained in these models is generally too rapid to allow a sufficient present day secular cooling rate geochemical estimates of radioactive element concentrations in the mantle then appear too low to explain the observed present mantle heat loss cooling models use scaling laws for the mean heat flux out of the mantle as a function of its rayleigh number of the form q ra b recent studies have introduced very low values of the exponent b which can help reduce the cooling rate of the mantle the present study instead focuses on the coefficient c in the relation q cr a b and in particular on its variation with the wavelength of convection the heat transfer strongly depends on the wavelength of convection the length scale of convection in earth s mantle is that of plate tectonics implying convective cells of wide aspect ratio taking into account the long wavelength of convection in earth s mantle can significantly reduce the efficiency of heat transfer the likely variations of this wavelength with the wilson cycle thus imply important variations of the heat flow out of the earth on a intermediate timescale of 100 ma which renders parameterized models of thermal evolution inaccurate for quantitative predictions

geodynamically consistent inferences on the uniform sampling of earth s paleomagnetic inclinations abstract paleomagnetism is a key method to reconstruct the earth s paleogeography and thus essential for understanding tectonic evolution but it assumes that the earth s magnetic field structure has always averaged to a geocentric axial dipole gad the gad hypothesis may be tested using the observed inclination frequency distribution but only if continents sampled all of the earth s latitudes uniformly which is not known here we provide new insight into the uniform sampling problem by employing a suite of 3d spherical mantle convection models that feature the self consistent evolution of mantle convection plate tectonics and continental drift over timescales of 2 gyr or more our results suggest that continents unlikely sampled latitudes uniformly during the phanerozoic consistent with previous suggestions this finding is robust for a variety of geodynamic evolutions with different mantle and lithosphere structures at least in the absence of true polar wander for longer sampling durations uniform sampling typically becomes more feasible but may only be achieved with confidence after time scales of minimum 1 3 gyr this time scale depends on the structure of the mantle and lithosphere and may be shortest when upper mantle viscosity is small such that reduced resistive drag at the cratonic base allows for faster continental drift weak plates low plastic yield strength promote more dispersed continent configurations which tends to facilitate uniform sampling if these conditions are not met the uniform sampling time scale can easily exceed several billion years even the minimum estimate of 1 3 gyr challenges the validity of using the phanerozoic inclination frequency distribution to infer the past average magnetic field structure the approach could however still be applicable using the precambrian inclination record

influence of initial cmb temperature and other parameters on the thermal evolution of earth s core resulting from thermochemical spherical mantle convection 1 here we present a wide ranging parameter study of the effects of initial core mantle boundary cmb temperature concentration of radioactive potassium in the core and density difference between harzburgite and mid ocean ridge basalt morb in a coupled spherical model of thermochemical mantle convection and parameterized core heat balance the initial cmb temperature is expected to be much higher than the solidus temperature of silicates at the base of the mantle the results indicate that as with previous purely thermal convection models the final state of the system is only weakly dependent on initial cmb temperature unless the cmb becomes blanketed by a global layer of dense material fully 3 d spherical cases have a very similar core evolution to cases in a 2 d spherical annulus giving confidence in the applicability of 2 d spherical annulus geometry for modeling earth s evolution obtaining a successful thermal evolution in the sense of obtaining the correct present day inner core size and maintaining a geodynamo over geological time is helped by the accumulation of piles of dense material at the cmb subducted morb in the present calculations and a concentration of radiogenic k in the core in the range 400 800 ppm the present day cmb heat flow is predicted to be around 9 tw while this is lower than estimates based on calculating temperature gradients in regions where the postperovskite transition is seismically imaged these tend to be areas of higher than average heat flux and thus likely overestimate the global heat flow

lower mantle structure from scs s differential travel times knowledge of the spectrum of structure in the lower mantle is crucial to our understanding of the dynamical evolution of the earth and in principle can be inferred from the analysis of global seismic data sets the long wavelength compressional velocity structure has usually been constrained through tomographic inver sion of the isc catalogue of p wave travel times1 3 whereas shear velocity has been inferred from waveform modelling of long period shear waves4 6 the models that have been produced are similar in only the largest scale features7 and explain little of the variance of the raw data used in their construction thus there is a legitimate concern that the current generation of global scale models give only a crude approximation to the largest scale structure and that there may be significant aliasing of short wavelength heterogeneity here we use scs s differential travel times to demonstrate that the three dimensional structure of the lower mantle is indeed dominated by continental scale features particularly convincing is the fact that the features are apparent in the raw data and are not the product of a complicated modelling procedure

generation of plumes under a localized high viscosity lid in 3 d spherical shell convection we conduct numerical simulations of incompressible infinite prandtl number convection in a spherical shell with a single localized high viscosity lid hvl on the top surface to understand the possible effects of the continental lithosphere on plume generation the temperature under the hvl increases rapidly after the emplacement of the hvl on constant viscosity convection with internal and bottom heatings later upwellings at the bottom merge into a large scale flow and a large plume emerges under the hvl this time scale depends on the existence of phase changes in our model whose rayleigh number is 10 6 the large plume is formed on a time scale of 1 gyr a simple scaling suggests that this time scale may be reduced by a several times if the rayleigh number is around 10 despite the complicated 3 d thermal structure it is dominated by an i 1 pattern controlled by the position of the hvl

temperature beneath continents as a function of continental cover and convective wavelength geodynamic modeling studies have demonstrated that mantle global warming can occur in response to continental aggregation possibly leading to large scale melting and associated continental breakup such feedback calls for a recipe describing how continents help to regulate the thermal evolution of the mantle here we use spherical mantle convection models with continents to quantify variations in subcontinental temperature as a function of continent size and distribution and convective wavelength through comparison to a simple analytical boundary layer model we show that larger continents beget warming of the underlying mantle with heating sometimes compounded by the formation of broader convection cells associated with the biggest continents our results hold well for purely internally heated and partially core heated models with rayleigh numbers of 10 5 to 10 7 containing continents with sizes ranging from that of antarctica to pangea results from a time dependent model with three mobile continents of various sizes suggests that the tendency for temperatures to rise with continent size persists on average over timescales of billions of years

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

organization of the tectonic plates in the last 200 myr the present tessellation of the earth s surface into tectonic plates displays a remarkably regular plate size distribution described by either one sornette and pisarenko 2003 or two bird 2003 statistically distinct groups characterised by large and small plate size a unique distribution implies a hierarchical structure from the largest to the smallest plate alternatively two distributions indicate distinct evolutionary laws for large and small plates the first tied to mantle flow the second determined by a hierarchical fragmentation process we analyse detailed reconstructions of plate boundaries during the last 200 myr and find that i large and small plates display distinct statistical distributions ii the small plates display little organisational change since 60 ma and iii the large plates oscillate between heterogeneous 200 170 myr and 65 50 ma and homogeneous 120 100 ma plate tessellations on a timescale of about 100 myr heterogeneous states are reached more rapidly while the plate configuration decays into homogeneous states following a slower asymptotic curve suggesting that heterogeneous configurations are excited states while homogeneous tessellations are equilibrium states we explain this evolution by proposing a model that alternates between bottom and top driven earth dynamics physically described by fluid dynamic analogies the rayleigh benard and benard marangoni convection respectively we discuss the implications for true polar wander tpw global kinematic reorganisations 50 and 100 ma and the earth s magnetic field inversion frequency

the timescales of plume generation caused by continental aggregation abstract to understand the thermal evolution of the mantle following the aggregation of non subductable thick continental lithosphere we study a numerical model in which a supercontinent simulated by high viscosity raft hvr covers a part of the top surface of a convection layer we model infinite prandtl number convection either in a three dimensional 3d spherical shell 3d rectangular box aspect ratios 8 and 4 or two dimensional 2d rectangular box aspect ratio 8 and except for the hvr we specify a constant viscosity the hvr which has a viscosity higher than that of its surrounding is instantaneously placed on the top surface of a well developed convection layer and its position is fixed our results from 3d spherical shell cases with and without phase transitions show the emergence of a large plume characterized by a long wavelength thermal anomaly a degree one pattern for a pangea like geometry we analyze the volume averaged temperature under the hvr t c the remaining oceanic area t o and total area t m to determine the timescale of plume generation the difference between t c and t o t co and t m show the existence of two characteristic timescales t co exhibits an initial rapid increase and may become constant or continue to gradually increase meanwhile t m shows a similar behavior but with a longer timescale we find that these timescales associated with the increase of t co and t m can be attributed to the formation of large scale flow i e plume and response of the whole system to the emplacement of the hvr respectively for 3d spherical cases we find that the timescale of plume generation is 1 2 gyr if the rayleigh number is 10 6 to determine the effects of the viscosity of the hvr 2d versus 3d modeling and the effects of the internal heating we have also studied 2d and 3d rectangular box cases a factor of about two variation exists in the timescale of plume generation it appears that the timescale becomes greater for a smaller amount of internal heating this may be attributed to the time dependent flow caused by the internal heating for 2d cases we find that the timescale of the high rayleigh number 10 7 case is shortened by a factor of three to five when compared to the ra 10 6 case which is consistent with the simple boundary layer theory this may imply that well developed plumes may arise with the timescale of 0 2 to 0 4 gyr for ra 10 7

normal mode and free air gravity constraints on lateral variations in velocity and density of earth s mantle with the use of a large collection of free oscillation data and additional constraints imposed by the free air gravity anomaly lateral variations in shear velocity compressional velocity and density within the mantle dynamic topography on the free surface and topography on the 660 km discontinuity and the core mantle boundary were determined the velocity models are consistent with existing models based on travel time and waveform inversions in the lowermost mantle near the core mantle boundary denser than average material is found beneath regions of upwellings centered on the pacific ocean and africa that are characterized by slow shear velocities these anomalies suggest the existence of compositional heterogeneity near the core mantle boundary

degree 1 mantle convection and the crustal dichotomy on mars the surface of mars consists of an old heavily cratered and elevated southern hemisphere and younger resurfaced and depressed northern hemisphere a feature often termed the crustal dichotomy the global crustal structure zuber et al 2000 revealed by topography and gravity data from the mars global surveyor spacecraft and the possible late formation of the boundary zone between the hemispheres mcgill and dimitriou 1990 have been proposed to indicate an endogenic origin for the dichotomy however degree 1 mantle convection that is required for any endogenic process to be viable cannot be produced with conventional mantle convection models schubert et al 1990 we have studied the role of radially stratified viscosity on mantle deformation by using rayleigh taylor instability analyses in a spherical shell geometry our analyses reveal that when mantle viscosity is stratified with a weak asthenosphere deformation at long wavelengths is more efficient than that at short wavelengths the weaker the asthenosphere the longer the wavelength at which the deformation is the most efficient a thicker asthenosphere also favors the deformation at long wavelengths both the rayleigh taylor instability analyses and numerical modeling of mantle convection show that degree 1 convection can be produced within the martian mantle provided that the mantle had a weak asthenosphere v500 km thick and v10 2 times weaker than the underlying mantle early in planetary history the degree 1 convection causes preferential heating of one hemisphere that may explain the primary features associated with the dichotomy in crustal structure fl 2001 elsevier science b v all rights reserved

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

the continental drift convection cell continents on earth periodically assemble to form supercontinents and then break up again into smaller continental blocks the wilson cycle previous highly developed numerical models incorporate fixed continents while others indicate that continent movement modulates flow our simplified numerical model suggests that continental drift is fundamental a thermally insulating continent is anchored at its center to mantle flow on an otherwise stress free surface for infinite prandtl number cellular convection with constant material properties rayleigh numbers exceed 107 while continent widths and chamber lengths approach earth s values the wilson cycle is reproduced by a unique rugged monopolar continental drift convection cell subduction occurs at the cell s upstream end with cold slabs dipping at an angle beneath the moving continent as found in many continent subduction regions on earth drift enhances vertical heat transport up to 30 especially at the core mantle boundary and greatly decreases lateral mantle temperature differences

predominance of long wavelength heterogeneity in the mantle analysis of travel time anomalies of long period shear waves recorded by the global digital seismographic network indicates that mantle heterogeneities which probably reflect patterns of mantle convection occur most prominently on length scales greater than about 6 000 km when projected onto a two dimensional map at the earth s surface models of mantle convection will need to be able to produce a similar power spectrum

thermochemical structures beneath africa and the pacific ocean large low velocity seismic anomalies have been detected in the earth s lower mantle beneath africa and the pacific ocean that are not easily explained by temperature variations alone the african anomaly has been interpreted to be a northwest southeast trending structure with a sharp edged linear ridge like morphology the pacific anomaly on the other hand appears to be more rounded in shape mantle models with heterogeneous composition have related these structures to dense thermochemical piles or superplumes it has not been shown however that such models can lead to thermochemical structures that satisfy the geometrical constraints as inferred from seismological observations here we present numerical models of thermochemical convection in a three dimensional spherical geometry using plate velocities inferred for the past 119 million years we show that earth s subduction history can lead to thermochemical structures similar in shape to the observed large lower mantle velocity anomalies we find that subduction history tends to focus dense material into a ridge like pile beneath africa and a relatively more rounded pile under the pacific ocean consistent with seismic observations

heterogeneity and time dependence in 3d spherical mantle convection models with continental drift abstract feedback between continents and large scale mantle flow through thermal blanketing has long been surmised as a mechanism for continental drift and wilson cycles paleomagnetism provides evidence for extensive continental displacements 10 000 km on time scales of 100 200 million years comparable to an intrinsic overturn in whole mantle convection here we model continental motions in vigorous 3d spherical convection models focusing on the effects of continent size mantle heating mode and a strong increase in lower mantle viscosity continents covering 30 10 and 3 of earth s surface representative of the former supercontinent pangea present day asia and antarctica respectively are introduced into simple end member mantle convection models characterized by pure core or internal heating and uniform or layered mantle viscosity supercontinents promote temperature anomalies on the largest scales spherical harmonic degrees 1 and 2 primarily through the organization of the long wavelength convective planform inherent in models with a high viscosity lower mantle bottom heating can promote long wavelength heterogeneity by clustering plumes beneath the continent however in isoviscous models small scale structure persists away from the continent regardless of the heating mode supercontinents respond to long wavelength heterogeneity by following great circle paths with variations in velocity on time scales of 1 billion years smaller continents are unable to promote long wavelength structure and the resulting motions are governed by bursts in velocity on time scales of the order of 100 million years continental velocities are roughly a factor of 3 smaller than those in oceanic regions an observation that may help explain the observed difference in the speed of predominantly continental or oceanic plates

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

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

numerical simulations of the cooling of an oceanic lithosphere above a convective mantle abstract numerical simulations of two dimensional rayleigh benard convection are designed to study lithospheric cooling above a convective mantle a strongly temperature and pressure dependent viscosity fluid is heated from below or from within an imposed velocity at the surface of the box mimicks the plate motion between the ridge on one side and the subduction zone on the other side as the lithosphere cools its upper part remains rigid and therefore conductive while its bottom part is convectively unstable dripping instabilities are not observed close to the ridge nevertheless the material flows along the slope defined by the lower part of the lithosphere and feeds the first descending drip afterwards cold downgoing instabilities develop continuously and randomly at the base of the lithosphere and are replaced by hot material from the convecting core of the box the lithosphere continues to thicken even after the onset of the first instability surface heat flow subsidence and lithospheric temperature structure obtained by the convective simulations are compared to the predictions of three conductive models the plate chablis and modified chablis models these models differ by their applied bottom boundary condition which represents the lithosphere asthenosphere convective coupling i e by the presence or absence of instabilities developing at the base of the lithosphere the conductive model which best explains the lithospheric cooling obtained by convective simulations is the modified chablis model in this model a variable heat flow depending upon the viscosity at the base of the lithosphere is applied along an isotherm located in the lower unstable part of the lithosphere

effects of a realistic mantle thermal conductivity on the patterns of 3 d convection abstract a physical model describing the temperature and pressure dependences of mantle thermal conductivity has recently been provided by a m hofmeister science 283 1999 1699 1706 we have studied numerically the influences of such a temperature and pressure dependent thermal conductivity on 3 d constant viscosity convection a large aspect ratio box of 4 4 1 has been taken for rayleigh numbers greater than 104 to 106 the power law index governing the phonon contribution to the thermal conductivity controls the style of convection for silicates the pattern of convection is quite different from that of constant conductivity whereas the pattern of convection associated with conductivity of oxides is close to the case for constant conductivity both boussinesq and extended boussinesq models with viscous and adiabatic heatings have been examined major effects of variable thermal conductivity on mantle convection are 1 heating up of the lower mantle 2 longer wavelength boussinesq convection 3 shorter wavelength for extended boussinesq convection 4 thick stable plumes with large plumeheads 5 thicker thermal boundary layer of around 500 km at the base of the mantle the contributions from the new terms due to the variable conductivity in the energy equation have magnitudes several times that of chondritic heating at the boundary layers a large region of superadiabatic lower mantle with about a 400 to 600 k excess is caused by variable thermal conductivity this finding has an interesting implication on the recent seismic finding of a lighter density in the deep portion of the lower mantle

dynamical consequences of depth dependent thermal expansivity and viscosity on mantle circulations and thermal structure the effects of both depth dependent thermal expansivity and depth dependent viscosity on mantle convection have been examined with two dimensional finite element simulations in aspect ratio ten boxes surface rayleigh numbers between 107 and 6 107 have been considered the effects of depth dependent properties acting singly or in concert are to produce large scale circulations with a few major upwellings the interior of the mantle is cooled by the many cold instabilities which are slowed down and eventually swept about by the large scale circulation the interior temperature of the mantle can be influenced by the trade off between depth dependent properties and internal heating for chondritic abundance of internal heating and depth dependent thermal expansivity the viscosity increase across the mantle can be no greater than a factor of around ten in order to keep the lower mantle adiabatic the thermal contrasts between the cold blobs and the surrounding mantle are strongly reduced by depth dependent properties whereas the lateral differences between the hot upwelling and the ambient lower mantle can be significant over several hundred degrees depth dependent properties also encourage the formation of a stronger mean flow in the upper mantle which may be important for promoting long term polar motions

heat flow scaling for mantle convection below a conducting lid resolving seemingly inconsistent modeling results regarding continental heat flow numerical models of mantle convection below a conducting lid meant to mimic a continent have been used 1 to argue that heat flow variations in stable continental regions result principally from lithospheric thickness variations and 2 to argue that the relationship between lithospheric thickness and continental heat flow is too weak to allow for this we reconcile these results using a theoretical heat flow scaling which shows that the relationship between heat flow and lid thickness can take on two end member forms as the ratio of lid thickness to convecting layer depth increases the effects of lid thickness variations on heat flow move from weak to strong modeling studies that concluded that lithospheric thickness variations could lead to significant continental heat flow variations assumed a convecting layer depth appropriate to upper mantle convection and thus maximized the relative thickness of the continental lithosphere i e the conducting lid studies that concluded that the relationship is weak assumed whole mantle convection which placed them on the flatter end of the heat flow versus relative lid thickness curve

degree 1 convection in the martian mantle and the origin of the hemispheric dichotomy 1 the surface of mars appears dramatically different between the northern and southern hemispheres any endogenic origin for this hemispheric dichotomy must involve a pattern of mantle convection that reflects the shape of the dichotomy primarily spherical harmonic degree 1 we investigated two mechanisms by which degree 1 convection may be initiated in the martian mantle 1 an endothermic phase change near the cmb and 2 viscosity layering in the mid mantle using two dimensional 2 d and 3 d spherical finite element convection models we explored the conditions under which each mechanism can produce degree 1 structures the phase transition is only effective at generating degree 1 structures when the mantle viscosity is constant or weakly temperature dependent activation energy 100 kj mol but the degree 1 pattern requires several billion years to develop increasing convective vigor in phase change models leads to reduced wavelengths for convective structures degree 1 convection can also develop in a layered viscosity mantle with temperature and depth dependent viscosity an overall sublithospheric radial viscosity variation of a factor of 100 including a factor of 8 25 jump in the midmantle can lead to formation of degree 1 structure in a timescale ranging from 100 my to several hundred my consistent with the timescale for the formation of the dichotomy neither convective vigor nor the internal heating rate greatly affects the formation of degree 1 structures we propose that degree 1 mantle convection induced by a layered viscosity structure may be responsible for the formation of the crustal dichotomy

constraints on mantle viscosity structure from continental drift histories in spherical mantle convection models abstract earth s continents drift in response to the force balance between mantle flow and plate tectonics and actively change the plate mantle coupling thus the patterns of continental drift provide relevant information on the coupled evolution of surface tectonics mantle structure and dynamics here we investigate rheological controls on such evolutions and use surface tectonic patterns to derive inferences on mantle viscosity structure on earth we employ global spherical models of mantle convection featuring self consistently generated plate tectonics which are used to compute time evolving continental configurations for different mantle and lithosphere structures our results highlight the importance of the wavelength of mantle flow for continental configuration evolution too strong short wavelength components complicate the aggregation of large continental clusters while too stable very long wavelength flow tends to enforce compact supercontinent clustering without reasonable dispersal frequencies earth like continental drift with episodic collisions and dispersals thus requires a viscosity structure that supports long wavelength flow but also allows for shorter wavelength contributions such a criterion alone is a rather permissive constraint on internal structure but it can be improved by considering continental oceanic plate speed ratios and the toroidal poloidal partitioning of plate motions the best approximation of earth s recent tectonic evolution is then achieved with an intermediate lithospheric yield stress and a viscosity structure in which oceanic plates are 103 more viscous than the characteristic upper mantle which itself is 100 200 less viscous than the lowermost mantle such a structure causes continents to move on average 2 2 1 0 slower than oceanic plates consistent with estimates from present day and from plate reconstructions this does not require a low viscosity asthenosphere globally extending below continental roots however this plate speed ratio may undergo strong fluctuations on timescales of several 100 myr that may be linked to periods of enhanced continental collisions and are not yet captured by current tectonic reconstructions

convection under a lid of finite conductivity heat flux scaling and application to continents 1 a scaling law for the heat flux out of a convective fluid covered totally or partially by a finitely conducting lid is proposed this scaling is constructed in order to quantify the heat transfer out of the earth s mantle taking into account the effect of the dichotomy between oceans and continents which imposes heterogeneous thermal boundary conditions at the surface of the mantle the effect of these heterogeneous boundary conditions is studied here using simple two dimensional models with the mantle represented by an isoviscous fluid heated from below and continents represented by nondeformable lids of finite thermal conductivity set above the surface of the model we use free slip boundary conditions under the oceanic and continental zones in order to study in an isolated way the possible thermal effect of continents independently of all mechanical effect a systematic study of the heat transfer as a function of the rayleigh number of the fluid of the width of the lid and of its thermal properties is carried out we show that estimates of continental lithosphere thickness imply a strong insulating effect from continents on mantle heat loss at least locally the heat flux below continents was low in the past and of the order of the present one if the continental thickness has remained broadly constant over the earth s history

global love wave phase velocity variation and its significance to plate tectonics abstract global love wave phase velocity variation was constructed for periods between 80 and 200 s by using approximately 9000 paths from 971 earthquakes with m 5 5 the data set was from gdsn and geoscope networks between 1980 and 1987 we examined both the spherical harmonic expansion method and the block parameterization method with a simple constant damping parameter approach synthetic tests showed that more accurate results were obtained by the block parameterization method than by the spherical harmonic expansion method we adopted the block inversion method with a nearly equal area block 5 5 near the equator discretization the general pattern of the resulting maps were consistent with previous global and local studies with a discretization of 5 by 5 the maps were detailed enough to test some plate tectonic models for the pacific atlantic and indian oceans surface wave velocities increased smoothly to plate ages older than 100 ma simple forward modeling showed that seismic phase velocity variation with a continuous thickening of lithosphere up to about 150 ma fits the present observation disagreeing with the model deduced from the heat flow and ocean depth data which change variations at about 60 80 ma the seismic phase velocity variations in different oceans showed systematic differences at younger ages and convergence beyond 100 ma the difference at younger ages implies a failure of scaling derived from a simple thermal boundary layer model for oceanic plates age seismic phase velocity relationships on each side of ridges were also examined and asymmetric velocity variations were found which suggests differences in thermal states from one side of the ridge to the other in order to further examine the thermal state of the lithosphere average age phase velocity relations were established for each ocean and subtracted from phase velocity variation maps the results indicated broad low velocity regions in the south pacific super swell region the south and west indian ocean and high velocity regions east of the east pacific rise and in the north to northeast indian ocean the results reflect the asymmetry of phase velocity variation about ridges there is some correlation between hot spot locations and low velocity anomalies but additional large scale thermal anomalies exist under old oceanic plate

on the effect of continents on mantle convection at the earth s surface continents and oceans impose different thermal boundary conditions at the top of the mantle laboratory experiments are used to investigate the consequences of this for mantle convection the upper boundary of the experimental tank was made of copper plates enforcing a fixed temperature and had a conductive lid of finite width in the middle beneath this lid the thermal boundary condition was of the mixed type with a biot number depending on the dimensions and thermal conductivity of the lid experimental values of the biot number were scaled to earth values experiments were run for a large range of rayleigh numbers from 104 to 107 and for several lid widths the effects of temperature dependent viscosity and of the shape of the lid were investigated at steady state in all cases there is an upwelling beneath the conductive lid which feeds two symmetrical and elongated convective cells three different dynamic regimes were identified as a function of rayleigh number independently of the lid width at rayleigh numbers lower than 1 2 105 the upwelling is steady both in geometry and temperature structure at rayleigh numbers between 1 2 105 and 2 106 this central upwelling is intermittent at larger values of the rayleigh number there is no longer a simple upwelling structure but a set of small plumes rising together and distorted by a cellular circulation of large horizontal extent thus the conductive lid always imposes a large scale flow pattern the length of these convective cells is a function of lid width it is equal to the lid width at large values and decreases to the rayleigh benard value as the lid width decreases to zero a fluid loop model explains the most important features of this form of convection the cell length is such that the upwelling temperature is minimized for a given rayleigh number and lid width and is an increasing function of lid width and a decreasing function of rayleigh number transient experiments demonstrate that the large scale flow structure develops rapidly with even small horizontal temperature differences implications for the earth are that large scale convection cells exist in conditions which in the absence of continents would probably lead to a chaotic convection pattern dominated by plumes at high rayleigh number continental breakup is effected by a large scale line upwelling structure which includes a number of individual plumes

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