whole layer convection in a heterogeneous planetary mantle 1 geochemical observations demonstrate that earth s mantle is heterogeneous but the sizes forms and characteristics of its reservoirs are not constrained using laboratory experiments we have systematically studied a simple nonhomogeneous system where two layers of miscible fluids with different densities depths and viscosities are subjected to a destabilizing temperature contrast when the buoyancy number b i e the ratio of the stabilizing chemical density anomaly to the destabilizing thermal density anomaly is lower than 0 3 0 5 the whole layer regime develops with a deformed interface and convective patterns over the whole tank depth the system systematically evolves toward one fluid rayleigh benard convection because of stirring however the two isolated fluids can persist for very long time compared to the characteristic timescale of thermal convection and give rise to numerous transient behaviors of particular interest for planetary mantles are the pulsatory dynamics where the interface between the two layers deforms in large domes moving up and down quasiperiodically according to the scaling laws derived from the experiments such a mechanism could indeed provide a simple and single physical explanation for the superswells observed at present on earth and more generally for the long term episodicity in planetary interiors observed in geological records

continental tectonics and continental kinetics abstract we present a model of continental growth which combines the results of geochemical studies and tectonic ideas about the evolution of continents through geological time the process of continental growth is mainly controlled by surface phenomena continental material is extracted from the mantle along subduction zones at the periphery of oceans and is destroyed in collision zones where it is remobilized and made available for subduction we derive an equation for s the portion of the earth s surface occupied by continents which reads as follows ds dt a 1 s b s coefficients a and b depend on the geometry of plates on their number and on their velocities we assume that they decrease exponentially with time with the same time scale this model satisfies both geochemical and tectonic constraints and allows the integration of several current observations in a single framework

a thermo chemical regime in the upper mantle in the early earth inferred from a numerical model of magma migration in a convecting upper mantle abstract a numerical model of mantle magmatism in a convecting upper mantle has been developed to study the thermo chemical evolution of the upper mantle of the early earth the solid state convection in the upper mantle is modeled by a convection of a binary eutectic material with a newtonian temperature dependent rheology in a two dimensional rectangular box placed on a heat bath as a model of the lower mantle the density depends on the chemical composition and melt content as well as temperature of the material the material contains heat producing elements that are incompatible and exponentially decay with time mantle magmatism is modeled by a permeable flow of melt generated by a pressure release melting induced by the solid state convection through matrix the permeable flow is driven by a buoyancy due to the density difference between the melt and the matrix the thermo chemical evolution in the box occurs in two stages if the deeper part of the box is not so strongly depleted in heat producing elements in spite of the upward migration and concentration of heat producing elements into a crustal layer along the top surface boundary due to magmatism in the earlier stage active magmatism occurs because of a strong internal heating due to the heat producing elements a chemically stratified structure develops well in the box with dense magmatic products in the deeper part and less dense residual materials in the shallower part and the temperature distribution becomes strongly superadiabatic over the entire box the temperature at the base of the box becomes as high as the solidus temperature the chemically stratified structure is however suddenly destroyed by convective mixing and the temperature in the deeper part of the box suddenly drops by several hundred degrees when the internal heat source becomes too weak owing to the decay of heat producing elements which sustain the active magmatism and hence keep the effect of chemical differentiation due to the magmatism stronger than the effect of convective mixing in the later stage of the evolution the box becomes chemically homogeneous and magmatism occurs only mildly if heat producing elements are efficiently transported into the crustal layer and the deeper part of the box becomes strongly depleted in heat producing elements owing to the magmatism only a mild magmatism occurs even at the beginning a chemically stratified structure does not develop well and the temperature in the box rapidly decreases to a stationary value the regime of hot and chemically stratified upper mantle suggested from the earlier stage of the case with mild depletion of heat producing elements at depth fits in with many observations of the archean continental crust

development and tropical transition of an alpine lee cyclone part i case analysis and evaluation of numerical guidance abstract the development and tropical transition tt of a subsynoptic scale cyclone in the gulf of genoa during the mesoscale alpine project map demonstration of probabilistic hydrological and atmospheric simulation of flood events in the alpine region d phase project is investigated using analyses and model simulations cyclogenesis occurs in association with the passage of a synoptic scale trough and attendant surface cold front across the alps on 15 november 2007 an embedded coherent tropopause disturbance ctd plays an important role in promoting the initial development of the lower level vortex by simultaneously providing quasigeostrophic forcing for ascent and reducing the bulk column stability over warm mediterranean waters persistent convection thereafter erodes the ctd as the storm transitions into a hurricane like vortex in addition to this upper level forcing a pair of diabatically generated lower level cyclonic potential vorticity pv features associated with distinct flow regimes i

thermal convection in a volumetrically heated infinite prandtl number fluid with strongly temperature dependent viscosity implications for planetary thermal evolution parameterized models of the thermal evolution of planets are usually based on the assumption that the lithosphere convecting mantle boundary can be defined by an isotherm at a temperature below which viscosity is infinite on geologic timescales recent experimental results argue against this assumption we have investigated both the definition of the lithosphere convecting mantle boundary and the power law relation describing convecting heat transfer based on numerical experiments of thermal convection in a volumetrically heated fluid with temperature dependent viscosity other recent studies have treated only the heating from below but volumetric heating is likely to be the dominant mode of heating in planetary mantles either as a consequence of radioactive heating or as a proxy for secular cooling convection can occur either in the whole box or be located under a stagnant lid in the lid regime convection is driven by a temperature contrast depending on the rheology of the fluid and the interior temperature this result in agreement with experimental studies indicates that boundary between the stagnant lid and the convecting layer similar to the lithosphere convecting mantle boundary cannot be defined as a fixed isotherm during thermal evolution of planets the viscosity contrast in the convecting mantle remains constant not the temperature at the bottom of the lithosphere we present an example showing that the evolution of planets is strongly dependent on the criterion chosen to define the lithosphere convecting mantle boundary for reasonable values of the activation energy for thermally activated creep the temperature defining the lithosphere convecting mantle boundary the mantle temperature and the thickness of the lithosphere could be larger than expected from previous models which treat the base of the lithosphere as a fixed isotherm

on the sensitivity of parameterized convection to the rate of decay of internal heat sources thermal histories for the earth based on parameterized mantle convection models have previously indicated that the earth departs significantly from a steady thermal state the non steady state is manifest by a present day excess of heat loss over heat production we investigate the dependence of the heat production heat loss ratio and mantle viscosity on heat source decay rate by varying the relative and absolute concentrations of the heat producing isotopes of k u and th in the mantle we examine three models with progressively increasing effective half lives respectively characterized by k u ratios of 6 104 chondritic 1 104 terrestrial and 0 25 104 low ka u each of these models can be constrained to yield a common present day heat flow mantle temperature and mantle viscosity thus demonstrating the inability of those present day constraints to differentiate between widely varying blends of the earth s nuclear fuel the present day heat production heat loss ratio ranges from about 73 for the chondritic model to about 86 for the low k u model other possible criteria diagnostic of the earth s radioisotope mix are the present day isotopic abundances the low k u model requires u and th greater by a factor of 2 5 over the chondritic model and k less by a factor of 10 however measurements of concentrations in candidate mantle rocks reveal a range that far exceeds the relatively small variations that distinguish the different compositional models paleothermal conditions also may be indicative of the earth s radioisotope blend the thermal state in the archean calculated for the low k u earth model is characterized by a mean mantle temperature about 100 c hotter and heat flow about 2 times greater than the present day whereas a chondritic earth model yields a mantle temperature 300 c hotter and heat flow 4 times greater however current estimates of paleo heat flow and mantle melting temperatures are burdened with uncertainties sufficiently large to preclude their use as criteria diagnostic of the earth s radioisotope endowment

models for the archean thermal regime a variety of different regionalized thermal evolution models are presented all models include an oceanic style of heat loss in which mantle convection penetrates to the surface in the form of spreading and subducting plates in continental regions the lithosphere is assumed to act as a conductive lid on mantle convection that can be either layered or mantle wide the continental lithosphere is defined in different ways it can be of fixed thickness insensitive to temperature or extend to some fixed cutoff temperature a thermally controlled rheological lithosphere when a fixed temperature is used widespread melting occurs in the archean and one has the further option of allowing these melts to erupt onto the surface thus providing a new heat transfer mechanism and also a general subsidence of the continental lithosphere due to the continuous volcanic loading the models are first used to determine the concentration of heat producing elements required to have a present day mantle potential temperature of 1350 c starting from a high temperature 2000 c 4 5 billion years ago the results depend primarily on whether the mantle is layered if layered 15 30 ppb uranium normalized to the silicate portion of the earth and withk u 104 th u 3 8 are needed while mantle wide cases need uranium concentrations in excess of 35 ppb the models are also used to calculate the thermal structure of continental lithosphere through time only lithospheres of fixed thickness 175 km can explain the recent discovery of diamonds with model ages of 3 2 3 4 billion years for a thick lithosphere to have existed in the archean it would seem most likely that its thickness be the result of some chemical distinction rather than simply its rheological properties such chemically distinct lithosphere would have greater likelihood of surviving to the present which raises the issue of biased preservation

a kinematic thermal history of the earth s mantle kinematic convection models of the earth s thermal history are computed assuming that subducted slabs along with some entrained material sink all the way to the core mantle boundary the temperatures within the lithosphere and within the mantle away from sinking slabs are computed assuming that the return flow from the core mantle boundary to the surface can be considered as slow vertical advection in the models a drop in asthenospheric temperature occurs near the end of the archean when subducted material first returns to the surface this drop is about 200 c if the subducted material does not mix thermally with the mantle on its way down and if only a thin thermal layer exists at the core mantle boundary we consider the possibility that this temperature drop is an explanation for the transition between archean and proterozoic tectonic styles an implication of the kinematic scheme is that the asthenospheric temperature increases gradually during the archean until the cooler material reaches the surface after the archean the thermal evolution is similar to a well mixed model a difficulty with the convection scheme as well as with any temperature profile in the mantle which is basically adiabatic is that excessively low temperatures in the core are implied if a 100 km thick thermal boundary layer at the core mantle boundary is included then higher core temperatures occur but there is a smaller drop in asthenospheric temperature at the end of the archean

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

double diffusive convection in this paper we present a rather personal view of the important developments in double diffusive convection a subject whose evolution has been the result of a close interaction between theoreticians laboratory experimenters and sea going oceano graphers more recently applications in astrophysics engineering and geology have become apparent in the final section we attempt to draw some general conclusions and suggest that further progress will again depend on a close collaboration between fluid dynamicists and other scientists

archaean plate tectonics revisited 1 heat flow spreading rate and the age of subducting oceanic lithosphere and their effects on the origin and evolution of continents a simple model which relates the rate of seafloor creation and the age of the oceanic lithosphere at subduction to the rate of continental accretion can successfully explain the apparent differences between archaean and phanerozoic terrains in terms of plate tectonics the model has been derived using the following parameters 1 the spreading rate at mid ocean ridges 2 the age of the oceanic lithosphere at the time of subduction 3 the area age distribution of the seafloor 4 the continental surface area as a fraction of the total surface area of the earth and 5 the erosion rate of continents as a function of continental surface area and the total number of continental masses observations in phanerozoic terranes suggest that there are profound differences in the nature and volume of subduction zone igneous activity depending upon the age of the oceanic lithosphere being subducted and the nature of the overriding plate that is either continental or oceanic the subduction of young oceanic lithosphere less than 50 m y old which is thermally buoyant appears to result in a reduced volume of igneous activity most of the igneous activity caused by subduction of young oceanic lithosphere is either siliceous plutonism or bimodal tholeiitic rhyolitic volcanism when very young lithosphere is being subducted 50 m y old appears to result in greater volumes of igneous activity including the eruption of andesitic magmas thus andesites could only begin to be abundant in the rock record when older oceanic lithosphere began to be subducted our model predicts that as the earth aged and as heat flow from the interior of the earth diminished the proportion of old oceanic lithosphere being subducted increased fundamentally changing the nature of subduction zone igneous activity and the rate of continental accretion if the subduction of old oceanic lithosphere results in an 8 10 times greater volume of subduction zone magmatism our model predicts or explains all of the following observed features of earth history 1 archaean terranes appear to record two periods of rapid continental accretion between 3 8 and 3 5 b y ago and between 3 1 and 2 6 b y ago 2 there are very few differences and many marked similarities between rocks from archaean terranes and equivalent rocks from phanerozoic terranes 3 the total continental area appears to have remained essentially constant for the past 2 b y 4 archaean andesites are comparatively rare and the relative abundances of mafic and siliceous rocks appear to change during the archaean and the proterozoic with siliceous volcanics becoming proportionately more abundant in the geologic record with time 5 plutonic tonalites and trondhjemites appear to have been relatively much more abundant during the archaean plate tectonics is thus shown to have evolved over time due to a gradually decreasing rate of creation of oceanic lithosphere meaning that archaean tectonics and phanerozoic tectonics are but two points on an evolutionary continuum

lower mantle convection and geomagnetism the statistical properties of recent marine magnetic anomaly time scales covering the period from 165 ma to the present are analyzed via the methods presented in the companion paper mcfadden this issue the data no longer support the hypothesis that during the last 86 ma there were two periods separated by a discontinuity at about 45 ma when the properties were stationary instead there is strong evidence that the rate of reversals decreased in an approximately linear manner with time from 165 ma until it reached zero resulting in the cretaceous normal polarity interval at about 86 ma ago the process of reversals began again and the rate of reversals increased linearly with time there is a slight indication that the rate of reversals reached a maximum about 10 ma ago and is again decreasing analysis of the reversal sequences shows there is no good evidence for the concept of differences in the relative stabilities of the two polarity states nor need such a concept be invoked to explain long intervals without reversals such as the cretaceous normal polarity interval quite clearly there has been some form of thermal perturbation at the base of the mantle with a characteristic time of the order of 108 years our interpretations require convection deep within the mantle and suggest that the temperature at the base of the mantle attains a maximum during long magnetic quiet intervals

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

fundamental issues in the geology and geophysics of venus a number of important and currently unresolved issues in the global geology and geophysics of venus will be addressable with the radar imaging altimetry and gravity measurements now forthcoming from the magellan mission among these are the global volcanic flux and the rate of formation of new crust the global heat flux and its regional variations the relative importance of localized hot spots and linear centers of crustal spreading to crustal formation and tectonics and the planform of mantle convection on venus and the nature of the interactions among interior convective flow near surface deformation and magmatism

the thermal regime of venus models for the thermal evolution of venus are constructed numerically the mantle is proposed to consist of two independently convecting layers upper and lower mantles the floating crust keeps the temperature of the upper surface of the convecting mantle near 1200 c and the core may solidify at temperatures below the liquidus previously these models were calculated with the usual parameterization of convection based mostly on investigations of constant viscosity convection now this parameterization is modified to take into account new numerical investigations of convection in media with complicated rheology the thermal evolution of venus is assumed to have begun 4 6 billion years b y ago it can be divided into three periods 1 adjustment of the upper mantle to the thermal regime of the lower mantle 0 5 b y 2 transition of the entire mantle to the asymptotic regime 3 4 b y 3 asymptotic regime parameters of the convecting planet in the asymptotic regime do not depend on initial conditions the planet forgets its initial state and are found analytically the present day heat flux is equal to 50 erg cm 2s 1 the results are close to those obtained previously comparison of the present thermal models of venus and earth with the recent studies of melting of the fe fes system suggest that the absence of a dipole magnetic field is closely connected to the absence of solidification of the venusian core at present the position of the iron triple point e liquid makes this conclusion very probable the thermal regime of the venusian crust is also discussed convection in the lower part of the crust is shown to play a role in certain regions with specific crustal composition the prevailing mechanism of heat transfer to the surface is advection by magmas produced by melting the lower layers of the crust

development and tropical transition of an alpine lee cyclone part ii orographic influence on the development pathway abstract the development and subsequent tropical transition of a subsynoptic scale cyclone over the gulf of genoa gog on 15 november 2007 led to the rapid onset of tropical storm force winds near the islands of corsica and sardinia this study evaluates the influence of two key ingredients on the cyclogenesis event a near surface warm potential temperature perturbation in the lee of the alps and a mountain scale potential vorticity pv banner a high resolution modeling system is used to perform a set of attribution tests in which modifications to the alpine orography control the presence of the cyclogenetic ingredients when either feature exists in the initial state a gog cyclone develops even when the alpine barrier is removed however when neither the warm perturbation nor the pv banner is present there is insufficient lower level pv to couple with the upper level trough to promote cyclogenesis a conceptual model involving the complimentary interaction of the two pv features is presented that

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

double diffusive convection in groundwater wells 1 double diffusive convection caused by variations in solute concentration and temperature within a fluid body has previously been studied in connection with oceanic mixing processes astrophysics metallurgy geology and vadose zone hydrology but has not previously been studied in connection with thermohaline transport in a groundwater well this paper considers whether double diffusive convection induced by salinity and or temperature variations is a plausible mechanism for heat and solute transport in a groundwater well this is examined theoretically using rayleigh number stability onset criteria for fluid in a cylinder that considers the cylindrical well geometry and geothermal solute boundary conditions theoretical results suggest that both monotonic and oscillatory double diffusive convection are plausible transport phenomena in groundwater wells these analyses have important implications for hydrogeology because they provide another theoretically plausible mechanism by which heat and solute may mix in a well this previously unaccounted for thermohaline mixing phenomenon may therefore be critical in the interpretation of well hydrogeologic and hydrochemical data

mid to late holocene land use change and lake development at dallund s0 denmark study aims natural and cultural setting chronology and soil erosion history dallund s0 a lake on the island of funen denmark is positioned in a landscape that has been heavily impacted by human activities and land use change over thousands of years in 1998 a project was initiated to utilize a variety of palaeoecological analyses to investigate lake response to changing land use through the period of agricultural impact on the danish landscape i e the last 6000 years this paper describes the overall aims of the study the natural and cultural setting sediment core collection sampling and physical properties the chronology and erosion history the long term changes in the terrestrial and aquatic ecosystem are assessed in the following papers in this research set using i pollen ii diatoms macrofossils and pediastrum and iii zooplankton these papers are followed by a synthesis paper focusing on the linkage between land use change and lake development

the effect of a shallow low viscosity zone on the mantle flow the geoid anomalies and the geoid and depth age relationships at fracture zones summary using a 2 d finite element method we studied the flow that is driven by the horizontal temperature gradient at a fracture zone and calculated the resulting geoid and topography anomalies assuming a three layered viscosity structure for the upper mantle consisting of a conducting lid overlying a low viscosity channel which in turn overlies a unit viscosity layer extending to the base of the upper mantle we studied the effect of varying 1 the viscosity contrast between the fluid layers 2 the rayleigh number based on the viscosity of the bottom layer and 3 the thickness of the low viscosity channel the flow at first downwells immediately adjacent to the fracture zone on the older side its time scale and characteristic wavelength depend on the viscosity and depth of the top layer which is nearest the largest temperature gradient in the fluid after the initiation of the driven flow additional flows are generated away from the fracture zone through shear and thermal coupling and boundarylayer instabilities eventually however the flow extends throughout the fluid so that the time scales and the characteristic wavelengths of the flow depend on the thickness and viscosity of both layers when the rayleigh number that is based on the viscosity of the top layer and the depth of both fluid layers is less than lo6 the geoid anomalies are dominated by the convective signal when this rayleigh number exceeds lo6 the geoid anomalies retain a step across the fracture zone out to large ages we compared our results with geoid anomalies over the udintsev fracture zone and found that the predicted geoid anomalies are in good agreement with the observed anomalies when the viscosity of at least the top layer is greater than one order of magnitude less than post glacial rebound values 102 pas however we also compared the calculated topographic steps with those predicted by the average depth age relationships observed in the oceans and found that a viscosity contrast of at least one order of magnitude at a depth in the uppermost mantle is required to produce realistic topographic steps

stable regions in the earth s liquid core summary slow cooling of the whole earth can be responsible for the convection in the core that is required to generate the magnetic field previous studies have assumed the cooling rate to be high enough for the whole core to convect here we study the effects of a low rate of cooling by assuming the temperature at the base of the mantle to remain constant with an initially entirely molten adiabatic core we argue that in such a situation convection would stop at the top of the core and calculate the consequent thermal evolution a stable density stratified layer grows downwards from the core mantle boundary reaching a thickness of 100 1000 km in a few thousands of millions of years there is some geomagnetic evidence to support belief in the existence of such a stable layer

the origin of terrestrial heat flow summary a theory of the origin of the earth s heat which agrees with all observations is presented the radiogenic heat production from the decay of u and th was computed from their abundances in ordinary chondrites from which the earth accreted and from the abundance of potassium in the mantle plus crust the total radiogenic heat production is 1 14 1013 w because u and th are incompatible in the silicates they have migrated upward into the continental rocks the sediments eroded from the continents are returned to the continents on subducting oceanic slabs therefore about 90 per cent of u and th are concentrated in the continents this is confirmed by a worldwide survey of helium in the oceans which found only 5 per cent of the helium that should have been there had the heat come from radioactive decay subtracting the radiogenic heat production of 1 14 1013 w from the total heat loss of 4 2x1013 w yields 3 06 1013 w to be supplied by the non radioactive sources in the mantle it is proposed that non radiogenic heat originates from secular cooling and from the release of gravitational potential energy by the absorption of feo from the mantle into the core this reaction has been produced in the laser heated diamond anvil cell at temperatures and pressures of the core mantle boundary layer as the molten iron extracts most of the feo out of the perovskite of the mantle a light residue consisting of an iron depleted perovskite and stishovite a form of silica rises in the form of plumes and megaliths generating heat by viscous friction if the oxygen now present in the core got there by this process 1027 g of feo have descended into the core generating energy at an average rate of twice the present rate of loss of non radiogenic heat adding the contribution of secular cooling an average rate of non radiogenic heat production of 1014 w could have been sustained for the last 4 6 billion yr

archaean plate tectonics revisited 2 paleo sea level changes continental area oceanic heat loss and the area age distribution of the ocean basins in a previous paper we derived plate tectonic models for continental accretion from the early archaean 3800 m y b p until the present the models are dependent upon the number of continental masses the seafloor creation rate and the continental surface area the models can be tested by examining their predictions for three key geological indicators sea level changes stable isotopic evolution e g continental surface area and oceanic heat loss models of paleo sea level changes produced by the accretion of the continents reproduce the following features of earth history 1 greater continental emergence lower sea level during the archaean than the proterozoic 2 maximum continental emergence about 3000 m y b p and 3 maximum continental submergence high sea level from 30 to 125 m y b p the high sea level stand between 380 525 m y b p is only weakly reproduced probably due to the simplified nature of the model changes in the number of continental masses can result in tectonic erosion or accretion of the continents with resulting changes in sea level the two major transgressions in the phanerozoic although still requiring some increase in the total terrestrial heat loss can be sucessfully explained by a combination of increases in continental surface area and in seafloor creation rate changes in the total heat loss of the ocean basins predicted by our plate tectonic models closely parallel the changes in terrestrial heat production predicted by wasserburg et al 1964 this result is consistent with thermal history models which assume whole mantle convection the history of changes in continental surface area predicted by our best continental accretion models lies within the ranges of estimated continental surface area derived from independent geochemical models of isotope evolution

the topographic and gravitational expression of density anomalies due to melt extraction in the uppermost oceanic mantle abstract evidence suggests that basaltic extrusion can decrease the density of the depleted source region by up to 2 for 20 partial melting this hypothesis is tested by calculating the effect of the density anomaly between the depleted and undepleted mantle on the topography gravity and geoid fields and comparing the anomalies to the observed topography gravity and geoid anomalies over volcanic features in the oceans if the source region lies at the base of the lithosphere we find that the gravity and geoid anomalies are proportionally more sensitive to the density contrast than the topography anomaly this effect is most pronounced for wavelengths less than 1000 km since mid ocean ridge volcanism the largest source of volcanism in the oceanic plates is fairly uniform along the ridge the depleted material in the oceanic plates and the corresponding topography and gravity anomalies should also be somewhat uniform in extent any long wavelength anomalies will be obscured in the topography and geoid fields by other anomalies at similar wavelengths such as slab and deep mantle anomalies however at mid plate swells and seamounts if the density contrast is greater than 0 4 the topography gravity and geoid anomalies are measurable to be consistent with the wavelengths represented in the geoid and topography data at hawaii the depleted material must be spread into a thin layer by convective flow at mid plate swells even in the thin layer model the topography and geoid anomalies due to the depleted material would still be as large as 200 m and 2 m respectively after the convective flow producing the bulk of the swell is removed the anomaly due to the depleted material would remain and would be apparent in the geoid and topography fields at seamounts if the source region is near the base of the plate then the presence of depleted material should be distinguishable in the geoid field but be somewhat obscured by flexural effects therefore although a topographic or geoid anomaly due to depletion has not been observed the density anomaly cannot be discounted because only careful scrutiny and modelling of mid plate swells and seamounts would distinguish its effect

speculations on the thermal and tectonic history of the earth summary the connection between the earth s thermal history and convection in the mantle is exploited to elucidate the early evolution of the earth it appears probable that convection extending over almost all of the mantle has dominated vertical heat transport throughout the whole of the earth s history only in boundary layers at the surface and at a depth of 650 700 km is conduction likely to be important the resulting evolution appears to be consistent with geological observations on early precambrian rocks various arguments are put forward in favour of two horizontal scales of convective flow in the mantle at depths less than 650 km the large scale flow is related to the motion of major plates and must be ordered over distances of more than 5000 km its evolution and energetics are discussed and there are no obvious problems in maintaining the proposed convective motions small scale flow with an extent of the order of 500 km appears necessary both to explain the heat flow through older parts of the earth s surface and to reconcile the geophysical observations with the results of numerical experiments though the existence of the small scale flow is at present speculative various tests of its presence are proposed

recognizing oib and morb in accretionary complexes a new approach based on ocean plate stratigraphy petrology and geochemistry abstract we present a new approach for recognizing the origin of accreted basaltic rocks based on ocean plate stratigraphy ops and on the petrology and geochemistry of basalts from mid oceanic ridges morb and oceanic islands oib using examples from four accretionary complexes ac in sw japan akiyoshi mino tamba chichibu and shimanto the key to the problem is the model of ops which includes an association of igneous and sedimentary rocks that form on an oceanic plate during its travel from a mid oceanic ridge to a subduction zone we propose the reconstruction of the tectonic settings of basalts according to their relationships with associated ops sediments their petrogenesis and their geochemical features five types of ops are recognized in the accretionary complexes of sw japan 1 sandstone shale 2 sandstone shale and chert 3 sandstone shale chert and morb 4 sandstone shale chert morb and gabbro peridotite 5 seamount ops including oib cap carbonates slope clastics and basal shale chert the alkaline tholeiitic or calc alkaline composition of basaltic melts which are typical of oceanic islands mid oceanic ridges and island arcs respectively can be identified by the sequence in crystallization of their major phenocrysts i e olivine ol clinopyroxene cpx and plagioclase pl and by their compositions alkaline and calc alkaline mafic lavas are characterized by an ol cpx pl succession whereas tholeiitic melts by their ol pl cpx succession titanium rich minerals e g ti augite kaersutite ti biotite are typical of alkaline lavas the application of geochemistry based tectonic discrimination diagrams is also a powerful tool if not supported by geological and petrological data may result in confusion due to magma contamination post magmatic alteration and secular change of mantle thermal conditions we propose that a direct comparison of normalized multi element patterns and key binary plots from older volcanic rocks with their modern analogues provides a more viable and reliable method of basalt discrimination our ops petrology geochemistry method allows us to confirm the above conclusions that the lavas of the akiyoshi mino tamba and southern chichibu ac formed in oceanic islands because they are associated with seamount ops sediments crystallized from ol to cpx and pl contain ti augite and kaersutite and are enriched in tio2 lree and nb in this paper we present geochemical data from the inuyama basalts of the mino tamba ac and from the toba complex in the huge mikabu greenstone belt of the chichibu ac the inuyama basalts are in contact with jurassic pelagic cherts but their geochemical features are confusing they contain phenocrysts of ol ti augite and kaersutite and therefore probably formed in seamounts the toba volcanic rocks are a part of the huge ophiolite belt they have flat to slightly lree enriched ree patterns are characterized by an ol cpx succession of phenocrysts and they plot in the oib field in binary plots suggesting they formed in an oceanic plateau

effects of terrain height and blocking initialization on numerical simulation of alpine lee cyclogenesis abstract a series of numerical experiments were performed to test the evolution of lee cyclones with various terrain representations and also to test forecast sensitivity to initial wind fields using the data set collected during the operational phase of the alpex field experiment a mesoscale model was initialized with data from two markedly different cases 12 hours prior to formation of a cyclone in the mediterranean the terrain used ranged from flat sea level terrain to orography that conserved the maximum barrier height of the alps similar to envelope terrain currently in use at the european centre for medium range weather forecasting results showed that even in the 12 hour period preceding cyclogenesis the mountain plays a crucial role in the evolution of the cyclone sharp variation in position and strength was evident depending on the terrain employed comparison of terrain versus no terrain cases showed perturbations that compare well with those proposed in a recently published theory

mechanisms for lithospheric heat transport on venus implications for tectonic style and volcanism the tectonic and volcanic characteristics of the surface of venus are poorly known but these characteristics must be closely related to the mechanism by which venus rids itself of internal heat on the other solid planets and satellites of the solar system lithospheric heat transport is dominated by one of three mechanisms 1 plate recycling 2 lithospheric conduction and 3 hot spot volcanism we evaluate each mechanism as a candidate for the dominant mode of lithospheric heat transfer on venus and we explore the implications of each mechanism for the interpretation of venus surface features despite claims made to the contrary in the literature plate recycling on venus cannot be excluded on the basis of either theoretical arguments or present observations on topography and radar backscatter landforms resulting from plate convergence and divergence on venus would differ substantially from those on the earth because of the high surface temperature and the absence of oceans on venus the lack of free or hydrated water in subducted material the possibility that subduction would more commonly be accompanied by lithospheric delamination and the rapid spreading rates that would be required if plate recycling removes a significant fraction of the internal heat if plate recycling occurs on venus the rolling plains and lowlands provinces would be approximate analogs to terrestrial ocean basins in terms of age igneous rock type and formative process highlands on venus would be roughly analogous to terrestrial continents the hypothesis that lithospheric conduction dominates shallow heat transfer on venus leads to the prediction that the lithosphere is thin if venus has a global heat loss per mass equal to that for earth then temperatures marking the base of the thermal lithosphere on earth would be reached on venus at an average depth of about 40 km unless the mantle convective planform can maintain lithospheric regions of persistently low heat flow or unless the present atmospheric greenhouse on venus is geologically recent then such a lithospheric thickness leads to the conclusion that the topographic features contributing to the 13 km of relief on the planet must be geologically young the hypothesis that hot spot volcanism dominates lithospheric heat transfer on venus leads to the prediction that the surface must be covered with numerous active volcanic sources in particular if a typical venus hot spot has a volcanic flux equal to the average flux for the hawaiian hot spot for the last 40 m y then 104 such hot spots are necessary to remove the venus internal heat by volcanism such a number would produce enough volcanic material to resurface the entire planet to a depth of 1 km every 2 m y few areas of the planet would escape resurfacing for geologically long periods of time we find that none of the mechanisms for lithospheric heat transfer on venus can be excluded as unimportant at present it is likely that as on earth a combination of mechanisms operates on venus the strongest conclusion to emerge from this evaluation is that most of the major topographic features and probably many of the surface geological units on venus are young by comparison with the surfaces of the smaller terrestrial planets

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

secular cooling of the earth as a source of intraplate stress abstract as a result of secular cooling and contraction of the earth an increasingly extensional horizontal stress is imposed on the central portions of the plates while the rate of increase of this stress is small in most situations it is enhanced for large plates and during any episodes of accelerated global cooling this source of stress may have contributed to the rifting and breakup of long lived supercontinental plates

review mesoscale modelling in complex terrain abstract this review focuses on those aspects of mesoscale models which require special techniques and parameterizations when modelling flow over complex terrain the basic concepts and limitations of various approaches are discussed and applications of models to specific problems are presented

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

effect of a shallow low viscosity zone on small scale instabilities under the cooling oceanic plates we have studied the role of a low viscosity zone in the uppermost mantle on convective instabilities in the cooling oceanic plates the upper mantle is represented by three layers in a finite element model a conducting lid overlies a low viscosity zone which in turn overlies a layer of constant viscosity extending to the base of the upper mantle at 675 km in depth the viscosity contrast the rayleigh number the relative fluid layer thicknesses and the conducting lid thickness are varied if the rayleigh number of the low viscosity zone exceeds a critical value then convection will be confined to the low viscosity zone for a period which depends on the viscosity contrast and the rayleigh number however the scale of the convection will eventually grow and extend throughout the upper mantle we compare our model to the small scale geoid and topography anomalies observed in the central pacific which are 50 80 cm in geoid and 250 m in topography 10 40 m y after plate formation and whose wavelength 150 500 km increases with age the magnitude early onset time and lifetime of the anomalies suggest a viscosity contrast of greater than 2 orders of magnitude the increase in wavelength with time also suggests a high rayleigh number 106 and the initial 150 250 km wavelength indicates a low viscosity zone thickness of 75 125 km small scale convection does not alter the slope of the depth age curve but does elevate the depth age curve by 250 m it is not until the onset of long wavelength convection that the depth age curve departs from age predicted by a cooling half space these results agree with the depth age behavior observed in the pacific where the depth age curve is elevated in the region of small scale anomalies and departs from age at 70 m y the models also predict heat flow values on old ocean floor which are higher than the plate model 50 55 mw m2 but which are in agreement with heat flow measurements in the atlantic and pacific