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

the backus gilbert approach to the three dimensional structure in the upper mantle i lateral variation of surface wave phase velocity with its error and resolution summary the backus gilbert method is applied to obtain the phase velocity variations on a sphere from the measured phase velocity narrow peak kernels with radii of about 2000 km are obtained for almost everywhere on the sphere the phase velocity results are thus interpreted as an average within such regions the most trouble comes from the antipodal peak in the resolution kernel this is evaluated as contamination and is incorporated in the error estimation the total error which is a root mean square of contamination from the antipodal peak and statistical error estimated from the data covariance matrix is about 1 per cent of the phase velocity in the average earth model which is the preliminary reference earth model prem however there is about a factor of 2 variation of errors on the sphere maximum variations of phase velocity are about 3 4 per cent of the phase velocity in the average earth model and thus there still remain anomalies which exceed estimated errors the estimated errors correspond to one standard deviation under the assumptions of uncorrelated gaussian distribution for high confidence interval they show that statistically significant anomalies are scarce for the current data set generally love wave phase velocity maps show more resolved features than rayleigh wave maps and we can see in high confidence maps fast velocities in old oceans and old continents and slow velocities in tectonically active regions like the east pacific rise and various back arc regions

rheology of the lower mantle abstract the rheology of the lower mantle of the earth is examined from the viewpoint of solid state physics recent developments in high pressure research suggest that the lower mantle contains a considerable amount of mg fe o with fe mg fe 0 2 0 3 the pressure and temperature dependences of diffusion in mg fe o are estimated by the theory of diffusion in ionic solids of the materials composing the lower mantle mg fe o may be the softest and therefore the rheology of the lower mantle may be that of mg fe o unless the framework effect is important temperatures in the lower mantle are inferred from the depths of phase transitions and the melting temperatures of the core materials a thermal boundary layer at the base of the mantle is suggested the physical mechanisms of creep are examined based on a grain size stress relation and non newtonian flow is shown to be the dominant flow mechanism in the earth s mantle the effective viscosity for the temperature models with and without the thermal boundary layer is calculated for constant stress and constant strain rate with depth for constant strain rate which may be appropriate for discussing the mechanics of descending slabs the increase in effective viscosity with depth is smaller than for the constant stress case which may be appropriate for discussing the flow induced by the surface motion of plates the relatively small depth gradient of viscosity for constant strain rate suggests that the lower mantle could also participate in convection the effective viscosity increases with depth however by at least 10 2 to 10 3 from the top to the bottom of the lower mantle for a reasonable range of activation volumes and temperatures there will be a low viscosity layer at the base of the mantle in contrast to the high viscosity layer at the top of the mantle plates if a thermal boundary layer is present the constant newtonian viscosity inferred from rebound data may be an apparent feature resulting from the difference in deformation mechanisms between isostatic rebound and large scale flow

geoid and topography of earth like planets a comparison between compressible and incompressible models for different rheologies abstract a systematic study of 2d axisymmetric spherical shell models of compressible and incompressible mantle convection with constant and variable viscosity and constant and depth dependent thermodynamic properties is presented to account for compressibility effects we employ the anelastic liquid approximation in the case of variable viscosity an arrhenius law with strongly temperature and pressure dependent viscosity is considered we show that assuming compressible convection with depth dependent thermodynamic properties strongly influence the geoid undulations using compressible convection with constant thermodynamic properties is physically inconsistent and may lead to spurious results for the geoid and convection pattern in addition we examine the impact of compressibility as well as different rheologies on the power law relation that connects the nusselt number to the rayleigh number we discover that the power law index of the nu ra relationship is controlled by the rheology independent of which approximation is used instead the bound of this relation is controlled by a combination of different approximation and rheology

formation of ridges in a stable lithosphere in mantle convection models with a viscoplastic rheology numerical simulations of mantle convection with a viscoplastic rheology usually display mobile episodic or stagnant lid regimes in this study we report a new convective regime in which a ridge can form without destabilizing the surrounding lithosphere or forming subduction zones using simulations in 2 d spherical annulus geometry we show that a depth dependent yield stress is sufficient to reach this ridge only regime this regime occurs when the friction coefficient is close to the critical value between mobile lid and stagnant lid regimes maps of convective regime as a function of the parameters friction coefficients and depth dependence of viscosity are provided for both basal heating and mixed heating situations the ridge only regime appears for both pure basal heating and mixed heating mode for basal heating this regime can occur for all vertical viscosity contrasts while for mixed heating a highly viscous deep mantle is required

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

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

numerical simulations of subduction zones effect of slab dehydration on the mantle wedge dynamics abstract in oceanic subduction zones dehydration of slab s minerals may favor asthenospheric flow in the mantle wedge by decreasing rocks strength this should enhance the upper plate base reheating and markedly alter its thermal structure to quantify this phenomenon we model slab subduction within a viscous mantle dehydration hydration processes and the rock strength dependence on water content we use accurate phase diagrams for a h2o satured mantle peridotite and a gabbroic crust to determine at each time step the amount of water released or absorbed by each unit of rock transition phases are supposed to be not metastable water is released from the oceanic crust and from the altered peridotite portion of the slab dehydration of the subducting lithosphere occurs first at 60 75 km depth when the crust is eclogitized and second deeper around 105 km when serpentine and chlorite in serpentinite layer below the crust become unstable for high convergence rates because of cold p t t paths in the slab serpentine can be transformed into the hydrated phase a and water is recycled by the slab until great depth however in all investigated cases the released water is sufficient to hydrate by dissolution the whole mantle wedge until 217 55 km away from the trench and as it goes up to form hydrated minerals in the overlying lithosphere over a significant volume the convergence rate slightly shifts dehydration fronts location and consequently widens or reduces the hydrated mantle wedge note that for the dynamic corner flow modelled here with a non newtonian rheology the slab surface is significantly warmer than for an isoviscous analytical corner flow model yielding plausible crust melting we assume a strength reduction associated to hydration larger for rocks containing nominally hydrous minerals than for rocks with only dissolved water the rock strength thus becomes quite uniform at the base of the hydrated upper plate and in the wedge this results in cooler temperatures along the slab top but in an enhanced corner flow effect on the upper plate thermal structure for large hydration strength reductions a strong thermal erosion of the overlapping lithosphere develops in less than 15 myr due to convective destabilization this weakens drastically the upper plate at a distance from 110 to 220 km away from the trench the geometry of the eroded region could correspond to the low velocity zone observed below the arc region

steady state secondary convection beneath lithospheric plates with temperature and pressure dependent viscosity we have constructed a thermomechanical model for upper mantle convection such that the thickness and structure of the lithosphere are determined self consistently by the heat transported by convection in this study of the interaction between the lithosphere and upper mantle strongly temperature and pressure dependent rheologies for both newtonian and non newtonian creep mechanisms are employed for a strictly temperature dependent rheology an insignificant amount of heat less than 12 5 mw m2 can be transported convectively for an interior viscosity 0 1021 pas compatible with postglacial rebound on the other hand for similar values of the interior viscosity steady heat fluxes between 20 and 40 mw m2 are produced by introducing pressure dependence into the rheology for the temperature and pressure dependent flow law the horizontally averaged interior temperature displays very little variation with the amount of heat evacuated once all of the rheological parameters are fixed this finding may have important ramifications for parameterized convection we employ both the single mode mean field approximation and the complete two dimensional equations using finite elements to obtain solutions for the various types of rheologies from evaluating the geophysically relevant observables such as topography free air gravity anomalies surface heat flow and stress fields in the lithosphere we find that the lateral variations of these quantities predicted by a non newtonian rheology are much smaller than those derived from a linear rheology these results suggest that surface variations of geophysical observables are more compatible with a non newtonian rheology in the upper mantle

convection in a variable viscosity fluid newtonian versus power law rheology abstract a number of finite element calculations of convection in a variable viscosity fluid have been carried out to investigate the effects of non newtonian flow when rheology is also subject to a strong temperature and pressure influence a variety of cases has been studied in the range of effective rayleigh numbers between 104 and 106 including different modes of heating and a range of values for activation energy and activation volume power law creep with a stress exponent of 3 turns out to lead to considerably different flow pattern and heat transfer properties than newtonian rheology in general the effect is to reduce viscosity contrasts imposed by p t dependence which can lead in some circumstances to the mobilisation of otherwise stagnant regions within the cell the properties of non newtonian flow can be closely imitated by a newtonian fluid with a reduced value of the activation enthalpy bh with b 0 3 0 5 it appears possible that non newtonian rheology plays a key role in determining the convective style in a planetary mantle

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

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

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

numerical studies of non newtonian mantle convection abstract numerical model computations have been carried out to determine how the stress dependence of non newtonian viscosity affects the flow structure of thermal convection the viscosity laws have been chosen in accordance with present knowledge of upper mantle rheology based on the diffusion and dislocation creep laws of olivine the results show that there are important differences between the structures of newtonian and non newtonian convection while the newtonian models are insufficient in some respects the non newtonian solutions can explain the characteristics of the real mantle flow however this may require a faster plastic deformation than power law dislocation creep at least in the high stress regions of the mantle e g at the active plate margins

stress and flow beneath island arcs summary the flow pattern stress distribution topography and gravity anomalies were computed from numerical models having density and viscosity distributions resemblant to the aleutian arc the results were compatible with the hypothesis that the excess density of the slab drives its descent and that hydrodynamic forces are responsible for topographic and gravity highs over the outer rise seaward of the trench and the frontal arc and lows over the trench in models with simple distributions of rheological parameters the force from the slab was transmitted directly upward producing a negative gravity anomaly over the arc material with low resistance to flow was needed along the fault plane above the slab or within the crust of the frontal arc and within the wedge of asthenosphere above the slab to reduce that force and to allow the horizontal lithosphere to move with the slab models with the resistance to flow thus reduced had outer rises deep trenches horizontal tension seaward of the trench horizontal compression under the trench and downdip tension in the slab free air gravity anomalies which are the sum of between deflections of the free surface due to hydrodynamic forces and direct attractions from the masses driving the flow were not fit excellently by any of the models in part because the coarse grid used precluded accurate representation of the fault zone above the slab and the frontal arc an alternate to the hypothesis that about 5 kb of stress on the fault plane is needed to produce an outer rise is offered by these models shear stress between the slab and the island arc was always below 700 bars in the more successful models if the density distribution was scaled to match the topography of the trench this is much less than the 2000 bars stresses needed if frictional heating causes island arc volcanism

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

newtonian versus non newtonian upper mantle viscosity implications for subduction initiation 1 the effect of rheology on the evolution of the slab tip during subduction initiation is analyzed using 2 d numerical flow models experimentally determined flow laws have both strong temperature and stress dependence which leads to large local variations in viscosity with direct consequences for subduction initiation we find that models with newtonian viscosity lead to flat or coupled subduction due to hydrodynamic stresses that pull the slab tip up towards the overriding plate non newtonian rheology reduces these hydrodynamic stresses by decreasing the wedge viscosity and the slab coupling to wedge corner flow rendering the small negative slab buoyancy of the slab tip sufficient to maintain its dip during the early stages of subduction

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 early geodynamic evolution of mars type planets abstract it is not clear whether mars once possessed active tectonics yet the question is critical for understanding the thermal evolution of mars and the origin and longevity of its early dynamo to address these issues we have coupled mantle flow simulations together with parameterized core evolution models to simulate the early evolution of mars like planets and constrain the influence of early mobile lid tectonics on core evolution we have explored a wide parameter suite encapsulating a range of uncertainties in initial conditions rheological parameters and surface strength we present successful models that experience early mobile lid behaviour with a later transition into a stagnant lid mode which reproduce core dynamo histories similar to the magnetic history of early mars

pluto s ocean is capped and insulated by gas hydrates many icy solar system bodies possess subsurface oceans on pluto sputnik planitia s location near the equator suggests the presence of a subsurface ocean and a locally thinned ice shell to maintain an ocean pluto needs to retain heat inside on the other hand to maintain large variations in its thickness pluto s ice shell needs to be cold here we show by thermal evolution and viscous relaxation calculations that the presence of a thin layer of clathrate hydrates gas hydrates at the base of the ice shell can explain both the long term survival of the ocean and the maintenance of shell thickness contrasts clathrate hydrates act as a thermal insulator preventing the ocean from completely freezing while keeping the ice shell cold and immobile the most likely clathrate guest gas is methane derived from precursor bodies and or cracking of organic materials in the hot rocky core nitrogen molecules initially contained and or produced later in the core would probably not be trapped as clathrate hydrates instead supplying the nitrogen rich surface and atmosphere the formation of a thin clathrate hydrate layer cap to a subsurface ocean may be an important generic mechanism to maintain long lived subsurface oceans in relatively large but minimally heated icy satellites and kuiper belt objects pluto s subsurface ocean and thickness variation in its ice shell may be maintained by a layer of methane clathrates forming an insulating cap to the ocean according to calculations of thermal evolution and viscous relaxation

seismic attenuation in finely layered porous rocks effects of fluid flow and scattering scattering caused by fine layering is known to play an important role in seismic attenuation if the rock is also porous and permeable additional attenuation can be caused by a flow of the pore fluid induced by the passing wave see e g white 1983 at frequencies higher than 100 khz standard biot s attenuation biot 1962 bourbie et al 1987 may also contribute to the overall attenuation in a layered poroelastic rock while standard biot s attenuation has been well known for decades the effects of scattering by fine layering and interlayer flow have been studied extensively both theoretically and numerically in recent years however in all theoretical approaches proposed thus far these effects have been treated separately scattering was studied for purely elastic rocks burridge and chang 1989 shapiro et al 1994 while attenuation caused by interlayer flow was considered either for periodically stratified media that causes no scattering norris 1993 or for frequencies at which scatterin

conduit diameter and buoyant rising speed of mantle plumes implications for the motion of hot spots and shape of plume conduits 1 mantle plumes are expected to be affected by large scale flow in the earth s mantle related to plate motions subducted slabs and possibly large scale upwellings motion of plume conduits will depend on both large scale flow and buoyant rising speed of the conduit through the mantle here we present a model of depth dependent plume conduit temperature viscosity radius and buoyant rising speed and use it to compute plume and hot spot motion results support a temperature anomaly of about 500 k at the plume base in this case sublithospheric temperature anomaly is about 150 k for the iceland plume transition zone anomaly is between 150 and 200 k for iceland about 250 k for samoa and about 300 k for hawaii thermal plume radii are about 100 km in the upper mantle increasing to about 200 km in the lower mantle beneath the lithosphere viscosity in the vicinity of plumes is substantially reduced compared to the underlying mantle and fast moving plates deflect plumes by 200 km or less corresponding to a plume conduit buoyant rise time of about 3 myr between 400 and 100 km depth where most of the shear flow due to plate motions occurs during 100 myr plume conduits rise buoyantly from about 1500 2000 km depth in many cases computed hot spot motion agrees with previous computations south southeastward motion of the hawaiian hot spot during the past 100 myr louisville hot spot motion in a similar direction but at slower speed during the past 50 myr and westward motion of the easter hot spot relative to hawaii and louisville however the previously computed substantial southward motion of the kerguelen hot spot is not confirmed if plume sources in the lowermost mantle are assumed to move with large scale flow they are predicted to be displaced toward the two large scale upwellings beneath africa and the pacific relative to hot spot surface locations for fixed sources predicted tilts of the lower part of conduits tend to be opposite to that

interior structure of the moon constraints from seismic tomography gravity and topography abstract seismic tomography can be combined with constraints from geoid topography and other surface observations to gain information about mantle structure and dynamics this approach has been taken with much success for the earth mantle and here it is for the first time applied to the moon lunar tomography has much lower resolution as for the earth and is mostly restricted to the near side nevertheless we can assess under what assumptions the fit between predicted geoid based on a tomography model and observed geoid is best among the models tested we find the most similar pattern correlation about 0 5 if we only consider tomography below 225 km depth if density anomalies cause little or no dynamic topography and if we compare to the geoid with the flattening l 2 m 0 term removed this could mean that a like for the earth seismic anomalies shallower than 225 km are caused by a combination of thermal and compositional effects and therefore cannot be simply converted to density anomalies b the lithosphere is sufficiently thick to prevent dynamic topography more than a small fraction of total topography and c flattening is a fossil bulge unrelated to present day mantle anomalies however we have to be cautious with interpreting our results because for models with a comparatively higher correlation and a conversion from seismic velocity to density anomalies similar to the earth s upper mantle the amplitude of the predicted geoid is much lower than observed this could either mean that the tomography model is strongly damped or that the geoid is mostly due to shallow causes such as crustal thickness variations with only a small part coming from the deeper mantle

the rheology and thermal history of mars revealed by the orbital evolution of phobos the evolution and internal structure of mars are by comparison to its present day surface poorly known although evidence of recent volcanic activity1 suggests that its deep interior remains hot and convectively cooling the cooling rate of mars is related to its early thermal state and to its rheology which determines its ability to deform and to dynamically evolve2 attempts to reconstruct the dynamic history of mars and reveal its present day structure by combining the study of thermal evolution with surface observations are limited by the interplay between several key quantities including temperature composition and rheology here we show that by considering phobos the closest satellite of mars the orbital evolution of which is governed by the thermochemical history of mars through tidal interactions we can gain insight into the thermal history and rheology of the planet we investigated the long term evolution of the main envelopes of mars these comprise a liquid metallic core that is overlain by a homogeneous silicate convecting mantle underneath an evolving heterogeneous lithospheric lid that includes a crust enriched in radiogenic elements by exploiting the relationship between mars and phobos within an established in situ scenario for the early origin of the moons of mars3 we find that initially mars was moderately hotter 100 to 200 kelvin than it is today and that its mantle sluggishly deforms in the dislocation creep regime this corresponds to a reference viscosity of 1022 2 0 5 pascal seconds and to a moderate to relatively weak intrinsic sensitivity of viscosity to temperature and pressure our approach predicts a present day average crustal thickness of 40 25 kilometres and a surface heat flow of 20 1 milliwatts per square metre we show that combining these predictions with data from future and ongoing space missions such as insight could reduce uncertainties in martian thermal and rheological histories and help to uncover the origin of phobos insights into the thermal and rheological history of mars are generated by considering the interplay between the thermochemistry of the planet and the orbital evolution of its closest satellite phobos

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

the interaction of a subducting lithospheric slab with a chemical or phase boundary we have used a finite element model of time dependent convection to determine the conditions for penetration of the subducted plate into the lower mantle a temperature dependent and non newtonian rheology is applied to achieve platelike behavior of the upper and sinking thermal boundary layer of convection the 650 km discontinuity is taken as either a chemical or phase boundary or as a combination of both it is represented by a marker chain which effects additional buoyancy when distorted out of its equilibrium position when the compositional density contrast is greater than about 5 the descending slab is deflected sidewards at the boundary and two layer convection prevails a resulting depression of the boundary in the range of 50 200 km should be detectable with seismic methods below 5 density difference the slab plunges several hundred kilometers into the lower mantle and below 2 it will probably not stop before reaching the core mantle boundary and extensive mixing would be expected with a pure phase change a negative clapeyron slope of about 6 mpa k 60 bar k is required to establish a type of leaky double layer convection a more moderate slope can aid a small compositional density difference to prevent slab penetration into the lower mantle with the present uncertainties about the physical nature of the 650 km discontinuity a variety of convective styles appears possible on dynamical grounds

controls on trench topography from dynamic models of subducted slabs a finite element method with constrained elements and lagrange multipliers is used to study tectonic faults in a viscous medium a fault representing the interface between overriding and subducting plates has been incorporated into a viscous flow model of a subduction zone in which both thermal buoyancy and the buoyancy associated with the phase change from olivine to spinel are included the fault causes stress to concentrate in its vicinity giving rise to a weak plate margin and a mobile plate if a power law rheology is used surface dynamic topography with either a newtonian or a power law rheology and with typical subduction zone parameters is characterized by a narrow and deep trench and a broadly depressed back arc basin this suggests that oceanic trenches and back arc basins over subduction zones are dynamically compensated by viscous flow our models show that trench depth increases with fault dip angle slab dip angle slab length and age of oceanic lithosphere just prior to subduction the influence of fault dip angle and age of lithosphere on trench depth is greater than the influence of slab dip angle and slab length these relationships of trench depth versus subduction zone parameters explain well the statistics of observed trench depths for those subduction zones with oceanic lithosphere on both sides of the trench observed trench depths have been corrected for fault and slab dip angles based on the relationships from the dynamic models after correction to a common set of parameters trench depth correlates linearly with age of lithosphere prior to subduction with a slope which is close to what models having high viscosities within the transition zone and lower mantle predict comparison between the trench depths corrected for fault and slab dip angles and model trench depths suggests that the resisting tangential stress on faults in subduction zones may range from 15 mpa to 30 mpa depending on model details

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

thermal structure of oceanic transform faults we use three dimensional fi nite element simulations to investigate the temperature structure beneath oceanic transform faults we show that using a rheology that incorporates brittle weakening of the lithosphere generates a region of enhanced mantle upwelling and elevated temperatures along the transform the warmest temperatures and thinnest lithosphere are predicted to be near the center of the transform previous studies predicted that the mantle beneath oceanic transform faults is anomalously cold relative to adjacent intraplate regions with the thickest lithosphere located at the center of the transform these earlier studies used simplifi ed rheologic laws to simulate the behavior of the lithosphere and underlying asthenosphere we show that the warmer thermal structure predicted by our calculations is directly attributed to the inclusion of a more realistic brittle rheology this temperature structure is consistent with a wide range of observations from ridge transform environments including the depth of seismicity geochemical anomalies along adjacent ridge segments and the tendency for long transforms to break into small intratransform spreading centers during changes in plate motion

on the interaction between small and large scale convection and postglacial rebound flow in a power law mantle abstract some consequences arising from the superposition of flows of two different kinds or scales in a non newtonian mantle are discussed and applied to the cases mantle convection plus postglacial rebound flow as well as small plus large scale mantle convection if the two flow types have similar magnitude the apparent rheology of both flows becomes anisotropic and the apparent viscosity for one flow depends on the geometry of the other if one flow has a magnitude significantly larger than the other the apparent viscosity for the weak flow is linear but develops direction dependent variations about a factorn n being the power exponent of the rheology for the rebound flow lateral variations of the apparent viscosity about at least 3 are predicted and changes in the flow geometry and relaxation time are possible on the other hand rebound flow may weaken the apparent viscosity for convection secondary convection under moving plates may be influenced by the apparent anisotropic rheology other mechanisms leading to viscous anisotropy during shearing may increase this effect a linear stability analysis for the onset of convection with anisotropic linear rheology shows that the critical rayleigh number decreases and the aspect ratio of the movement cells increases for decreasing horizontal shear viscosity normal viscosity held constant applied to the mantle this model weakens the preference of convection rolls along the direction of plate motion under slowly moving plates rolls perpendicular to the plate motion seem to have a slight preference these results could be useful for resolving the question of newtonian versus non newtonian or isotropic versus anisotropic mantle rheology

modes of mantle convection and the removal of heat from the earth s interior earth thermal histories based on two layer and whole mantle parameterized convection models have been explored to determine the influence of the mode of mantle convection on the content and distribution of mantle radioactive heat sources and on the temperatures and heat transfer properties of the mantle two layer mantle convection thermally insulates the lower mantle and is less efficient at heat removal than whole mantle convection consequently two layer mantle convection requires a lower mantle depleted of radioactive heat sources contrary to the undepleted lower mantles of recent geochemical models whole mantle convection removes 3 times more primordial heat from the earth s interior and 6 times more heat from the core in 4 5 billion years than does two layer convection the average mantle volumetric heat generation rates for both modes of convection are comparable to that of a potassium depleted chondrite thus no potassium is necessary in the core to balance the observed present day surface heat flux however most of the radioactives are concentrated in the upper mantle for two layer convection model geotherms for whole mantle convection compare well with independent estimates of temperature at various depths including the core mantle boundary while the lower mantle is too hot for two layer convection models thermal histories of the upper mantle in two layer models are similar to those of whole mantle models thermal histories for the lower mantle in two layer models are similar to those of the core in whole mantle convection models this is because the lower mantle is thermally insulated by the upper mantle if it convects separately just as the core is thermally insulated by the whole mantle the differences between whole and two layer mantle convection are mostly due to the thermal insulation of the lower mantle and the smaller efficiency of heat removal of the upper mantle compared to that of the whole mantle which is much larger in volume a whole mantle convection model reconciling the need for distinct geochemical reservoirs with the physics of mantle convection is presented

on the effects of the lithosphere on mantle convection and evolution abstract an idealized model is discussed for plate motion and mantle convection it consists of a numerical square box filled with a newtonian boussinesq fluid heated from below at the surface the fluid has a high viscosity i e it contains a stiff lid which may or may not be laterally decoupled by weakness zones lid stiffness and coupling were varied systematically only if the lid is effectively decoupled laterally does it move as a quasi rigid plate it is then driven by the lateral pressure differential from the rising and descending plumes in the fluid and it moves against viscous shear at its bottom gravitational sliding and sinking may also drive the plate if allowed for in the model a decoupled freely moving stiff plate effectively removes heat from the interior a strongly coupled stiff lid on the other hand or one with a very large aspect ratio inhibits heat transfer through the convecting layer if heating occurs by a given flux through the bottom or internal heat generation the internal cell temperatures become very high because the stagnant surface lid can only conduct the heat by assuming the required temperature gradient throughout its thickness since the earth is partly covered by conducting continental lids which in addition contain much of the heat sources the thermal history may be affected caution must be exercised in parameterized convection modelling in this respect the overall effect cannot easily be predicted because mantle flow and continental plates will interact the importance of mechanical decoupling for plate motion strongly calls for thorough studies of the decoupling mechanisms particularly at convergent plate boundaries bending stick slip processes and the role of volatiles

onset of small scale instabilities at the base of the lithosphere scaling laws and role of pre existing lithospheric structures summary numerical simulations of 2 d rayleigh benard convection are designed to study the devel opment of convection at the base of the cooling lithosphere a zero temperature is suddenly imposed at the mantle surface which has initially a homogeneous temperature the strongly temperature dependent viscosity fluid is heated from within in order to balance the internal temperature drift resulting from global fluid cooling for a while the lithosphere cools approx imatively as a conductive half space and the lithospheric isotherms depth grows as the square root of age as instabilities progressively develop at the base of the lithosphere lithospheric cooling departs from the half space model we propose two different parametrizations of the age of the first dripping instability using boundary layer marginal stability or quantifying the characteristic timescale of the instability exponential growth as a function of the rayleigh number and of the viscous temperature scale both parametrizations account very well for our numerical estimates of onset times but with a slightly better adjustment of the viscous tem perature scale dependence in the second case the absolute value of the onset time depends on the amplitude and location of initial temperature perturbations within the box and on the initial temperature structure of the thermal boundary layer tbl furthermore thermal perturba tions of finite amplitude located within the lithosphere such as the ones induced by transform faults for example strongly reduce the age of the first dripping instability however the onset time parametrization derived from transient cooling experiments well adjusts the lithospheric age of the first drip instability below a lithosphere cooling perpendicularly to the ridge axis this study emphasizes the role of the initial topography of the lithospheric isotherms on the development of instabilities

the relationship between plate velocity and trench viscosity in newtonian and power law subduction calculations convection with a newtonian temperature dependent rheology leads to little or no surface velocity unless zones of weakness are introduced plate like features are observed in calculations both with newtonian rheology employing imposed weak zones and with power law non newtonian rheology where high stresses at the trench reduce the effective viscosity since deformation at subduction zones involves faulting both of these parameterizations should be treated with some skepticism it is important to understand how the parameterizations affect the model results we study the relationship between trench viscosity and plate velocity using a newtonian rheology by varying the viscosity at the trench the plate velocity is a function of the trench viscosity for fixed rayleigh number and plate slab viscosity slab velocities for non newtonian rheology calculations are significantly different from slab velocities from newtonian rheology calculations at the same effective rayleigh number both models give reasonable strain rates for the slab when compared with estimates of seismic strain rate non newtonian rheology eliminates the need for imposed weak zones and provides a self consistent fluid dynamical mechanism for subduction in numerical convection models