Present Thermal State Research Articles

Model development for numerical analysis of the bonding strength for friction welded lightweight structures

The rotary friction welding (RFW) is a robust, precise, productive and economical joining process that is used in many areas of mechanical engineering to produce lightweight structures consisting of combinations of ferrous and non-ferrous materials, for instance aluminium alloy and steel. Crucial for the design of such lightweight structures is the knowledge about the bonding strength. The bonding strength is the result of the bond formation depending on the present transient kinematic, kinetic and thermal states during the welding process being directly determined by the welding process parameters. Despite several years of empirical research, no reliable numerical modelling approach exists for the RFW process to analyse the bonding strength based on these transient state variables. For this reason, an improvement of the bond formation and therefore an increase in the bonding strength can only be tested experimentally. The main motivation of this paper is to develop an appropriate modelling approach for the estimation of the bonding strength for friction welded lightweight structures manufactured of an aluminium alloy and a structural steel. Therefore, a couple of aluminium alloy and steel welding experiments with different process parameters were performed and subsequently analysed concerning to the resulting bonding strength. Moreover, all the welding experiments were simulated in regard to the corresponding welding process in order to determine the present kinematic, kinetic and thermal state variables, like the strain rate, the stress and the temperature. Thus, a model for the characterization of the bond formation can be developed, which allows a correlation between the bond formation and the resulting bond strength based on the chosen welding process parameters. Finally, the model will be examined and discussed in terms of its plausibility and applicability.

Development of a Small-Sized Line Heat Source Apparatus for the Thermal Conductivity Measurement of Extraterrestrial Soils

The thermal conductivity of planetary soils, or regolith, is essential for understanding the present global thermal state of bodies. The thermal conductivity of lunar soils is important with respect to lunar crustal heat flow. Although in situ measurements were performed by the Apollo 15 and 17 missions, laboratory measurements of the returned lunar samples have not reproduced the estimated subsurface values. Since the amount of extraterrestrial soil samples is limited, a small apparatus is needed to measure their thermal conductivity. In this study, we developed an apparatus enabling the measurement of the thermal conductivity of a small amount of soil (< 10 g) via the line heat source method as a function of compressional pressure under vacuum conditions. The thermal conductivity of glass beads and lunar regolith simulant derived by the new apparatus is higher than that obtained from the larger line heat source, and then, reliable apparatus. To evaluate the experimental results, we performed numerical simulation of the temperature evolution during the line heat source measurement, and found that the thermal conductivity derived from the simulation data is higher than the input thermal conductivity. This is consistent with the experimental results and is caused by the heat loss through a line heat source with a limited length. The difference depends on the contact conductance between the sample and the line heat source, and the calibration factors for each sample are determined.

Thermal and maturation history for Carboniferous source rocks in the Junggar Basin, Northwest China: implications for hydrocarbon exploration

The reconstruction of thermal history is an important component of basin evolution and hydrocarbon exploration. Based on vitrinite reflectance data, we integrate the paleo-temperature gradient and paleo-heat flow methods to reconstruct the thermal history of Junggar Basin. Compared with present thermal state, the Junggar Basin experienced much a higher heat flow of ca. 80–120 mW/m2 during the Carboniferous. This feature can be attributed to large-scale volcanic events and related thermal effects. The hydrocarbon maturation history of Carboniferous source rocks indicates that the temperature rapidly reached the threshold of hydrocarbon generation during the Late Carboniferous and has never achieved such a high level since then. This characteristic resulted in the early maturation of hydrocarbons in Carboniferous source rocks. Meanwhile, the results reveal that hydrocarbon maturities are different among various tectonic units in Junggar Basin. The kerogen either rapidly broke through the dry gas period so that cracking of gas occurred or remained in the oil maturation window forming oil reservoirs, which depended on the tectonic background and depositional environment. In this study, we present the thermal and hydrocarbon maturation history since the Carboniferous, which has important implications for further hydrocarbon exploration in Junggar Basin.

Development of concepts for the management of thermal resources in urban areas – Assessment of transferability from the Basel (Switzerland) and Zaragoza (Spain) case studies

The shallow subsurface in urban areas is increasingly used by shallow geothermal energy systems as a renewable energy resource and as a cheap cooling medium, e.g. for building air conditioning. In combination with further anthropogenic activities, this results in altered thermal regimes in the subsurface and the so-called subsurface urban heat island effect.Successful thermal management of urban groundwater resources requires understanding the relative contributions of the different thermal parameters and boundary conditions that result in the “present thermal state” of individual urban groundwater bodies. To evaluate the “present thermal state” of urban groundwater bodies, good quality data are required to characterize the hydraulic and thermal aquifer parameters. This process also involved adequate monitoring systems which provide consistent subsurface temperature measurements and are the basis for parameterizing numerical heat-transport models.This study is based on previous work already published for two urban groundwater bodies in Basel (CH) and Zaragoza (ES), where comprehensive monitoring networks (hydraulics and temperature) as well as calibrated high-resolution numerical flow- and heat-transport models have been analyzed.The “present thermal state” and how it developed according to the different hydraulic and thermal boundary conditions is compared to a “potential natural state” in order to assess the anthropogenic thermal changes that have already occurred in the urban groundwater bodies we investigated. This comparison allows us to describe the various processes concerning groundwater flow and thermal regimes for the different urban settings. Furthermore, the results facilitate defining goals for specific aquifer regions, including future aquifer use and urbanization, as well as evaluating the thermal use potential for these regions. As one example for a more sustainable thermal use of subsurface water resources, we introduce the thermal management concept of the “relaxation factor”, which is a first approach to overcome the present policy of “first come, first served”. Remediation measures to regenerate overheated urban aquifers are also introduced.The transferability of the applied methods to other urban areas is discussed. It is shown that an appropriate selection of locations for monitoring hydraulic and thermal boundary conditions make it possible to implement representative interpretations of groundwater flow and thermal regimes as well as to set up high-resolution numerical flow- and heat-transport models. Those models are the basis for the sustainable management of thermal resources.

Thermal modeling and heat flow density interpretation of the onshore Northwest Java Basin, Indonesia

Studies pertaining to heat flow density distribution in Indonesian tertiary sedimentary basins have been conducted intermittently throughout more than two decades. Even so, all of these studies have always concentrated on the basic compilations of thermal gradient, thermal conductivity, and terrestrial heat flow datasets or the study of basin thermal history rather than on the investigations into their present thermal regime. In addition, syntheses on the possible causes to the observed heat flow density distribution in these basins have been largely determined only on the basis of its correlation with geological and geophysical evidences. One basin experiencing this particular problem is the onshore Northwest Java Basin, where knowledge of the present-day subsurface temperature structure is virtually absent and interpretation of heat flow distribution has been mainly qualitative. For these reasons, in this study we have attempted to quantitatively characterize the present subsurface temperature distribution and surface heat flow density of the onshore Northwest Java Basin using a simple numerical thermal modeling approach, based on the most recent heat flow datasets. Taking into account a conductive heat transfer process, the modeling exercise is aimed at deriving a 3-D subsurface temperature distribution. The temperature distribution is translated into the predicted surface heat flow distribution. The modeled temperature field reveals its dependence on the geometrical aspects of the basin’s basement. Comparison between the computed and the observed heat flow densities, taking into account the uncertainties of both, suggests that advective heat transport by groundwater flow may be present, in addition to conduction. The modeling results are thus capable of demonstrating the importance of a quantitative approach in studying the present thermal state of a sedimentary basin.

The thermal consequences of river-level variations in an urban groundwater body highly affected by groundwater heat pumps

The extensive implementation of ground source heat pumps in urban aquifers is an important issue related to groundwater quality and the future economic feasibility of existent geothermal installations. Although many cities are in the immediate vicinity of large rivers, little is known about the thermal river–groundwater interaction at a kilometric-scale. The aim of this work is to evaluate the thermal impact of river water recharges induced by flood events into an urban alluvial aquifer anthropogenically influenced by geothermal exploitations. The present thermal state of an urban aquifer at a regional scale, including 27 groundwater heat pump installations, has been evaluated. The thermal impacts of these installations in the aquifer together with the thermal impacts from “cold” winter floods have also been spatially and temporally evaluated to ensure better geothermal management of the aquifer. The results showed a variable direct thermal impact from 0 to 6°C depending on the groundwater–surface water interaction along the river trajectory. The thermal plumes far away from the riverbed also present minor indirect thermal impacts due to hydraulic gradient variations.

Thermal management of an unconsolidated shallow urban groundwater body

Abstract. This study presents the development of tools for the sustainable thermal management of a shallow unconsolidated urban groundwater body in the city of Basel (Switzerland). The concept of the investigations is based on (1) a characterization of the present thermal state of the urban groundwater body, and (2) the evaluation of potential mitigation measures for the future thermal management of specific regions within the groundwater body. The investigations focus on thermal processes down-gradient of thermal groundwater use, effects of heated buildings in the subsurface as well as the thermal influence of river–groundwater interaction. Investigation methods include (1) short- and long-term data analysis, (2) high-resolution multilevel groundwater temperature monitoring, as well as (3) 3-D numerical groundwater flow and heat transport modeling and scenario development. The combination of these methods allows for the quantifying of the thermal influences on the investigated urban groundwater body, including the influences of thermal groundwater use and heated subsurface constructions. Subsequently, first implications for management strategies are discussed, including minimizing further groundwater temperature increase, targeting "potential natural" groundwater temperatures for specific aquifer regions and exploiting the thermal potential.

Rocky super-Earth interiors

Aims. We present interior structure models of the recently discovered exoplanets CoRoT-7b and Kepler-10b addressing their bulk compositions, present thermal states, and internal dynamics. We investigate how mantle convection patterns are influenced by the depth-dependence of thermodynamic parameters (e.g., thermal expansivity and conductivity) caused by the extended pressure and temperature ranges within rocky super-Earths. Methods. To model the interior of rocky exoplanets, we construct a four-layer structural model solving the mass and energy balance equations in conjunction with a generalized Rydberg equation of state providing the radial density distribution within each layer. The present thermal state is calculated according to a modified mixing-length approach for highly viscous fluids. Furthermore, the obtained internal structure is used to carry out two-dimensional convection simulations to visualize the mantle convection pattern within massive exoplanets such as CoRoT-7b and Kepler-10b. Results. Both CoRoT-7b and Kepler-10b most likely have large iron cores and a bulk composition similar to that of Mercury. For a planetary radius of Rp = (1.58 ± 0.10) R⊕, a revised total mass of Mp = (7.42 ± 1.21) M⊕, and the existence of a third planet in the CoRoT-7 planetary system, calculations suggest that an iron core of 64 wt-% and a silicate mantle of 36 wt-% is produced owing to the relatively high average compressed density of ρavg = (10.4±1.8) g cm −3 . Kepler-10b’s planetary radius and total mass yield an iron core of 59.5 wt-%, which complements the silicate mantle of 40.5 wt-%. An enhanced radiogenic heating rate owing to CoRoT-7b’s young age (1.2−2.3 Gyr) raises the radial distribution of temperature by only a few hundred Kelvin, but reduces the viscosity by an order of magnitude. The planform of mantle convection is found to be strongly modified for depth-dependent material properties, with hot plumes rising across the whole mantle and cold slabs, which stagnate in the mid-mantle because of the loss of buoyancy. Conclusions. We use a new model approach to determine the detailed interior structures and present thermal states of CoRoT-7b and Kepler-10b. Both planets are found to be enriched in iron. The results imply that modest radiogenic heating does not play a significant role in determining the internal structure of rocky exoplanets. The depth-dependence of thermodynamic properties, however, strongly influences the mantle convection patterns within exoplanets such as CoRoT-7b and Kepler-10b. This may have a significant effect on the thermal evolution and magnetic field generation of close-in super-Earths.

Interior structure models of solid exoplanets using material laws in the infinite pressure limit

The detection of low-mass extrasolar planets has initiated growing interest in massive rocky bodies (super-Earths) for which no Solar System analogue does exist. Here, we present a new model approach to investigate their interior structure and thermal state. We improve and extend previous interior models mainly in two areas: the first improvement is due to the consequent application of equations of state (EoS) that are compliant with the thermodynamics of the high-pressure limit and facilitate reinvestigating mass–radius relations for terrestrial-type exoplanets. To quantify the uncertainty due to extrapolation, we compare a generalized Rydberg and a Keane EoS, which are both consistent with the high-pressure limit. Furthermore, we consider a reciprocal K′ EoS that fits the seismologically obtained Preliminary Reference Earth Model (PREM), thereby accounting for the mineralogical composition of the Earth. As a result, the predicted planetary radii of terrestrial-type exoplanets of up to 10 Earth masses would differ by less than 2% between all three EoS, well within current observational limits. The second extension arises from the adoption of a mixing length formulation instead of the commonly used, more simplified parameterized approach to model convective heat transport in planetary mantles. In comparison to parameterized convection models, our results indicate generally hotter interiors with increasing planetary mass and a cumulative tendency to extended regimes of sluggish convection in the lowermost mantle. The latter is attributed to less efficient convective heat transport with increasing mantle pressures. An improved knowledge of the present thermal state is prerequisite to gain a better understanding of the pathways of internal evolution of terrestrial-type exoplanets.

Scale aspects of heat transport in the diamond anvil cell, in spectroscopic modeling, and in Earth's mantle: Implications for secular cooling

Examining length and time scales reveals ruinous problems in diverse determinations of thermal conductivity ( k) involving the diamond anvil cell (DAC). (1) Conditions in laboratory experiments are optically thick (diffusive) for low-frequency phonons, but optically thin (ballistic) for high-frequency photons. Because speeds of photons are about ×10 5 those of phonons, ballistic photons transport heat over the short length and time scales of pulse-heating measurements in the DAC intended to measure phonons. Ballistic transport was confirmed by conducting pulse-heating experiments under various conditions. Not accounting for this time-dependent effect produces fallacious values for the lattice contribution to k. (2) In DAC optical spectroscopy, strong refraction was misinterpreted as sample absorption and its affect on path length went unnoticed, resulting in invalid calculations of the radiative diffusive component of k. Better estimates of lower mantle k are summarized. Scaling aspects point to the controls exerted by radiative transfer early in Earth's history and the importance of mantle layers to Earth's present thermal state. Diffusion of radiation is fast, making retention of primordial heat improbable: thus today's Earth is in quasi-steady-state, wherein its emitted heat is derived solely from current radiogenic contents.

Processes and modes of permafrost degradation on the Qinghai-Tibet Plateau

Climate warming must lead the mainly air temperature controlled permafrost to degrade. Based on the numerical simulation, the process of permafrost degradation can be divided into five stages, i.e., starting stage, temperature rising stage, zero geothermal gradient stage, talic layers stage, and disappearing stage, according to the shape of ground temperature profile. Permafrost on the Qinghai-Tibet Plateau (QTP) is generally considered a relic from late Pleistocene, and has been degenerating as a whole during Holocene. According to spatial-temporal compensation, the present thermal state discrepancy of permafrost in different areas on the QTP may correspond with their degradation stages. On the QTP, permafrost in the high and middle mountains belongs to temperature rising stage, the permafrost thermal state is transiting from late rising temperature stage to zero geothermal gradient stage that is distributed in the middle-low-mountains. Permafrost that is in a zero gradient stage mainly appears in the high plateau and valley, whereas the transition from zero gradient stage to talic layers stage of permafrost is located in the vicinity of the lower limit of permafrost, and permafrost is disappearing from margin of perennially frozen ground. There are two modes of perennially frozen ground thawing, thawing from top to bottom and thawing from bottom to top respectively. During the temperature rising stage, when the heat flux in the perennially frozen soil layer is less than that in the unfrozen soil underlying frozen soil layer, the geothermal flux is partly used to thaw the base of permafrost, and permafrost thaws from bottom to top. With the decrease of thermal gradient in the perennially frozen ground, the heat that is used to thaw permafrost base increases, and geothermal heat will be entirely consumed to thaw the base of permafrost until the temperature gradient reaches zero thermal gradient state. On the other hand, the disappearance of permafrost may be delayed by “thermal offset” and “seasonal offset” effects in the upper of permafrost layer. When ground surface temperature rises to the level that can counteract the thermal offset effect, heat accumulation in the active layer would start, and the thickness of the active layer increases until a talic layer to appear. This process can be intensified by the “seasonal anti-offset effect”.

On the origin of cores in simulated galaxy clusters

The diffuse plasma that fills galaxy groups and clusters (the intracluster medium) is a by-product of galaxy formation. The present thermal state of this gas results from a competition between gas cooling and heating. The heating comes from two distinct sources: gravitational heating associated with the collapse of the dark matter halo and additional thermal input from the formation of galaxies and their black holes. A long-term goal of this research is to decode the observed temperature, density and entropy profiles of clusters and to understand the relative roles of these processes. However, a long-standing problem has been that cosmological simulations based on smoothed particle hydrodynamics (SPH) and Eulerian mesh-based codes predict different results even when cooling and galaxy/black hole heating are switched off. Clusters formed in SPH simulations show near power-law entropy profiles, while those formed in Eulerian simulations develop a core and do not allow gas to reach such low entropies. Since the cooling rate is closely connected to the minimum entropy of the gas distribution, the differences are of potentially key importance. In this paper, we investigate the origin of this discrepancy. By comparing simulations run using the GADGET-2 SPH code and the FLASH adaptive Eulerian mesh code, we show that the discrepancy arises during the idealized merger of two clusters and that the differences are not the result of the lower effective resolution of Eulerian cosmological simulations. The difference is not sensitive to the minimum mesh size (in Eulerian codes) or the number of particles used (in SPH codes). We investigate whether the difference is the result of the different gravity solvers, the Galilean non-invariance of the mesh code or an effect of unsuitable artificial viscosity in the SPH code. Instead, we find that the difference is inherent to the treatment of vortices in the two codes. Particles in the SPH simulations retain a close connection to their initial entropy, while this connection is much weaker in the mesh simulations. The origin of this difference lies in the treatment of eddies and fluid instabilities. These are suppressed in the SPH simulations, while the cluster mergers generate strong vortices in the Eulerian simulations that very efficiently mix the fluid and erase the low-entropy gas. We discuss the potentially profound implications of these results.

Thermal evolution and geometry of the descending lithosphere beneath the SE-Carpathians: An insight from the past

Mantle heterogeneities imaged by seismic tomography in the SE-Carpathians contain information on the present thermal state of the mantle. Based on P-wave seismic velocity anomalies we develop a model of the present mantle temperature beneath the region and combine the model with a model of crustal temperature constrained by heat flow data. The modeled temperatures are assimilated into the geological past using the information on the regional movement in the Early and Middle Miocene. Prominent thermal states of the lithospheric slab descending in the region are restored from its diffuse present state. In Miocene times the slab geometry clearly shows two portions of the sinking body. The northwest–southeast oriented portion of the body is located in the vicinity of the boundary between the East European and Scythian platforms, and this portion of the sinking body may be a relic of cold lithosphere that has traveled eastward. Another portion has a northeast–southwest orientation and is related to the present descending slab. Above a depth of 60 km the slab had a concave thermal shape, confirming the curvature of the Carpathian arc, and a convex surface below that depth. The slab maintained its convex shape until it split into two parts at a depth of about 220 km. We propose that this change in the slab geometry, which is likely to be preserved until the present, can cause stress localization due to the slab bending and subsequent stress release resulting in large mantle earthquakes in the region. Also we hypothesize that either the processes of dehydration and partial melting of the descending lithospheric slab or dragging down of hotter rocks from the adjacent uppermost mantle by the slab are possible causes of the reduction in seismic velocities beneath the Transylvanian Basin.

Source parameters and three‐dimensional attenuation structure from the inversion of microearthquake pulse width data: Qp imaging and inferences on the thermal state of the Campi Flegrei caldera (southern Italy)

The three‐dimensional P wave attenuation structure of the Campi Flegrei caldera and the estimate of source parameters for 87 local microearthquakes is obtained by the nonlinear inversion of pulse width and rise time measurements by using the method described by Zollo and de Lorenzo (this issue). Source radii represent the better resolved parameters with values ranging from 70 m to 230 m; the dip and strike angles defining fault orientations are usually affected by larger uncertainties and are well constrained only for 11 events. The dip fault is usually confined in the range 30°–60° (with an average uncertainty of 12°); the fault strikes mainly range between −60° and 60° and seem to define preferential directions oriented radially from the symmetry axis of the ground deformation. Stress drop estimates indicate rather low values (0.01–1 MPa) which suggest low strength properties of the incoherent and brittle materials filling the caldera (primarily yellow tuffs). The three‐dimensional Qp images obtained from the inversion of P pulse durations show two significant low‐Qp anomalies between 0 and 1 km of depth, in the north‐eastern sector and at 2–3 km of depth in the central eastern sector of the caldera. The high degree of spatial correlation of the low‐Qp zone and low‐Vs (as inferred by Aster and Meyer (1988)) at 0–1 km in depth and other geophysical and geochemical observations suggest that this anomaly can be related to the presence of densely fractured, porous, and fluid‐filled rocks in the NE sector of the caldera. The deeper low‐Qp anomaly is interpreted as being related to a dominant thermal effect. We used the surface and deep borehole temperature measurements available in the area to obtain a local calibration curve to convert Qp in temperature at Campi Flegrei. The retrieved T(Qp) map shows a high thermal deep disturbance (450°–500°C) at depths between 2 and 3 km in the eastern sector of the caldera, where the most recent eruptive activity is concentrated. The present‐day temperature field retrieved by Qp images has been interpreted by using a three‐dimensional thermal conduction model assuming an extended heat source (initial temperature of 800°C) located underneath the attenuation anomalous region. The results indicate that the Qp‐inferred temperature field can be related to the heat conduction effect of one or more molten bodies whose top should be at about 4‐km depth, consistent with recent seismic estimates of the magma chamber top at Campi Flegrei (Ferrucci et al., 1992). This study suggests that the present thermal state and rock rheology of the inner caldera could be controlled by the cooling of molten bodies that originally intruded at depths of 1.4–1.6 km, during one or more recent (time of &lt;10 kyr) eruptive events.

On the thermal evolution of Venus

Several models are calculated in order to assess the effects of different physical parameters on the thermal evolution of Venus. The models are based on three‐dimensional thermal convection calculations in an incompressible mantle of infinite Prandtl number using a modified Boussinesq approximation. The mantle is assumed to have a temperature‐ and pressure‐dependent viscosity, temperature‐dependent thermal conductivity, depth‐dependent thermal expansion coefficient, and time‐dependent internal heat generation rate. The physical parameters considered are the initial temperature distribution, a possible D″‐like layer at the base of the mantle, the temperature at the core/mantle boundary, the core solidification, the decrease of thermal expansion coefficient with depth, the rate of internal heat generation, the radially dependent viscosity, and the velocity boundary condition at the surface. A constant temperature at the core/mantle boundary develops a strong thermal boundary layer at the base of the mantle, resulting in highly oscillatory mantle convection. Allowing the core to cool suppresses the boundary layer and reduces the amplitude of the oscillations substantially. The initial temperature distribution, the core solidification, and a D″‐like layer have minor effects on the overall cooling of the mantle, although the enhanced heat of fusion of the core hampers the cooling of the core. The decrease of the thermal expansion coefficient with depth lowers the slope of the adiabatic temperature gradient in the mantle and reduces the temperature in the lower part of the mantle and the core appreciably. The heat generation rate has a significant effect on the present thermal state of the mantle; a higher rate of heat generation enhances the mantle temperature, Similarly, a higher mantle viscosity decreases the convection velocities and hampers the heat loss from the mantle. However, the most important parameter that controls the thermal evolution of the planet is the velocity boundary condition at the surface. A stress‐free (we examined semifree) surface allows mantle material to approach the surface and cool efficiently, whereas a rigid (we examine semirigid) surface hampers heat loss from the planet, resulting in a hot planet even when the internal heat sources are reduced by about an order of magnitude.

Fluid flow and heat transfer in sedimentary basins

Abstract One of the major assumptions underlying the science of geothermics over the last 100 years has been that heat is transported through the Earth’s crust only by conduction, except in the immediate vicinity of active volcanoes. In old shields this assumption may be justifiable, but in sedimentary basins the ability of water to move through permeable aquifers provides a means of heat transport that may under certain conditions be as effective as conduction. The thermal history of a basin depends on its tectonic origin and the circumstances of its development. The dissipation of excess heat associated with basin formation and the transfer of the continuous heat supply from the basement depend on the thermal properties of the strata and their water content. In some basins widespread contrasts of heat flow are observed, both laterally and vertically, suggesting forced convection by water migration. In basins where part of the surface is above sea-level a hydrological drive may be inferred from the topographic surface. In sub-sea basins this drive is not available in the same form. Nevertheless, patterns of heat-flow variation have been observed for which some form of water flow seems to be the most probable explanation. A complete quantitative description of the present thermal state has not yet been developed for any basin. Some two-dimensional numerical models have been developed, but, since flow directions may vary between aquifers, three-dimensional models must be the ultimate objective. There is scope to extend such models to the geological past by using palaeotemperature indicators such as vitrinite reflectance and fission-track measurements. So far we have been able to establish only an understanding of the principles and processes that control the thermal state of basins, so that detailed description of small parts or two-dimensional models may be developed.

From tectonic reconstruction to upper mantle model: An application to the Alpine-Mediterranean region

De Jonge, M.R., Wortel, M.J.R. and Spakman, W., 1993. From tectonic reconstruction to upper mantle model: An application to the Alpine-Mediterranean region. In: M.J.R. Wortel, U. Hansen and R. Sabadini (Editors), Relationships between Mantle Processes and Geological Processes at or near the Earth's Surface. Tectonophysics, 223: 53–65. The seismic velocity structure of the upper mantle and lithosphere in the Mediterranean region is very complex: many areas with anomalous P-wave velocities can be recognized by means of seismic tomography. In view of the Complicated tectonic evolution of the peri-Mediterranean orogens and basins this is not surprising. In this study we will show results of a modelling approach we have recently developed to predict this structure. In this approach we make a quantitative connection between the tectonic evolution on one hand and the present seismic velocity structure on the other. Our model predicts the evolution of temperature distributions in the lower lithosphere and upper mantle, by simulating the flow of material inferred from a kinematic description of lithosphere-scale processes. From the modelled present thermal state (the endpoint of an evolution) we calculate expected seismic velocity anomalies that can be compared with results obtained by seismic tomography. Thus, the method enables us to compare the implications of geological reconstructions, describing the past tectonic processes, with seismological results for the present structure. The predicted mantle models show a good correlation with the tomographic results obtained for the mantle. This means we can verify many features present in the tectonic scenarios with the seismologically determined deep structure.

Time-dependent convection in the Earth's mantle

The range of Rayleigh numbers accessible to 2-dimensional numerical models of mantle convection has been increased, by almost two orders of magnitude, through the use of high resolution numerical grids with up to 200 intervals in each of the horizontal and vertical directions. The range of Rayleigh numbers studied is believed to encompass conditions which would have existed in a hot Archaean mantle. Although the models are highly idealized, in that they neglect the compressibility and variations of viscosity in the Earth's mantle, they suggest that during the Archaean (and earlier), boundary layer instabilities developed more frequently than at present, and did so with a scale and separation comparable to the thickness of the thin thermal boundary layers, rather than to the depth of the convecting layer itself. The rising and sinking plumes which develop from these instabilities drive transient flows which nevertheless have a horizontal scale comparable to the depth of the convecting layer. Thus although surface motions during the Archaean may have been more variable than at present, in terms of speed and direction, they might have occurred on a horizontal scale which is similar to that of present day plate motion. The numerical models indicate that motions at the upper surface of time-dependent convection cells are (1) predominantly controlled by transient sinking plumes, and (2) converge directly towards the source region of the sinking plumes. On the other hand, rising plumes have a more diffuse influence on the upper surface, and surface divergence does not always occur immediately above a rising plume. If oceanic plates on Earth constitute the upper surface of mantle wide convection cells, the more pronounced geophysical signature of subduction zones, compared to oceanic ridges, may be simply due to the fact that buoyancy is most concentrated at the Earth's surface in the form of sinking plumes. The total surface heat flow is found to fluctuate significantly in the time-dependent convection models. Since estimates of the present-day heat loss from the Earth's interior are, at best, instantaneous measurements, it is possible that these estimates are not representative (in a time-averaged sense) of the present thermal state of the planetary interior.

Heat transport by variable viscosity convection and implications for the Earth's thermal evolution

The case is presented that the efficiency of variable viscosity convection in the Earth's mantle to remove heat may depend only very weakly on the internal viscosity or temperature. An extensive numerical study of the heat transport by 2-D steady state convection with free boundaries and temperature dependent viscosity was carried out. The range of Rayleigh numbers ( Ra) is 10 4−10 7 and the viscosity contrast goes up to 250000. Although an absolute or relative maximum of the Nusselt number ( Nu) is obtained at long wavelength in a certain parameter range, at sufficiently high Rayleigh number optimal heat transport is achieved by an aspect ratio close to or below one. The results for convection in a square box are presented in several ways. With the viscosity ratio fixed and the Rayleigh number defined with the viscosity at the mean of top and bottom temperature the increase of Nu with Ra is characterized by a logarithmic gradient β = ∂ln( Nu)/ ∂ ln( Ra) in the range of 0.23–0.36, similar to constant viscosity convection. More appropriate for a cooling planetary body is a parameterization where the Rayleigh number is defined with the viscosity at the actual average temperature and the surface viscosity is fixed rather than the viscosity ratio. Now the logarithmic gradient β falls below 0.10 when the viscosity ratio exceeds 250, and the velocity of the surface layer becomes almost independent of Ra. In an end-member model for the Earth's thermal evolution it is assumed that the Nusselt number becomes virtually constant at high Rayleigh number. In the context of whole mantle convection this would imply that the present thermal state is still affected by the initial temperature, that only 25–50% of the present-day heat loss is balanced by radiogenic heat production, and the plate velocities were about the same during most of the Earth's history.

Geodynamics and state of the earth's interior

The paper is concerned with the connection of planetary geodynamics and properties of the material inside the Earth. The notion “state” is considered both in the local and in the global sense. We discuss various interpretations of phase boundaries in the Earth's mantle and propose a new idea on the description of seismic discontinuities. The present thermal state of the Earth's core is investigated by using data about the attenuation of seismic waves. Because of some peculiarities in the phase diagram of the favoured core material Fe-S we come to the conclusion that the dynamics in the outer core may be characterized by the motions of small droplets. The corresponding rate of release of gravitational potential energy is enough to drive a geodynamo with an average toroidal field of mean size. According to our point of view, global planetary evolution started from an originally homogeneous Earth. The differentiation of core and mantle started in upper layers. It is an important source of energy for all following processes.