isotopic abundances inferences on solar system and planetary evolution members of the royal swedish academy ladies and gentlemen in thinking over why i am here today i recalled the story of tom sawyer a character of mark twain s on a beautiful bright saturday morning when all of his friends were playing he appeared by the wall in front of his aunt s house with a bucket of whitewash paint and a long handled brush before him stood about thirty meters of continuous wooden fence three meters tall he dipped his brush and passed it over a plank and then repeated it then he stopped and compared the insignificant whitewashed streak with the far reaching continent of unpainted fence and became melancholy then he took up the brush again and went to work a friend came by and teased him for working on saturday when he could be swimming or playing tom said it wasn t so bad because a boy didn t get the chance to whitewash a fence every day tom took a new brush stroke at the fence and stepped back to note the beauty of the effect his friend got interested and then asked permission to make a stroke or two he then offered tom the core of an apple he had just started to nibble on tom told him that it was doubtful that his friend could help because this was the front fence and that a very good and sophisticated job had to be done possibly only but one child in a thousand possibly two thousand could do it well after this denial his friend just had to try and offered tom the whole apple for a chance to paint then more young friends came around to attempt this challenging task by the end of the afternoon tom was the wealthiest boy in town he had twelve marbles a key that didn t unlock anything a piece of blue glass to look through a tin soldier a dog collar but no dog and lots of other valuable things the fence had been coated three times and if he had not run out of whitewash tom would have bankrupted every kid in the village my presence here is due to an ability to attract young talent to help whitewash the fence the only difference is that we have just started on the job

early plate tectonics versus single plate tectonics on mars evidence from magnetic field history and crust evolution 1 the consequences of an early epoch of plate tectonics on mars followed by single plate tectonics with stagnant lid mantle convection on both crust production and magnetic field generation have been studied with parameterized mantle convection models thermal history models with parameterized mantle convection not being dynamo models can provide necessary but not sufficient conditions for dynamo action it is difficult to find early plate tectonics models that can reasonably explain crust formation as is required by geological and geophysical observations and allow an early magnetic field that is widely accepted as the cause for the observed magnetic anomalies dating of crust provinces and topography and gravity data suggest a crust production rate monotonically declining through the noachian and hesperian and a present day crust thickness of more than 50 km plate tectonics cools the mantle and core efficiently and the core may easily generate an early magnetic field given a sufficiently weak mantle rheology plate tectonics can explain a field even if the core is not initially superheated with respect to the mantle because the crust production rate is proportional to temperature however an early efficient cooling will frustrate later crust production and therefore cannot explain for example the absence of prominent magnetic anomalies in the northern crustal province and the northern volcanic plains in the early hesperian voluminous crust formation following plate tectonics is possible if plate tectonics heat transfer is inefficient but then the crust growth rate has a late peak about 2 ga b p which is not observed these models also require a substantial initial superheating of the core to allow a dynamo if one accepts the initial superheating then as we will show a simple thermal evolution model with monotonic cooling of the planet due to stagnant lid mantle convection underneath a single plate throughout the evolution can better reconcile early crust formation and magnetic field generation

the longevity of lunar volcanism implications of thermal evolution calculations with 2d and 3d mantle convection models abstract lunar volcanism as is generally accepted started well before the emplacement of the mare fill at 3 1 3 9 ga b p and likely extended well into the eratosthenian 3 1 1 1 ga b p the early volcanism is relatively easily understood the extension of the activity to possibly 1 5 ga b p albeit at a decreasing rate poses a problem since a relatively small body such as the moon may be expected to cool rapidly and freeze a partially molten mantle layer quickly we present thermal history models in which a region of partial melt forms in the mantle underneath the lithosphere almost immediately after the start of the model at depths between 300 and 700 km depending on the chosen initial depth of the magma ocean to calculate the thermal histories we use axisymmetric 2d and fully 3d spherical shell convection codes with viscosity depending on the azimuthally averaged temperature the thermal evolution of the moon is found to be characterized by the growth of a massive 700 to 800 km thick lithosphere while the lower mantle and core cool only by 100 200 k the partial melt zone decreases in thickness with time from top to bottom until it vanishes at times between 3 4 and 2 2 ga b p the maximum degree of partial melting is between roughly 10 and 20 the partial melt layer is initially global and is disrupted by cold downwellings as cooling proceeds the melt zone freezes from above due to the thickening of the lithosphere which implies that the source region of volcanic rock proceeds to increasing depth with time this corresponds nicely with the variation of titanium with age of lunar mare basalts mixing of the melt zone with the underlying mantle chemically rejuvenates the melt zone to some degree and thus the source region of the mare basalts

time dependent models of single and double layer mantle convection one outstanding problem of great geophysical importance is the vertical extent of convection in the earth s mantle1 steady state models of convection in the mantle have yet to produce a description of the mantle which is consistent with geochemical and geophysical observations here we present time dependent numerical models of two dimensional convection which simulate mantle convection starting from a fluid initially at rest with a purely conductive temperature profile we now find that for a rayleigh number ra of 107 the model experiences a transient period of double layer convection which lasts on the order of hundreds of millions of years when scaled to the earth s mantle it is suggested that transient periods of double layer convection in the earth s mantle may have existed in the past whether or not such a period exists today

thermal equilibration of the earth following a giant impact b the earth is found to equilibrate thermally after a giant impact melts a significant portion of the planet on a time scale of a few million years a simple thermal evolution model for the cooling of a terrestrial planet a prescribed fraction of which is melted during a giant impact is presented two model geometries are considered the first has a laterally inhomogeneous distribution of melt and solid through a mega crater geometry and the second has a global magma ocean the model assumes convective heat transfer in the melt and in the case of the mega crater geometry convection in the solid part of the planet in the magma ocean case the solid interior is not convecting the melt region may cool due to heat transfer to the planet s surface and to the solid region and due to melting of solid the solid region cools by heat transfer to the planet s surface in the mega crater model the viscosities of the melt and the solid are assumed to be dependent on the exponential of the inverse absolute temperature convective heat transfer is parametrized by using semi empirical boundary layer thickness scaling laws most model parameters including planetary size are absorbed into a cooling time scale of the remaining parameters of the scaled model the rate of change of melt viscosity with temperature the surface temperature and for small melt fractions the melt region geometry are most important in determining the cooling time the initial melt temperature the heat capacities of the solid and the melt and the stefan number a measure of the latent heat of melting determine the proportion of the solid that is melted during cooling of the impact melt it is found that almost the whole planet may melt if the impact originally melted half of the planet and if the initial melt temperature was twice a representative planet melting temperature for reasonable choices of parameter values it is found that thermal equilibration of the earth occurs on a time scale of 1 to 10 million years

some geodynamical effects of anisotropic viscosity summary rheological anisotropy in the mantle may arise from various causes the most important are the preferred orientation of single crystals and the orientation of streaks of eclogitic material in a marble cake mantle in both cases the orientation can be achieved by the flow kinematics and in steady state convection the planes of easy slip will eventually be orientated parallel to the stream lines the dynamic equations for a 2 d incompressible anisotropic viscous fluid are derived and some geodynamic consequences are studied a difference of the order 10 100 between shear and normal viscosity is considered post glacial rebound would be affected by the mechanical properties in deeper parts of the mantle the observed uplift history near the ice margin has been taken as argument against strong viscosity stratification in the mantle it is shown here that with strong viscous anisotropy at least in the upper mantle the uplift history is compatible with a significant increase in viscosity between upper and lower mantle the topographic and geoid signal can show a spatial offset from a generating mass anomaly in the mantle this may provide the opportunity for in situ observation of anisotropic flow properties in the mantle in numerical case studies of steady state convection streamline orientated anisotropy is considered at high rayleigh number for bottom heated convection the formation of velocity boundary layers is observed with no flow in the stagnant core of the convection cell with internal heating or strong pressure and temperature dependence of viscosity this is no longer found but in the latter case anisotropy enhances the channelling of flow into lowviscosity regions e g hot rising plumes a few experiments have been performed for time dependent convection the results suggest that the onset of time dependent boundary layer instabilities may be somewhat retarded but would not be strongly suppressed by anisotropy strong time dependence may destroy any large scale coherence in the orientation of anisotropy and thus render the mantle to appear viscously isotropic

the depths of the deepest deep earthquakes the maximum depth of seismic activity is a fundamental observation providing a constraint on models of mantle dynamics although most recent investigations of mantle seismicity and dynamics state that seismicity extends to about 700 km focal depths of 720 km have been reported for large earthquakes as well as depths greater than 800 km for small events we have examined focal depths of events in several catalogs and conclude that 1 the deepest reliable focal depths are at about 670 680 km and events with focal depths beneath 600 km occur in several widely separated geographic regions 2 observations supporting focal depths exceeding 680 km are usually few poor or inconsistent 3 the reduction of seismic activity beneath about 650 km is quite abrupt however we cannot determine whether activity stops completely at 670 680 km or the maximum size of events decreases gradually beneath 650 km with magnitudes of 6 5 7 0 occasionally occurring at 650 km magnitudes of 5 5 6 0 at 680 km 4 0 4 5 at 695 km etc several models can explain the absence of seismic activity in the lower mantle two models are consistent with the abrupt termination of activity at about 650 680 km in widely separated areas a barrier which resists penetration by the subducting lithosphere or a phase transition which modifies the properties of the subducted material as it goes into the lower mantle

lithospheric thinning by midplate mantle plumes and the thermal history of hot plume material ponded at sublithospheric depths mantle plumes supply hot material to the asthenospheric channel which spreads beneath initially normal oceanic lithosphere at midplate hotspots the fate of this material and the thermal structure of the lithosphere depend on the vigor of secondary convection through the steep thermal gradient above the ponded plume material it has been proposed either that 1 secondary convection is so vigorous that material hotter than the normal mantle adiabat is cooled a short distance downstream of the hotspot such that the geotherm resembles that of younger lithosphere or 2 that the plume material retains its excess temperature for a significant time and the lithosphere thins slowly a parameterized method of modeling transient secondary convection is developed to examine this question calculations indicate that secondary convection is likely to be sluggish unless partial melting greatly lowers viscosity in addition vigorous secondary convection would greatly retard upstream asthenospheric flow of plume material beneath the nose of the hawaiian swell and asthenospheric flow of hot material away from hotspots on slowly moving plates like cape verde this conclusion is compatible with limited seismic evidence that indicates that the lithosphere is not detectably thinned beneath the hawaiian swell

volcanic degassing of argon and helium and the history of crustal production on venus we develop a new methodology linking 40ar and 4he degassing to crustal production on venus in order to examine two different scenarios for the history of magmatism on that planet both consistent with recent analyses of the cratering record of the venus surface the first scenario includes episodic global resurfacing events and modest levels of magmatism between such events while the second scenario invokes different rates of steady magmatism before and after a given transition time our degassing models include distinct mantle crustal and atmospheric reservoirs diffusive transfer of 40ar and 4he from the crust to the atmosphere is also taken into account the 40ar abundance in the present atmosphere reflects the integrated degassing and magmatism over most of planetary history in contrast helium escapes from the planetary atmosphere within a characteristic residence time of 200 myr to 1 8 gyr so the present atmospheric 4he abundance is relevant to the volume of magma produced during the last global resurfacing event and the rate of the magmatism subsequent to that event under the first scenario and to the two steady rates of magmatism and the transition time under the second unfortunately large uncertainties in mineral partition coefficients and in the ar and he mixing ratios in the lower atmosphere of venus presently prevent the use of our degassing models to distinguish among crustal formation history models we therefore explore the influence of these uncertain parameters on the degassing history in order to identify those new laboratory and in situ measurements that will most strongly constrain crustal production history as an important step in the development of the ar degassing model the k budget in the bulk silicate fraction of venus is re examined on the basis of venera and vega ray measurements of k u and th concentrations in surface materials for u and th concentrations in the bulk silicate planet of 18 29 ppb and 64 94 ppb respectively the degree of mantle melting that formed the surface materials at the venera 9 and 10 and vega 1 and 2 landing sites is calculated to lie between 0 02 and 0 16 the degree of melting calculated for materials at each landing site is combined with measurements of surface k concentration to estimate the k concentration in the bulk silicate portion of the planet at between 100 and 300 ppm these results suggest that venus and earth have similar heat production

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

mantle convection with spherical effects results of a similarity theory for spherical mantle convection are presented the single mode mean field equations are analyzed for convection which is so vigorous that temperature disturbances become localized in thin thermal boundary layers our purpose is to study effects of spherical geometry density interfaces heat source distribution and cell size steady state solutions are found for isoviscous spherical shells in which the field of motion is spatially periodic in a single spherical harmonic degree calculations are carried out over the range 2 l 40 and for various fractions of internal versus base heating three configurations are examined 1 convection in a single layer of cells extending through the whole mantle 2 convection in two layers separated by a density interface at 670 km depth and 3 convection in a single layer terminating at 670 km results of these calculations are used to give estimates of surface horizontal velocities in terms of the heat loss viscosity stratification amount of internal heating and depth of circulation the surface velocity is most strongly affected by the thickness of the convecting shell deep mantle convection can achieve surface velocities which agree with observed plate speeds while convection restricted to the upper mantle does not at least on the scale of the major plates the temperature distribution is strongly affected by the spherical geometry and by the presence of density interfaces the principal difference between convection in one and two layers is that the latter produces a hot lower mantle while the former produces a warm one

glacial isostatic adjustment i the forward problem summary the isostatic adjustment of a radially stratified visco elastic spheroid is treated using space time green functions for the associated surface mass load boundary value problem these impulse response functions are convolved with a heaviside function to give the time dependent deformation of the planet which would be produced by a unit point mass brought up from infinity at t 0 and allowed to remain on the surface the resulting heaviside green functions can be employed to simulate all of the important signatures of glacial isostatic adjustment given a space time dependent surface mass load consisting of ice sheet ablation histories and a model of the simultaneous filling of the ocean basins these source terms are simply convolved with the heaviside green function appropriate to a specific response signature a realistic model of the spatial distribution of the main late pleistocene ice loads and of their temporal disintegration is constructed the response of two visco elastic earth models is computed and compared to a global set of relaxation data relative sea level curves on the basis of this initial comparison of theory and observation the possibility that the lower mantle has a viscosity which is significantly in excess of the viscosity of the upper mantle is excluded in addition clear evidence of the presence of the lithosphere has been found in relaxation data from sites which were near the edge of the laurentide ice sheet such data should therefore prove useful as a basis for analysis of lateral variations in lithosphere thickness further extensions of the calculation are suggested

regionalized models for the thermal evolution of the earth abstract traditional models for the heat loss in oceanic and continental regions are combined into a regionalized model for the thermal evolution of the earth the need for regionalization is obvious when one considers that the mantle loses 3 to 4 times as much heat per unit area in oceanic regions than in continental areas the present day rate of heat loss together with a geochemical estimate of the concentration of heat producing elements in the earth fixes the response time of the thermally convecting mantle the response time in turn can be used to select the most reasonable representation for mantle convection in terms of the sensitivity of viscosity on temperature and layering versus mantle wide circulation present geochemical estimates of the bulk composition of the earth are most easily reconciled with the observed heat flow if the mantle is layered and its rheology is slightly less temperature dependent than generally assumed the layered system can produce sufficiently high temperatures to explain the high magnesian komatiites of the archean one difficulty with the models is that they predict widespread melting at shallow depth in the early stages of earth history but do not address how such melting affects and alters the heat transfer mechanisms

interpretation of the d zone at the base of the mantle dependence on assumed values of thermal conductivity a common assumption in modeling dynamic processes in the earth s lower mantle is that thermal conductivity is sensibly constant throughout the lower mantle and equal to approximately 4 w m 1 k 1 this value is the result of extrapolation using a linearized theory with estimated parameters for lattice contributions to thermal conductivity furthermore this value is highly dependent on the assumed geotherm excluding theoretical uncertainties in the extrapolation recent experimental data for the pressure dependence of conductivity coupled with a revised geotherm lead to substantially higher estimated values for the lower mantle the hypothesis that the seismically resolved anomalous zone at the base of the mantle d is a thermal boundary layer can be questioned in this case of a higher estimation for thermal conductivity

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

parameterized convection and the thermal evolution of the earth abstract thermal convection is an efficient means of extracting heat from the interior of the earth heat lost from the earth s interior comes from the decay of radioactive isotopes and the cooling of the earth to determine the magnitude of each contribution detailed studies of the convective mechanism must be carried out one approach to this problem is to parameterize a nondimensional mantle temperature in terms of the mantle rayleigh number the time variation of the radioactive heat production and the transient cooling of the entire earth are included also included is the differentiation of radioactive isotopes into the continents important conclusions are 1 1 that between 25 and 30 of the surface heat flow can be attributed to the cooling of the earth this gives a mean concentration of uranium in the mantle close to 30 ppb 2 2 that two scales of mantle convection are occurring the first associated with convection of the surface plates and the second a turbulent convection beneath the surface plates 3 3 that the mean temperature of the mantle in archean times was 100 150 k hotter than at present but that the mean thickness of the lithosphere was about one half the present value 4 4 that 60 to 80 of the area of the continents was formed prior to 3 b y b p

coupled magmatism mantle convection system with variable viscosity abstract numerical models are presented for the thermal and chemical evolution of the mantle when it is controlled by both magmatism and mantle convection the mantle is modeled as a fluid with temperature and pressure dependent viscosity in a two dimensional square box heated by incompatible radioactive elements that decay with time the influence of phase transitions at 660 km between the upper and lower mantle is also included magmatism is modeled as permeable flow of magma produced upon pressure release partial melting of the convecting mantle materials it is shown that the mantle may exist in one of two regimes at first when the internal heating rate is higher than a threshold the mantle is on a regime where episodic but active magmatism takes place to make the mantle chemically stratified with the upper mantle occupied by magma residue harzburgite and the deeper part of the lower mantle occupied by basaltic materials there is a chemical discontinuity along the 660 km phase boundary mantle convection occurs as a layered convection punctuated by flushing events and is sluggish except at the time of flushing events owing to the compositional buoyancy from the chemical stratification the flushing events induce vigorous magmatic activity as the internal heating rate falls below the threshold owing to the decay of radioactive elements the thermal and chemical state jumps to another regime in this regime magma does not erupt and mantle convection occurs as layered thermal convection in spite of the stirring due to the thermal convection the chemical discontinuity and a portion of the chemical stratification formed in the earlier regime remains for billions of years the numerical models suggest that a mantle convection was much less active than expected from the strong internal heating and chemically distinct reservoirs are formed in the early earth and once formed b the reservoirs have survived convective stirring for billions of years

hard turbulent thermal convection and thermal evolution of the mantle this article summarizes the results of hard turbulent convection obtained in laboratory experiments and numerical simulations its applications to mantle convection are illustrated by two dimensional numerical solutions to 1 newtonian 2 non newtonian convection and 3 newtonian convection with multiple phase transitions in newtonian mantle convection the transition from soft to hard turbulence is marked by the appearance of disconnected plumes spectral analysis of the time series of the nusselt number reveals the presence of a spectral scaling subrange for hard turbulence but not for soft turbulence in hard turbulence there is correspondence between the spectra in frequency and wavenumber domains the slope of the seismic wave spectra measured from seismology suggests that the mantle convection today is strongly time dependent the transition to hard turbulence takes place at much lower nusselt numbers for non newtonian than for newtonian rheology for the mantle this would have important ramifications non newtonian plumes behave quite differently from newtonian ones in that large curvatures are developed in their trajectories in the hard turbulent regime mantle convection with phase transitions tends to become more layered with increasing rayleigh numbers the style of mantle convection might have changed from a layered to a more whole mantle type of flow with time catastrophic overturns associated with strong gravitational instabilities in the transition zone could be responsible for superplume events

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

convection in a two layer mantle with a strongly temperature dependent viscosity recent geochemical and isotopic data support the hypothesis that the earth s mantle convects in two separate layers with an interface at the 650 km seismic discontinuity this paper studies the implications of this hypothesis with regard to the thermal boundary layers that are expected to develop adjacent to the interface between the convecting layers we are particularly concerned with a possible decrease in the mantle viscosity across this interface in order to study the structure of the thermal boundary layers in a fluid with a strongly temperature dependent viscosity we utilize an approximate method developed by howard 1966 if the upper and lower mantle have the same viscosity law we find that stratified convection requires a lower mantle viscosity which is several orders of magnitude lower than the upper mantle viscosity this is not consistent with studies of postglacial rebound it is possible to obtain a viscosity law for the lower mantle that gives a viscosity nearly equal to that of the upper mantle and reasonable temperatures however the required law is not consistent with the currently available experimental data on lower mantle materials therefore we conclude that thermal arguments favor whole mantle convection

numerical models of thermally and mechanically coupled two layer convection of highly viscous fluids summary numerical solutions for thermal convection of two superposed viscous fluid layers with the same thicknesses as the earth s upper and lower mantles and separated by a fixed horizontal interface are obtained at the onset of convection and in the nonlinear regime several heating configurations and thermal boundary conditions are considered including an isothermal bottom boundary a prescribed heat flux bottom boundary and internal heating with an insulated lower boundary at the onset of convection and with the same material properties in each layer the lower layer is more unstable than the upper layer and long horizontal wavelengths proportional to the lower layer thickness predominate for layers with sufficiently different material properties the upper layer can be more unstable and short horizontal wavelengths proportional to the upper layer thickness can predominate at the onset of convection when the material properties are chosen to make the two layers equally unstable there are two stability curve rayleigh number ra versus wavelength minima with the lower minimum at long wavelength linear stability results typify weakly nonlinear convection except when both layers are equally unstable when the layers have unequal stability the stable layer has a conductive temperature field and its flow is viscously driven by the convective flow in the unstable layer when the two layers are equally unstable both layers are separately convecting even at rayleigh numbers of only twice the critical value for convection onset at large enough supercritical ra the lower layer convects with a long wavelength cell even when linear stability theory predicts short wavelength cells the upper layer always begins convecting with short wavelength cells however the upper layer cell over the lower layer downwelling plume increases in size with increasing ra thus horizontal wavelength plate dimension for example cannot be used to discriminate between whole mantle and layered mantle convection mechanical coupling of the layers downwelling plume over upwelling plume occurs for all cases with the same material properties in each layer and for the case with the same ra in each layer when the material properties of the layers are sufficiently different to produce short wavelength cells at the onset of convection the upper layer has two thermally coupled cells downwelling plume over downwelling plume and a shear zone at the interface over both lower layer plumes a large 50 per cent of total temperature difference across the interface occurs in all cases examined implying that two layer mantle convection should also have a large temperature change across the 670 km discontinuity however temperature dependent viscosity may reduce the magnitude of this temperature difference interpretations of geoid anomalies over subduction zones and seismic traveltime anomalies of slabs should account for possible thermal coupling of separate upper and lower mantle convective systems

heat transport efficiency for stagnant lid convection with dislocation viscosity application to mars and venus mantle convection on mars and venus is likely to occur in the regime known as stagnant lid convection we perform thermal boundary layer analyses as well as finite element simulations of stagnant lid convection with non newtonian viscosity which is believed to be more appropriate for the lithosphere and upper mantle and discuss one particular application of the results the efficiency of heat transport on the terrestrial planets as in the case of newtonian viscosity the efficiency of heat transfer in the stagnant lid regime is extremely low compared to plate tectonics for example in the absence of plate tectonics the mantle temperature on earth which is already close to the solidus would be about 700 1500 k higher for the present day value of the surface heat flux for venus the critical heat flux which can be removed without widespread melting is only 10 20 m w m2 for mars it is 15 30 m w m2 therefore there are no doubts that in the absence of mobile plates the mantle temperature would significantly exceed solidus during planetary evolution it is hypothesized that this could cause one or a combination of two possible processes 1 differentiation of radiogenic isotopes into the crust during early planetary magmatism and 2 initiation of some kind of plate tectonics as a result of plate weakening due to melting

episodic large scale overturn of two layer mantles in terrestrial planets it is usually assumed that the upper and lower mantles of a chemically stratified planet are arranged so that the upper mantle is chemically less dense and that these layers convect separately possible buoyant overturn of the two mantle layers has not previously been considered such overturn would initially occur when thermal expansion of a chemically denser lower mantle more than offsets the compositional density difference between the layers reversing the relative sense of buoyancy once overturn has occurred the chemically denser but thermally less dense upper mantle cools more efficiently than the lower mantle and loses its relative thermal buoyancy if mixing is slow this leads to repeated overturns that result in thermal histories that differ radically from those obtained without this large scale overturning thermal evolution calculations for a two layer mantle over a wide range of parameter space show that large scale overturn occurs cyclically with a well defined period this period depends most strongly on the viscosity of the lower mantle to which it is approximately proportional geologically interesting overturn periods on the order of 107 to 109 years result for lower mantle viscosities of 1022 to 1024 pa s for the earth and venus and 1021 to 1023 pa s for mars the mantles of mercury and the moon are too thin to permit two layer convection and therefore the model is not appropriate for them overturn cannot occur on earth or venus if the compositional density difference between the layers exceeds about 4 or on mars if it exceeds about 2 large scale mantle overturn could have significant tectonic consequences such as the initiation of a new plate tectonic cycle on the earth or a major resurfacing event on mars or venus such episodic events in the evolution of a planet are not easily explained by whole mantle thermal convection

comparison of the dynamic and parameterized models of mantle convection including core cooling the two dimensional cooling model of mantle convection including core cooling was studied the core temperature is assumed to be constant in space but it changes with time because of the convective retrieval of heat the viscosity is also constant in space but it is a function of the area averaged mean temperature in order to check the possible effects of temperature dependent viscosity on the cooling the rate of cooling is controlled by three factors the temperature change of the core by a unit change in the core heat flux the viscosity law governed by the mean temperature and the contribution of the internal heating several different types of temperature field were used as the initial conditions some results showed considerable fluctuations in the relation between the temporal rayleigh number and the nusselt numbers which are appropriately defined for both the upper and lower thermal boundary layers a parameterized model of the cooling history of the mean and bottom temperatures was calculated assuming the power law relation between the rayleigh and the nusselt numbers which is determined by the least square fit of the results of the dynamic calculations for the parameterized models we integrated backward in time the agreement between the dynamic and parameterized calculations is generally good except for the cases when the rate of cooling is large or the decay in internal heating is small when the rate of the cooling is large the lower thermal boundary layer disappears this results in unpredictability of the bottom temperature however this case is not applicable for the earth when the decay in internal heating is small we find that the agreement between the dynamic and parameterized models is sensitive to the change in the amount of internal heating assumed in parameterized models this is because the internal heat source directly affects the rate of cooling the value which is the power index of the nu ra relation varies from 0 3 to 0 4 when the bottom thermal boundary layer becomes weak because of the fast cooling of the core deviates from 0 3 considerably

thermo chemical evolution and global contraction of mercury the very limited amount of global contraction observed on mercury s surface poses severe constraints on models of the planet s thermo chemical evolution and current models rely on a very refractory thorium rich composition to slow planetary cooling however a refractory composition appears to be incompatible with evidence for pyroclastic eruptions which require a substantial amount of volatiles to be present in the planetary interior furthermore volcanic activity appears to have been ongoing for a considerable part of the planet s history while current models predict an early cessation of crustal production to address these inconsistencies we have reinvestigated the thermo chemical evolution of mercury using a non refractory compositional model taking the presence of a thermally insulating regolith layer into account we find that models with a stiff mantle rheology satisfy the observational constraints if the regolith layer is at least 2 km thick in these models inefficient mantle convection and thermal insulation significantly slow planetary cooling and prolong the phase of crustal production to 2 5 gyr after core formation allowing the volume increase associated with mantle differentiation to offset some of the radial contraction caused by planetary cooling models furthermore predict substantial core sulfur contents above 6 wt average crustal thicknesses between 10 and 40 km and secular cooling rates of 30 k gyr

adiabats of quartz coesite olivine and magnesium oxide to 50 kbar and 1000 k and the adiabatic gradient in the earth s mantle the adiabats of olivine magnesium oxide and quartz were measured up to 50kbar and 1000 k an end loaded piston cylinder apparatus with an in situ pressure gauge and a very fine thermocouple was used to measure t p s during adiabatic compression a power law between t p s and compression yields values of the power n ln t p s ln that agree with previous results from salts metals and fluids assuming constant values for n the adiabtic gradient for an olivine upper mantle and a magnesium oxide lower mantle was calculated the results agree well with some previous theoretical estimates the volume dependence of the gruneisen parameter was calculated from the thermodynamic equation ln ln b p n where b is the isothermal bulk modulus is found to a good approximation to be proportional to volume table 6 is available with entire article on microfiche order from american geophysical union 2000 florida avenue n w washington d c 20009 document j82 002 1 00 payment must accompany order

viscosity structure of a layered convecting mantle since the formulation of plate tectonics1 there has been vigorous debate among geophysicists and isotope geochemists concerning the depth extent of mantle flow associated with lithospheric plate motions2 9 some believed that the flow is confined to the upper mantle2 3 6 others that the flow may penetrate deeper or throughout the mantle4 5 8 9 recently it was suggested 9 10 that if the lower mantle convected separately then it would probably be so hot that it would melt extensively in its upper portion as there is no evidence for such melting it was concluded that whole mantle circulation was more probable here i present a related but more robust argument which leads to the same conclusion i demonstrate that in a layered mantle the lower mantle would probably have a viscosity two to three orders of magnitude less than the upper mantle and this is probably incompatible with observational constraints

destabilization of a 650 km chemical boundary layer and its bearing on the evolution of the continental crust a mechanism for the production of a chemical change in the mantle from primordial silicate compositions above the 650 km discontinuity to differentiated compositions below is reviewed some consequences of this are the stabilization of two layer convection with a temperature contrast between the anhydrous mantle solidus and the geotherm which at 650 km depth is lower than any other location in the mantle with thermal contributions from the concentration of the heat producing elements u th and k below the 650 km mantle boundary layer and the higher geotherms in the past widespread or catastrophic melting may have taken place at this location an episodic breach of this boundary layer by extensive heat and mass transport may have periodically destroyed any simple two layer convection geometry in the mantle such episodic injections of mass and energy into the upper mantle from below may have been the mechanism responsible for episodes of enhanced surface tectonism and thermal activity which appear to be recorded in apparent polar wandering paths and radiometric ages of continental rocks

a simple model of whole mantle convection isotopic evidence of the chemical variability of basalts implies the existence of distinct long lived chemical reservoirs in the mantle this has commonly been interpreted as evidence that mantle convection is layered since known models of whole mantle convection have too much shearing to allow preservation of these reservoirs however the geochemical evidence requires at least three reservoirs and models of layered convection have dynamical difficulties casting serious doubt on the viability of these models this difficulty has been resolved in the present paper by the development of a simple model of whole mantle convection which allows the preservation of chemically distinct reservoirs in this model heating of the mantle from below produces axisymmetric plumes which carry heat upward through the mantle without causing overturning hence the lower mantle is much less sheared than in the usual two dimensional model mantle convection is driven by the penetration of cold lithospheric slabs from above it is argued that the pattern of convection is governed primarily by the dependence of viscosity on temperature and this dependence drives the mantle toward an isoviscous state these ideas are quantified in a simple one dimensional model of mantle convection in which the slab mass flux as a function of radius is governed by the requirement that the temperature profile remains isoviscous the resulting convection cycles material through the upper mantle more rapidly than through the lower mantle this provides a mechanism for an initially homogeneous mantle to become chemically stratified with a depleted upper mantle and primitive lower mantle

possible flush instability in mantle convection at the archaean proterozoic transition the late archaean eon 3 to 2 5 billion years ago seems to have been a time of profound geological changes1 5 rapid growth of the continents of the volume of cratonic sediments and of the area of the continental shelves was accompanied by widespread emplacement of potassium rich granitic rocks leading to the cratonization of the continental crust3 6 there is also evidence for climate change7 8 at this time possibly reflecting changes in the composition of the atmosphere and the volume of the oceans the period ends with the huronian glaciation the first well documented glacial episode9 and this transition appears to be marked by a strong increase in the intensity of the geomagnetic field10 here we present simulations of mantle convection at the end of the late archaean and show that a breakdown of two layer convection a flush instability11 occurring at this time could have led to a period of volcanic and tectonic activity that might account for the reported geological and palaeoenvironmental changes

gradual entrainment of a chemical layer at the base of the mantle by overlying convection summary a dense chemical layer may exist at the base of the mantle the overlying convection tends to entrain some of this layer reducing its thickness through time the lower more dense fluid is dragged into cusps beneath upwelling limits of the overlying convection and some material is entrained it is obvious that a high density of intrinsically more dense material retards this entrainment an upper limit and probably a reasonable estimate for the amount of entrainment is obtained by considering the carrying capacity of the vertical flow above cusps and ignoring the complications within the cusps themselves flow through conduits formed by the reduced viscosity of hot material is less effective at entrainment than broad scale flow controlled by the background viscosity of the normal mantle cylindrical plumes are less effective at entrainment than 2 d flow intrinsic density contrasts of around 6 per cent are needed for the layer to persist through geological time assuming the thermal expansion coefficients is 2 10 5 in addition the chemical layer may convect internally this causes the layer to entrain less dense material from above and thus aids entrainment from above by reducing the excess density of the layer convection in the chemical layer and stripping of the layer into cusps by the overlying flow also cause much of the temperature contrast to be in the overlying mantle rather than the chemical layer the difficulty of having more than a few 100 k temperature contrast across the layer unless it is internally stratified negates a reason for supposing the layer exists

melting temperature of the earth s mantle and core earth s thermal structure abstract although the temperature at the top of the lower mantle is well constrained by phase equilibrium data for the transformation of transition zone minerals to the denser perovskite polymorphs the temperature distribution in the lower mantle is poorly known models depend strongly on the assumptions of the amount of internal heating and the viscosity profile new melting data on iron to pressures of the outer core 2 mbar and the observed strong decrease of eutectic melting depression in the fe feo fes system with increasing pressure however tightly constrain the temperature at the inner core boundary to slightly less than 5000 k this estimate can be reconciled with all recent static melting measurements on iron and lays within the uncertainty of shock temperature measurements the resulting temperature at the core mantle boundary of about 4000 k then requires a large temperature gradient at the bottom of the lower mantle of about 1500 k recent findings of the very high melting temperatures o

parameterized thermal convection in a layered region and the thermal history of the earth parameterized convective schemes for constant viscosity fluids are used to investigate the influence of layering on the relationship between the rate of heat loss from and heat supply to a number of convecting layers of different viscosity and thicknesses simple analytic expressions are obtained which accurately predict the behavior to a step decrease in the heat supply and show that layering considerably increases the response time the same arguments are applied to a planet consisting of spherical shells they show that the response of the earth s heat loss to the decay of radioactive elements depends strongly on whether or not mantle convection extends from the core to the surface if it does so the surface heat flux is only about 50 greater than the heat generation rate however if upper and lower mantle convection occurs in two separate shells as seismological and geochemical arguments suggest the response time is increased the present surface heat flux is then principally controlled by the thermal structure of the earth at the time it was formed the best estimate of the present ratio of the heat loss to heat generation is about two and this value is consistent with the behavior of an earth model consisting of a two layered mantle overlying a core

on some consequences and possible causes of layered mantle convection laboratory and numerical experiments are used to study convection confined to discrete layers the laboratory experiments which use the water content of a predominantly glycerine solution as a way of establishing chemical density variations show that convection will remain confined to superimposed layers when the chemical density contrast between layers is greater than the density change associated with the greatest temperature difference within the convecting system the numerical experiments show a double thermal boundary layer at the interface between layers a feature that would result in an average temperature increase of about 500 c in the mantle near 700 km depth if the lower mantle is isolated as suggested by recent geochemical models the possible causes of a layered mantle convection system include major element chemistry variations the combined effect of major element chemistry and a phase change or a phase change alone if it has a sufficiently negative clapeyron slope

the system al2o3 p2o5 h2o at temperatures below 200 c experimental data on the stability of variscite and metavariscite alpo4 2h2o the system al2o3 p2o5 h2o contains many phosphate minerals that occur in various geologic environments the natural occurrence of variscite alpo4 2h2o orthorhombic including its monoclinic polymorph metavariscite is largely restricted to soils and aluminous rocks like al rich igneous rocks and shales which interacted with p rich hydrothermal solutions or groundwater variscite dehydrates to berlinite alpo4 and a hydrous p al rich fluid this dehydration reaction alpo4 2h2o alpo4 2h2o is however metastable at low concentrations of p in the fluid because berlinite breaks down at lower temperature to augelite al2po4 oh 3 h3po4 h2o and trolleite al4 po4 3 oh 3 h3po4 h2o the variscite metavariscite berlinite equilibrium has been investigated by synthesis experiments from mixtures of al2o3 and excess phosphoric acid at pressures between 1 and 5 kbar and temperatures of 100 200 c using standard cold seal vessels the hydration dehydration equilibrium is mainly controlled by temperature and only weakly by pressure at 4 and 5 kbar variscite metavariscite were found at temperatures of 150 c at lower pressure at 115 125 c in accordance with their natural mode of occurrence in this t range however variscite metavariscite is not the sole phase but is always accompanied by variable but generally minor amounts of wavellite and trolleite al4 po4 3 oh 3 secondary wavellite al3 po4 2 oh 3 5h2o hydrated al phosphate alpo4 x h2o 1 1 x 1 3 and al metaphosphate hexahydrate al h2po4 3 formed during quenching and or drying of the runs berlinite is the reaction product at temperatures 200 c 4 5 kbar and 150 c 1 3 kbar and may be associated with augelite and trolleite

a test of approximations for modeling convection with temperature dependent viscosity abstract we compare two approximations for describing the influence of temperature dependent viscosity on thermal convection namely i depth dependent viscosity that is controlled by the horizontally averaged temperature and ii viscosity that depends only on the global mean temperature we perform two dimensional 2 d numerical simulations with both rigid and free slip upper boundaries and time decaying heating from within and or from the bottom monitoring the evolution of the mean temperature and surface heat flow we find large differences between the results of approach ii and those of the reference model with full temperature dependence of viscosity for approach i we get good agreement especially in the stagnant lid regime of convection we recommend this approximation as a useful tool for modeling mantle convection and thermal evolution in planets with a stagnant lithosphere

influence of a variable thermal conductivity on the thermochemical evolution of mars 1 the influences of variations in thermal conductivity due to composition temperature and pressure in mantle and crust on the thermochemical evolution of mars have been examined with parameterized convection models we use a temperature and pressure dependent thermal conductivity in the mantle and column averaged values between 1 5 and 4 wm 1k 1 for the crust with 2 wm 1k 1 as the representative value for a basaltic crust the major characteristic of the models is a slower cooling of the upper mantle with a long existing global partial melt zone and a stronger crustal production late in the evolution compared to earlier models which assume a constant thermal conductivity of 4 wm 1k 1 to explain the observed crustal thickness and the early crustal formation on mars the formation of an enriched primordial crust is required recent volcanism can be explained by lateral temperature variations that are caused by thickness variations of the low conducting crust these melt zones which occur underneath thicker than average crust may be the source region for the observed longstanding volcanism in tharsis and elysium instead of plumes rising from the core mantle boundary the evolution of the elastic lithosphere is characterized by a transition at which the elastic strength is first provided by the crust and later also by the upper mantle this finding may explain the estimated elastic lithosphere thickness of less than 16 km in the noachian and more than 100 km in the hesperian and amazonian

thermochemical structures within a spherical mantle superplumes or piles 1 heterogeneous compositional mantle models are frequently invoked to explain some observations obtained from geochemistry and seismology in particular two regions in the earth s lower mantle under the pacific and africa are often interpreted as being either piles or superplumes of dense material we perform numerical modeling of thermochemical convection in a three dimensional spherical geometry to investigate whether the geometry can focus a dense chemical component into a small number of isolated rounded piles or superplumes of material we study the effect of temperature and compositionally dependent viscosity and we find two different modes of dense layer deformation temperature dependent rheology leads to a low viscosity dense layer which is passively swept aside by downwellings into linear piles that are spread throughout the entire lower mantle the addition of compositionally dependent rheology in which the dense layer is more viscous results in active deformation of the dense material forming large isolated superplumes our results indicate that piles and superplumes are separate features which in general do not occur together and in order for isolated rounded superplumes to form an intrinsic compositional viscosity increase is required for the dense material

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

non newtonian stagnant lid convection and magmatic resur facing on venus abstract mantle convection on venus is likely to occur in the regime known as stagnant lid convection we investigate this regime for internally heated convection with temperature and pressure dependent power law viscosity dislocation creep scaling relationships obtained for large aspect ratio convection are different from steady state square box calculations but agree well with scaling theory and boundary layer stability analysis results for arrhenius viscosity and pressure dependent viscosity show that the efficiency of heat transport is sensitive to the viscosity function at the bottom of the lid new scaling relationships are applied to parameterized convection calculations of the thermal history of venus assuming that plate tectonics could not occur during evolution the onset of convection beneath the lid is delayed even for initial potential temperatures near the solidus during the conductive regime melting is suppressed due to the development of a thick cold lid at the surface after convection begins the lid becomes thinner and the planet undergoes a period of widespread melting and volcanism the timing of the beginning and ending of melting depends on various factors such as the initial conditions and mantle rheology the episode of melting predicted by the models can be reconciled with the cessation of global resurfacing on venus 300 800 myr ago the models yield present day lithospheric thicknesses around 200 km which is similar to previously suggested estimates

thermodynamically consistent decompression implications for lower mantle composition estimates of the composition of the lower mantle are commonly obtained by a process of adiabatic decompression in which zero pressure mantle parameters are determined with a least squares fit of an equation of state to mantle densities we show that this procedure may lead to biased estimates of the zero pressure density and compressibility of the mantle the bias can be eliminated or minimized by subjecting the equation of state fit to a thermodynamic constraint at zero pressure such inversions provide equations of state that are compatible with the lower mantle as well as the thermal properties of selected mineral models we used this method to evaluate assemblages containing mg fe sio3 perovskite and mg fe o with fe fe mg ratios as high as 0 2 thermodynamic systematics were used to place bounds on the anderson gruneisen parameter s for perovskite we find a fairly large range of acceptable models for the composition of the lower mantle they range from uppermantle like compositions to assemblages that are enriched in both si and fe relative to the upper mantle however a pure perovskite lower mantle whether enriched in fe or not seems improbable small fe enrichments of the order of 1 given density contrasts across the 670 km discontinuity that are probably insufficient to prevent convective mixing of the upper and lower mantles we therefore suggest that unless the mantle is homogeneous in its major oxide components the lower mantle is likely to be enriched in fe by at least several percent

modeling the distribution of isotopic ratios in geochemical reservoirs abstract we present an extension of the conventional geochemical reservoir model for the evolution of the earth s crust mantle system in which we calculate not only the mean isotopic ratios but also the distribution of those ratios within the reservoirs owing to low chemical diffusion rates subreservoirs that are created by mass transport into and out of the mantle effectively exist as distinct geochemical entities for all time by tracking these subreservoirs we obtain a model of the full range of isotopic values represented in the mantle using results from numerical calculations of mixing we also track the length scales associated with each subreservoir applying simple statistics we obtain the distribution of expected measurements as a function of the stirring time effective melt fraction sampling volume and mass transport history we present calculations of isotopic heterogeneity for two simple mantle evolution models and explore the sensitivity of geochemical observables to the variables mentioned we focus on the rb sr and sm nd systems and are able to reproduce much of the observed complexity of oceanic basalts we infer that the stirring time of the mantle falls between 250 and 750 myr and that the initial length scale of mantle heterogeneity before stirring is of the same order as the length scale of sampling we also conclude that the differences between isotopic data from mid ocean ridge basalts and ocean island basalts cannot simply be due to differences in sampling volume but must also reflect differences in the source reservoirs and or melting processes increasing the size of the ocean island basalt source region by 45 with respect to the mid ocean ridge basalt source region reproduces the offset between the two distributions but still fails to explain the more isotopically extreme measurements our results show that the argument suggesting that the absence of samples with a primitive isotopic signature indicates that no primitive material remains in the mantle is not valid

reconstruction of a destructive debris flow event via numerical modeling the role of valley geometry on flow dynamics debris flows are widespread natural phenomena characterized by high mobility high velocity and long runout distance and impact forces which frequently cause human casualties and significant damage to infrastructure to better understand the dynamics of such events analyzing in particular the effect induced by the valley geometry on flow velocity runout and mobilized volumes in this work we reconstruct a real debris flow event through numerical modeling specifically we used a modified version of the bing model a fluid dynamic depth integrated numerical model for debris flows which has been properly modified to account for width changes along the valley the studied event which occurred in scaletta zanclea messina north eastern sicily italy on october 1 2009 is exceptionally well constrained by field and topographic information in this respect the flow velocity estimated from two specific locations on the basis of field evidence the distribution of erosional and depositional areas along the racinazzo valley based on the comparison of pre and post event digital elevation models dems and the runout distance were used as constraints to calibrate the model furthermore we report a detailed description of the main event characteristics based on hydrological records and witness reports the numerical modeling results are consistent with witness reports and the severe damage recorded in the scaletta marina village and highlight the effect of the valley geometry on both the debris flow velocity and the erosion deposition processes the effect of changing valley width has been also quantified resulting in accelerations of the debris in correspondence of the valley narrowing and stagnations at the plateaus copyright 2015 john wiley sons ltd

modelling planetary dynamics by using the temperature at the core mantle boundary as a control variable effects of rheological layering on mantle heat transport abstract in planetary convection there has been a great emphasis laid on the usage of the rayleigh number as a control parameter for describing the vigor of convection however realistic mantle rheology not only depends on temperature pressure strain rate and composition but also on the nature of the dominant creep mechanism which varies with pressure and also with temperature it is difficult to study the effects of varying influences from the convective strength without also changing the mantle flow law in the process we have adopted the approach of using as the sole control parameter the temperature at the core mantle boundary t cmb in modelling planetary dynamics with a composite non newtonian and newtonian rheology which is temperature dependent in the upper mantle and both temperature and pressure dependent in the lower mantle increasing the t cmb strengthens convective vigor and leads to a non linear increase of averaged temperature heat flow and root mean squared velocity the interior viscosity decreases strongly with t cmb and internal heating due to radioactivity a viscosity maximum is found in the horizontally averaged viscosity profile at a depth around 2000 km this viscosity hill moves downward with diminishing amplitude in the face of increasing dissipation number and internal heating the bottom third of the lower mantle appears to be superadiabatic as a consequence of the stiff lower mantle rheology the scaling relationship between the nusselt nu number and t cmb shows a relatively insensitive increase of nu with t cmb in terms of an effective rayleigh number of the whole system ra e the power law exponent of the nu ra e relationship is very low around 0 12 strong pressure dependence of lower mantle rheology and its large volume relative to the entire mantle would induce a much lower cooling rate of the planet than previous models based on parameterized convection with a temperature dependent viscosity

timing of gold and arsenic sulfide mineral deposition at the getchell carlin type gold deposit north central nevada pregold mineralization at the getchell carlin type gold deposit includes quartz and base metal vein mineralization associated with intrusion of a cretaceous granodiorite stock the veins contain minor pyrite and trace chalcopyrite arsenopyrite galena and sphalerite the pyrite is moderately coarse and in thin section has high relief is well polished and is fractured and locally cemented by the gold ore assemblage white micas are associated with veins near the granodiorite intrusion gold was not observed or detected by fire assay analyses of samples or electron microprobe analyses of pyrites microprobe analyses show that pregold pyrites have near stoichiometric compositions variable low arsenic is present in pyrite in samples overprinted by gold mineralization secondary ion mass spectrometry sims analyses detected trace gold in the coarse near stoichiometric pyrite in overprinted samples the pregold vein assemblage was fractured and cemented by gold ore stage mineralization the gold ore stage assemblage consists of gold and arsenic enriched pyrite and marcasite encompassed by jasperoid and drusy quartz and local late fluorite orpiment and galkhaite the consistent spatial association of jasperoid and ore pyrite reflects their near contemporaneous formation the ore pyrite occurs as either fine irregularly shaped grains or rims on earlier gold free pyrite in thin section the pyrite is visibly distinct and has a low polishing relief and a poor polish sims and electron microprobe analyses show that ore pyrites commonly contain 8 to 11 wt percent arsenic and as much as 2 400 ppm gold near the end of the ore stage fluorite orpiment and galkhaite precipitated locally in open space created by faulting or limestone dissolution late ore stage mineralization consists dominantly of open space filling realgar and calcite with minor quartz stibnite and framboidal pyrite realgar conforms to euhedral crystal faces of ore stage quartz fluorite and galkhaite calcite filled most remaining open space and conforms to euhedral crystal faces of quartz fluorite and realgar significant textural observations argue against an earlier interpretation that the gold mineralization and arsenic minerals formed as two discrete events separated by 40 m y in a few areas where calcite and realgar are in contact with ore stage quartz containing gold bearing pyrite realgar and calcite enclose gold bearing pyrite grains massive realgar and calcite distal from these contacts do not contain the gold bearing pyrite the presence of ore pyrite in realgar calcite and jasperoid requires close timing of these minerals and shows that there is no major time break separating ore stage and late ore stage mineral deposition textures indicate instead that the ore stage and late ore stage formed as part of a single evolving hydrothermal system the consistent successive overgrowth of younger minerals on perfectly preserved euhedral faces of older minerals supports the continuous evolution of the gold ore stage into the late ore stage these results are consistent with fluid inclusions that indicate that paragenetically successive minerals precipitated from an aqueous ore fluid with consistent salinity and gas contents but at declining temperatures results show that within error the 34 39 and 42 ma ages determined for fluorite and galkhaite at getchell and adularia at the nearby twin creeks mine respectively most closely approximate the timing of gold deposition at getchell

thermal state and thermal regime of the earth s interior abstract a simplified version of the thermal state and thermal regime of the earth s mantle is given it is supposed that the large scale convection in the mantle is double layered convection in the upper mantle is determined by heat flux from below and in the lower mantle by internal heating it is estimated that the thermal relaxation time of the upper mantle is 10 8 y and the time of the thermal relaxation of the lower mantle lm is 1 5 10 9 y the thermal relaxation of the earth is determined by lm in the convective mantle the superadiabatic temperature drops are formed in the thermal boundary layers in the upper mantle t 1 is 600 k at the top of the lower mantle t 2 is 650 k at the bottom of the lower mantle t 3 is 650 k the adiabatic temperature at the core mantle boundary is 2900 k and the real temperature must be 3500 4500 k the thermal boundary layers in the mantle are the super heated zones and must coincide with low q zones q is the mechanical quality for s waves the first zone of low q is at a depth of 100 250 km the second one is at 670 850 km and the third one is at 2700 2900 km the source zone for hot spots may be in the second thermal boundary layer it is interesting that the horizontal velocity of the layer which is 1 cm y 1 must determine the limits of precision for absolute velocities in plate tectonics the boundary between the upper and lower mantle must be the weak chemical boundary because the upper mantle is the source for the earth s crust the thermal regime and instability of the third thermal boundary layer at a depth of 2600 2900 km may play a very important role in the magnetohydrodynamics of the earth s core and particularly for the change in polarity of the geomagnetic dipole and for understanding the geomagnetic time scale

layered mantle convection a model for geoid and topography the long wavelength geoid and topography are dynamic effects of a convecting mantle the long wavelength geoid of the earth is controlled by density variations in the mantle and has been explained by circulation models involving whole mantle flow however the relationship of long wavelength topography to mantle circulation has been a puzzling problem in geodynamics we show that the dynamic topography is mainly due to density variations in the upper mantle even after the effects of lithospheric cooling and crustal thickness variation are taken into account layered mantle convection with a shallow origin for surface dynamic topography is consistent with the spectrum small amplitude and pattern of the topography layered mantle convection with a barrier about 250 km deeper than the 670 km phase boundary provides a self consistent geodynamic model for the amplitude and pattern of both the long wavelength geoid and surface topography

chemical stratification in the silicate earth abstract the largest density contrast between magmas and common ferromagnesian minerals in the mantle occurs at two locations these are nearest the earth s surface and at about 650 700 km depth where the lower mantle mineral assemblage becomes stable at solidus temperatures the large density contrast between magmas and olivine nearest the surface diminishes to zero somewhere between the middle and lower stratigraphic sections of the upper mantle it is also here where the composition of all anhydrous magmas is most similar to that of an undepleted garnet iherzolite composition for an earth that has differentiated by fractional crystallization and melting processes which depend on the separation of crystalline phases from silicate liquids having different densities the 650 km discontinuity could represent a chemical boundary layer the chemical change in the early archean could have been from primordial upper mantle compositions above the boundary layer to differentiated lower mantle compositions below a primary stratigraphic model is offered for the distribution of depleted enriched and primordial isotopic mantle components formed by the transport fate of magmas in the beginning of earth history depleted morb source regions were established in the uppermost part of the upper mantle primordial mantle was located at the middle to the deepest regions of an upper mantle which was processed by anhydrous melting and crystallization enriched and depleted components could have been formed at these levels also by igneous processing in the presence of h 2 o or co 2 and involving highly compressible magmas the lower mantle became heterogeneous with enrichments at the top and depletions elsewhere it is suggested that the present day isotopic structure of the mantle has inherited elements of this primary stratification primordial 143 nd 144 nd and 87 sr 86 sr observed in oceanic islands basalts are located in the middle of upper mantle convection cells enriched ratios found in both oceanic islands basalt and kimberlite could have originated near and on either side of the 650 km chemical boundary layer

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

two layer mantle convection and the depletion of radioactive elements in the lower mantle only a small percentage of the mantle s total content of radioactive elements can be in the lower mantle if this region convects steadily and separately from the upper mantle recent geochemical models of a depleted upper mantle and an undepleted lower mantle are thus inconsistent with a steady thermal model involving distinct upper and lower mantle convection cells steady two layer mantle convection requires a depleted lower mantle and an undepleted upper mantle to match the observations of surface heat flow and mantle viscosity the constraint on the abundance of radioactive elements in the lower mantle depends on the existence of at least one thermal boundary layer at the upper mantle lower mantle interface with thickness comparable to that of the surface thermal boundary layer since the temperature drop across an interface boundary layer is limited by the relatively small difference between the solidus temperature and the upper mantle temperature the amount of heat which can be transferred across this layer is small compared with the surface heat flow the upper limit on the concentration of radioactive elements in the lower mantle can be relaxed only if both the lower boundary layer of the upper mantle cell and the upper boundary layer of the lower mantle cell are extremely thin or absent altogether which we consider however highly unlikely

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

convection experiments in high prandtl number silicones part 2 deformation displacement and mixing in the earth s mantle the evolution of structures in the earth s convecting mantle is studied in a simple but carefully scaled laboratory flow the geometrical scaling is constrained by the various geometries of convection cells possible in the earth s interior two layered mantle convection with a superposed small scale circulation in the top is favoured here the model flow has a rayleigh number 104 a prandtl number 108 and approximately axially symmetric cells with aspect ratio of unity the rheology and boundary conditions are aimed to be dynamically similar to that occurring in the mantle the flow is analysed on the basis on snapshots showing the progressive deformation and displacement of passive flow markers which allow the reconstruction of velocity vectors strain rate and vorticity inferences can be made about 1 1 the progressive deformation in individual rock masses and 2 2 the nature of the large scale mixing process caused by a combination of deformation and displacement in a convecting mantle this is discussed in terms of the kinematic vorticity number both geological and fluid mechanical studies of low inertia flows may benefit from the new experimental technique and analyses presented here until now it has been impossible to visualize and quantify the finite strains and rotation components of deformation in flowing fluids by other than numerical methods the laboratory method advocated here is quick and involves equipment which is relatively cheap if compared with those required for numerical analyses basic understanding of elementary fluid dynamics is sufficient to perform innovative investigations in this new field

reflection properties of phase transition and compositional change models of the 670 km discontinuity seismic observations of the amplitude ratio amplitude p 670p amplitude p p suggest a reflection coefficient r 7 13 for reflections from the underside of the 670 km discontinuity this can be compared with calculated reflection coefficients to constrain the nature of the mantle transition region velocity and density profiles through the transition region were calculated for olivine pyroxene garnet and olivine garnet model mineral assemblages for models with identical upper and lower mantle compositions the computed reflection coefficients from the phase transitions pertinent to the 670 km discontinuity are less than 0 5 these phase transitions produce their maximum r if they are effectively discontinuous which gives r 2 3 except for the garnet to perovskite transformation which gives r 8 in general given realistic impedance contrasts across a phase transition the change in material properties must occur over a region less than 3 km thick for r to be of the order of 5 a discontinuous change in chemical composition at 670 km depth coupled with a change in phase can also produce a reflection coefficient of the observed magnitude r 2 3 for a first order change in phase at 670 km with different iron concentrations on each side of the discontinuity and r 4 6 for cases with a discontinuous increase in silica content based on our analysis the thermal and chemical boundary layers which would occur across such a chemical discontinuity would probably have negligible effects on the reflection coefficient thus although limited by considerable uncertainties the mineralogical and seismic data suggest a two layered model of the mantle with a discontinuous change in both phase and composition at 670 km

hotspots basalts and the evolution of the mantle the trace element concentration patterns of continental and ocean island basalts and of mid ocean ridge basalts are complementary the relative sizes of the source regions for these fundamentally different basalt types can be estimated from the trace element enrichment depletion patterns their combined volume occupies most of the mantle above the 670 kilometer discontinuity the source regions separated as a result of early mantle differentiation and crystal fractionation from the resulting melt the mid ocean ridge basalts source evolved from an eclogite cumulate that lost its late stage enriched fluids at various times to the shallower mantle and continental crust the mid ocean ridge basalts source is rich in garnet and clinopyroxene whereas the continental and ocean island basalt source is a garnet peridotite that has experienced secondary enrichment these relationships are consistent with the evolution of a terrestrial magma ocean

on the spatial variability of the martian elastic lithosphere thickness evidence for mantle plumes 1 the present day elastic lithosphere thickness at the martian north pole has recently been constrained to de 300 km and this is a factor of 3 4 larger than elastic thickness estimates for other amazonian surface features like the tharsis volcanoes here we present a model for the martian elastic lithosphere thickness which takes the locally varying crustal thickness the local concentration of heat producing elements as well as variations of strain rate into account the model predicts de 196 km at the north pole today whereas elastic thicknesses at the tharsis volcanoes are best compatible with middle to late amazonian loading ages therefore although a large degree of spatial heterogeneity can be explained by the presented model large elastic thicknesses in excess of 300 km cannot be reproduced in order to fit all elastic thickness estimates derived from observations mantle heat flux at the north pole needs to be reduced by 35 however this can only be reconciled with a bulk chondritic concentration of heat producing elements in the martian interior if the excess heat is deposited elsewhere therefore this argues for the presence of recently active mantle plumes possibly underneath tharsis the size and strength of such a plume can be constrained by the elastic thickness at the tharsis montes and maximum average heat flux between 8 and 24 mw m 2 corresponding to a central peak heat flux of 40 to 120 mw m 2 is consistent with the observations such a plume would leave a clear signature in the surface heat flux and should be readily detectable by in situ heat flux measurements

a simple parameterized model of earth s thermal history with the transition from layered to whole mantle convection abstract recent studies of mantle convection suggest a possible scenario for earth s history in which the convection has changed its style from layered to whole mantle because of the existence of an endothermic phase boundary to understand the possible thermal consequence of this transition we shall re examine the thermal history of earth with different types of convection mode i e whole mantle convection layered mantle convection and convection with a transition using a simple parameterized scheme for the whole mantle convection model we shall confirm the results presented by previous workers i e a small of 0 2 with a high urey ratio 0 8 this is almost identical to the whole mantle case the implication is that because whole mantle convection is powerful enough earth may loose the memory of early layering that may have existed more than 1 ga b p the change in flow velocity associated with the transition is expected to be a factor of five or more the temperature of the upper mantle before the transition took place may be lower than the present mantle temperature

onset of mantle plumes in the presence of preexisting convection the onset of plumes where broad scale convection already exists is investigated along with the thermal history of the earth geological evidence relating to the onset time of mantle plumes is not definitive no well defined hotspot tracks older than mesozoic have been identified but it is difficult to tell whether this absence is a reliable indication of a late onset of mantle plumes since only continental crust of this age exists using the hotspot track distribution for the pacific the absence of pre mesozoic hotspot tracks on the canadian shield cannot easily be attributed to chance however young continental hotspot tracks are controversial and it is not clear whether tracks such as the monteregian hills white mountain magma series would be recognized as such without considering the contributing evidence of the adjacent oceanic crust and its well defined seamount chains our simple models yield potentially testable predictions the instability of plume formation in a system where broad scale convection already exists depends on horizontal conduit flow in the basal boundary layer toward the plume source geographically plumes are most likely to form where the boundary layer is thickest and where broad scale ascending flow already exists parameterized convection indicates that the heat transport by conduit flow in the boundary layer toward plumes depends linearly on the ratio of effective viscosity for broad scale convection to effective boundary layer viscosity in terms of material properties this ratio is the ratio of viscosity across the boundary layer to about the 0 45 power for the case where the broad scale convection is heated from below the viscosity contrast across the boundary layer depends on the temperature contrast across the layer a late onset of mantle plumes is implied if the temperature contrast at the base of the mantle has increased with time that is if the core has cooled more slowly than the interior of the mantel in one scenario before about 3 b y b p the mantle temperature varied slowly because surface heat flow was nearly balanced by internal radioactivity during this time the mantle was hotter than present and its internal viscosity lower hie temperature contrast at the base of the mantel was thus small after 3 b y internal radioactivity no longer balanced surface heat flow and the mantle cooled about a few hundred degrees celsius as indicated by petrological observations the core cooled slower than the mantle and the temperature contrast across the bottom boundary layer increased with time leading to a late onset of plumes phenomenological inferences are obtained as venus may have cooled more rapidly than the earth its mantle may be too cool for rapid plate tectonics and the gravity field and the convective pattern are dominated by hot upwelling regions

crustal influence in the generation of continental flood basalts the suggestion that primordial undifferentiated material may exist in the earth s mantle has recently been revived on the strength of nd isotope data for two types of young continental rocks flood basalts1 and kimberlites2 the limited published data show a clustering of nd isotopic compositions close to those for meteorites with chondritic relative rare earth ree abundance in contrast we now present data for samples from the columbia flood basalt province of the northwestern united states which show large isotopic variability suggestive of mixing processes acting after the separation of the primary magmas from their mantle source