Geothermal Flux Research Articles

Thermal fluxes and stability of the upper boundary of deep near-bottom layer in the Black Sea

Experimentally-derived data are used to scrutinize structural peculiarities of the upper boundary of deep near-bottom layer in the Black Sea. Thermal fluxes through the layer’s upper boundary have been evaluated and compared with the geothermal fluxes. Although there is significant divergence between the individual evaluations, the quantities at issue generally agree with one another. It is shown that in evaluating thermal fluxes, it is necessary to consider fine structure of the differential-diffusive type. Stability of the upper boundary of the deep near-bottom layer has been examined, and diagrams of stability/instability resulting from the development of convection have been plotted.

Sensitivity of a Greenland ice sheet model to ice flow and ablation parameters: consequences for the evolution through the last climatic cycle

Sensitivity experiments are conducted to test the influence of poorly known model parameters on the simulation of the Greenland ice sheet by means of a three dimensional numerical model including the mechanical and thermal processes within the ice. Two types of experiments are performed: steady-state climatic conditions and simulations over the last climatic cycle with a climatic forcing derived from the GRIP record. The experiments show that the maximum altitude of the ice sheet depends on the ice flow parameters (deformation and sliding law coefficients, geothermal flux) and that it is low when the ice flow is fast. On the other hand, the maximum altitude is not sensitive to the ablation strength and consequently during the climatic cycle it is driven by changes in accumulation rate. The ice sheet extension shows the opposite sensitivity: it is barely affected by ice flow velocity and the ice covered area is smaller for large ablation coefficients. For colder climates, when there is no ablation, the ice sheet extension depends on the sea level. An interesting result is that the variations with time of the altitude at the ice divide (Summit) do not depend on the parameters we tested. The present modelled ice sheets resulting from the climatic cycle experiments are compared with the present measured ice sheet in order to find the set of parameters that gives the best fit between modelled and measured geometry. It seems that, compared to the parameter set most commonly used, higher ablation rate coefficents must be used.

A convective model of water flow in Mururoa basalts

Even long after the end of volcanic activity, the background geothermal flux of Mururoa atoll (French Polynesia) maintains fluid convection. We present evidences that interstitial water is continuously renewed in the carbonate platform, as well as in the volcanic basement. In the carbonate rocks, the presence of a karst system allows convective fluxes high enough for the thermal equilibration of the formation with the ocean around. On the contrary, convection in the volcanic basement is, in most places, too slow to cause a measurable disturbance of temperature profiles. Thermal convection models indicate that the average permeability of the volcanic basement cannot be more than a few 10 mD (10 −14 m 2), implying a residence time of more than 10,000 years. The concentration of Sr in porewaters is used as an indicator of the rock/water ratio and of the residence time of the fluid. Considering the measured permeabilities and the estimated rates of reaction, residence times of more than 1 My, corresponding to average permeabilities of less than 10 −16 m 2, are unlikely in the studied upper kilometer of the volcano. However, the extrapolation of the rates of dissolution for basaltic glass measured in the laboratory to in situ conditions apparently leads to overestimate the rates of reaction. Chemically reactive surface area per volume of fluid is a critical parameter in this extrapolation and its value is dependent on the method used to measure it. Although it may not be the only explanation, the discrepancies can be caused by the presence of clays in conduits for fluid flow and as a replacement product of glass. Comparing our results with studies of Quaternary basalts in Iceland, the 10 Ma alteration history of the Mururoa basalt results in a decrease of the permeability of the aquifers by several orders of magnitude, but does not cause a large change of the chemically reactive surface area.

Heinrich-scale surge oscillations as an internal property of ice sheets

A dynamical model governing the variations of ice-sheet volume, basal-water amount and ice-surge flux has been formulated in its simplest form, based on fundamental thermomechanical properties of ice sheets governing the basal-melting process. This model includes the effects of the geothermal flux, internal thermal advection and basal friction, the latter two factors being particularly important in regulating the bottom temperature and bringing it to the melting point, i.e. to a state vulnerable to catastrophic ice surges. It is shown that, for certain values of the unknown rate constants, such a model can exhibit oscillations on roughly the same scale as observed Heinrich events, even when external climatic changes are neglected, which would support the view that such events are an internal properly of ice sheets.

Heinrich-scale surge oscillations as an internal property of ice sheets

A dynamical model governing the variations of ice-sheet volume, basal-water amount and ice-surge flux has been formulated in its simplest form, based on fundamental thermomechanical properties of ice sheets governing the basal-melting process. This model includes the effects of the geothermal flux, internal thermal advection and basal friction, the latter two factors being particularly important in regulating the bottom temperature and bringing it to the melting point, i.e. to a state vulnerable to catastrophic ice surges. It is shown that, for certain values of the unknown rate constants, such a model can exhibit oscillations on roughly the same scale as observed Heinrich events, even when external climatic changes are neglected, which would support the view that such events are an internal properly of ice sheets.

Thermal infrared satellite measurements of volcanic activity at Stromboli and Vulcano

The use of Landsat thermal infrared imagery gives a direct way of quantitatively monitoring the evolution of low‐amplitude thermal anomalies. Using nighttime Landsat thematic mapper images of Vulcano and Stromboli volcanoes on October 23, 1986, we have developed a simplified method for correcting atmospheric effects. We were then able to identify thermal anomalies around the craters. Part of the Stromboli lava flow, formed 1 year earlier, was also still warm enough to be detected. We obtained fairly accurate estimates of relative surface anomaly radiative heat fluxes: 29±5 W m−2, 21±4 W m−2, and 37±5 W m−2 for the Stromboli craters, Stromboli lava flow, and Vulcano crater, respectively. Accounting for the convective heat loss significantly increases the estimates of the relative internal heat flux of geothermal origin; we found values of 370±60 W m−2 for the Stromboli crater region, 220±50 W m−2 for the Stromboli lava flow, and 270±60 W m−2 for the Vulcano crater. Despite the low precision, these values are much higher than the 53–62 W m−2 limit (defined by Cassinis and Lechi, 1974) as the threshold where the geothermal flux can affect ground temperatures. Our study provides a unique systematic definition of thermal volcanic features found on Stromboli and Vulcano, the spatial extents of the anomalies, and their fluxes and associated errors.

Geophysical constraints on tectonic models of the Taubaté Basin, southeastern Brazil

Abstract Magnetotelluric, gravity and geothermal flux data are analysed to constrain the tectonic evolution of the Taubate Basin, a SW-NE 20 km wide and 170 km long rift-like Tertiary basin in southeastern Brazil. The basin is characterized by half-grabens and contains up to 1000 m of sediments cut by normal faults. The magnetotelluric measurements show the presence of two layers: an upper highly conductive one (less than 10 Ωm from 1-D inversions), associated with Tertiary sediments, and an extremely resistive (more than 10000 Ωm) lower layer, related to the crystalline basement. Gravity anomalies in the region are ascribed to both near-surface sources, sediments and granites, and a deep-seated source associated with crustal thinning towards the continental margin. Available geothermal flux values within the basin are anomalously high; however, they have probably been affected by convective transport because they were determined in water boreholes. These results suggest a stable thermal regime at present and, viewed together with the absence of magmatism and thermal subsidence, indicate that the mechanism related to the basin formation did not originate a deep-seated thermal anomaly in the region. The event can be seen as a shallow one, involving a small area in the upper part of the crust. The region can be characterized typically as a strike-slip mobile zone, with horizontal displacements between juxtaposed blocks. A transtensional model is suggested for the Taubate Basin to explain some of its principal geological features.

Permafrost and ground ice conditions reported during recent geotechnical investigations in the Mayo district, Yukon territory

AbstractThe Mayo District, Yukon Territory, lies in the widespread discontinuous permafrost zone. Permafrost thicknesses of up to 40 m have been measured in valleys, and of 135 m at higher elevations. Many observations of ground ice have been made by placer miners, but generally these are unrecorded. Recently, over 200 shallow geotechnical boreholes have been drilled in the area in association with municipal or highway construction. Ground ice is usually encountered at undisturbed sites within 4 m of the surface. In the main valleys at elevations below 1100 m a.s.l. coarse, clastic, outwash materials, sand dunes and slopes with southerly aspect are usually frost‐free. Stripping of vegetation for construction or placer mining leads to permafrost degradation, but permafrost can re‐establish as vegetation regenerates. Ground temperatures at Mayo and Keno Hill indicate a geothermal flux of over 0.1 W/m2.

Hydrography of the brines in the Bannock and Tyro anoxic basins (eastern Mediterranean)

The anoxic brine-filled Tyro and Bannock Basins (eastern Mediterranean) show strong temperature and conductivity gradients at the interface between normal water and anoxic brine (at ∼ 3276 m in the Bannock Basin, at 3328 m in the Tyro Basin), with temperature and conductivity increasing toward the bottom. Temperature reaches values of 15.14°C in the Bannock area and of 14.13°C in the Tyro Basin, and conductivity at the bottom is respectively 177.44 and 191.26 mS cm −1. In the deepest basin of the Bannock area (named Libeccio) a sequence of nearly homogeneous layers, separated by sharp interfaces, is present below the seawater-brine interface. Near the bottom a homogeneous 244-m-thick layer has been observed. The hydrological structure of brines in Tyro Basin shows no evidence of thermal layering. The present geothermal flux seems to be sufficient to create and maintain the temperature structure observed in the brines. A minimum of 4500 years would be needed to raise the Bannock brine body to its current temperature. Only a minimum of 150 years is needed to bring the Tyro brine to its current condition.

Extent of permafrost in southern Britain in relation to geothermal flux

Introduction The scarcity of relic permafrost features in southwest England, except on the high ground of Dartmoor, was noted by Williams (1965, 1969). Following Manley (1951, 1953) he concluded that this was due primarily to a moderation of the Pleistocene climate by invasions of milder Atlantic air. Subsequent work through the CLIMAP project ( McIntyre et al 1976 ), however, suggests that at 18000 years BP, the North Atlantic polar front was at about the latitude of Portugal. Comparison of Williams' map of the areal extent of permafrost in southern Britain with the detailed heat flow map of the UK ( Wheildon & Rollin 1986 ) indicates that regions where evidence of former permafrost is largely absent tend to coincide with areas of high heat flow. The technical note discusses possible relationships between heat flow and permafrost phenomena in southern England as it is clearly important that engineers making site assessments are aware of the likely causes and extent of the disturbance associated with former frozen ground. Extent and depth of former permafrost in southern Britain Figure la is a reproduction of Williams' (1969) map which was based on the deeper periglacial features, particularly ice-wedge casts. It shows that there are far fewer permafrost features in the southwest than in most of Britain. Since then more ice-wedge casts have been found in southwest England, but it is nevertheless generally accepted that in this area the frequency and depth of these is significantly less than

Birth, life and death of the Pannonian Lake

The Miocene-Pliocene Pannonian Lake formed in an extensional basin system behind the compressional arc of the Carpathians. Its size and depth were comparable to those of the Caspian Sea. Subsidence began in Middle Miocene times, forming deep, pelagic basins, separated by reef-bearing ridges. Clastic influx filled the marginal basins during Middle Miocene time. Prograding deltas dissected the lake and completed the infilling of the basin system by the end of the Pliocene. Basin plain, prodelta, delta front, delta plain, beach, fluviatile, and marsh environments can be recognized. Terminal Miocene uplift of the Carpathians isolated the Pannonian region from the rest of Paratethys. The subsequent decrease of salinity resulted in the evolution of an endemic, freshwater mollusc fauna. Rich nutrient influx from rivers supported high organic productivity (dinoflagellates, diatoms, nannoplankton, foraminifers, ostracods, etc.), yielding organic-rich sediments. Preservation of organic matter was helped by a stratified water column and oxygen deficient bottom conditions. Deep burial, continuing subsidence, and high geothermal flux due to an extremely thin crust, led to the formation of commercially exploitable oil and gas accumulations. Shallow lacustrine zones of basin margins provided suitable environments for a rich Congeria-Melanopsis mollusc fauna. Wave action on beaches produced commercially exploitable pure quartz sand deposits. Taxodium and Alnus forests flourished around the lake producing enormous lignite deposits. Besides a rich land snail and mammal fauna, prehominids lived in the forests. There was a warm, temperate climate, with probably frostfree winters. Basaltic volcanoes overlooked the landscape, and maars hosted minor lakes with rich algal flora forming oil shale. The catchment area included most of the Carpathians and parts of the Apls and Dinarides. The positive water balance resulted in a supposed overflow in the southern margin, supplying exotic fauna to the South Carpathian and Dacian basins of the Eastern Paratethys. The Pannonian Lake was completely filled by the end of Pliocene. Recent lakes in the Carpathian Basin are not descendants of it.

Marine heat flow observations on the Canadian Arctic continental shelf and slope

We present 36 new heat flow measurements, grouped within five separate sites on the Canadian Arctic continental shelf and slope, between 95°–115°W and 80°–82°N. Observations consist of temperature gradients and in-situ thermal conductivity using a modified, marine-type, multiple-penetration probe with a length of 4–6 m. Repeat measurements from nearby locations at different times of the year indicate that, for depths deeper than 200 m, the bottom water remains sufficiently stable to allow shallow measurements to characterize the deeper, geothermal flux. In this respect, the cold, ice-covered, deep-water Arctic margin is unique among the world's passive continental margins. Using these data, we construct a preliminary geothermal transect between the continental Sverdrup Basin to the south and the oceanic Canada Basin to the north. Values of 35–45 mW m −2 exist on the Axel Heiberg headland, Nansen Channel and on the continental slope, and indicate a broad-scale reduction from higher values of 55–60 mW m −2 within the Canadian Basin to values of 40–50 mW m −2 within the Sverdrup Basin. In contrast, there is a zone of high heat flow, with well-constrained values of 80 mW m −2 within Peary Channel. Low values in the northeastern sector of the margin suggest that the early Tertiary, Eurekean Orogen near Ellesmere Island has not thermally affected the margin. Based on calculations for pure-shear extension, the 15 mW m −2 reduction across the continental margin suggests that the Canada Basin proper may not have opened until Late Cretaceous, unless the pre-existing continental crust contains an extremely low amount of radiogenic material. Lithospheric models cannot account for the high values in Peary Channel which may indicate water movement within the sedimentary basin.

Potential For Basal Melting Under The Summit Coring Site, Central Greenland

The climatic record from Greenland boreholes is likely to extend well beyond the last interglacial only if the basal ice near the drilling sites has never reached its pressure melting point (−2°C). A simplified one-dimensional analysis (Paterson and Waddington, 1986) suggested that this would be true at Crête, Greenland, if the geothermal flux was less than 48 mW m−2. In that study, the vertical velocity pattern for an isothermal ice sheet was used. We have repeated the Crête calculations using the vertical velocity pattern derived by a finite element analysis. Using this temperature-dependent velocity pattern lowered the basal temperature by about 3°C.We have carried out a similar analysis for the Summit coring site further north on the Greenland ice divide. Here we find that the basal ice does not melt if the geothermal flux is less than 54 mW m−2, using the same mass balance and surface temperature histories as the previous study. We are repeating these one-dimensional calculations with more recently compiled histories and plan to present results from a full two-dimensional temperature model that includes processes only parameterized in the one-dimensional models. Using two dimensions, we will more realistically incorporate the special ice-flow patterns found at divides (e.g. Raymond, 1983; Dahl-Jensen, 1989). In steady-state flow models these patterns lead to significant horizontal temperature gradients and a “hot spot” beneath an ice divide (Paterson and Waddington, 1986). In addition, we will more accurately determine the transient effects on basal temperature resulting from the interaction of these flow patterns and the changing climate. Our discussion will include sensitivity to geothermal heat flux, ice thickness and paleoenvironmental history.

Potential For Basal Melting Under The Summit Coring Site, Central Greenland

The climatic record from Greenland boreholes is likely to extend well beyond the last interglacial only if the basal ice near the drilling sites has never reached its pressure melting point (−2°C). A simplified one-dimensional analysis (Paterson and Waddington, 1986) suggested that this would be true at Crête, Greenland, if the geothermal flux was less than 48 mW m−2. In that study, the vertical velocity pattern for an isothermal ice sheet was used. We have repeated the Crête calculations using the vertical velocity pattern derived by a finite element analysis. Using this temperature-dependent velocity pattern lowered the basal temperature by about 3°C. We have carried out a similar analysis for the Summit coring site further north on the Greenland ice divide. Here we find that the basal ice does not melt if the geothermal flux is less than 54 mW m−2, using the same mass balance and surface temperature histories as the previous study. We are repeating these one-dimensional calculations with more recently compiled histories and plan to present results from a full two-dimensional temperature model that includes processes only parameterized in the one-dimensional models. Using two dimensions, we will more realistically incorporate the special ice-flow patterns found at divides (e.g. Raymond, 1983; Dahl-Jensen, 1989). In steady-state flow models these patterns lead to significant horizontal temperature gradients and a “hot spot” beneath an ice divide (Paterson and Waddington, 1986). In addition, we will more accurately determine the transient effects on basal temperature resulting from the interaction of these flow patterns and the changing climate. Our discussion will include sensitivity to geothermal heat flux, ice thickness and paleoenvironmental history.

Interpretation of the Temperature Profile Measured at Vostok, East Antarctica

The temperature profile measured in the Vostok bore hole is analysed. The temperature distribution in polar ice sheets depends mainly on past surface temperature, geothermal flux, and accumulation rate. In the present work, the heat equation is solved both for ice and for the underlying bedrock. The Vostok ice core offers a 160 000 year climatic record which is used to define the past surface temperature, while accumulation-rate variations are assumed to be governed by the saturation vapour pressure. The model is run for a number of different sets of parameters in order to find the parameter associations giving a good fit between the observed and the computed temperature profiles. With this model, it is possible to simulate the measured temperature profile within 0.1°C. To obtain this good fit, geothermal flux has to be higher than 50 mW/m2 and present-day accumulation rate must be lower than 2.6 cm/year. Sensitivity of these results both to the amplitude of surface-temperature change and to the velocity profile with depth is also investigated. Finally, it is shown that ice is at the melting point at the base of the ice sheet, which is in agreement with the presence of a subglacial lake near Vostok Station.

Interpretation of the Temperature Profile Measured at Vostok, East Antarctica

The temperature profile measured in the Vostok bore hole is analysed. The temperature distribution in polar ice sheets depends mainly on past surface temperature, geothermal flux, and accumulation rate. In the present work, the heat equation is solved both for ice and for the underlying bedrock. The Vostok ice core offers a 160 000 year climatic record which is used to define the past surface temperature, while accumulation-rate variations are assumed to be governed by the saturation vapour pressure. The model is run for a number of different sets of parameters in order to find the parameter associations giving a good fit between the observed and the computed temperature profiles. With this model, it is possible to simulate the measured temperature profile within 0.1°C. To obtain this good fit, geothermal flux has to be higher than 50 mW/m2 and present-day accumulation rate must be lower than 2.6 cm/year. Sensitivity of these results both to the amplitude of surface-temperature change and to the velocity profile with depth is also investigated. Finally, it is shown that ice is at the melting point at the base of the ice sheet, which is in agreement with the presence of a subglacial lake near Vostok Station.

Modelling the Evolution of the East Antarctic Ice Sheet: Problems and Perspectives (Abstract)

Modelling the thermodynamics of a large ice sheet is in essence a problem of the deformation of a non-isothermal and relatively thin viscous layer. Reasons for forecasting the behaviour of a large ice sheet are: (a) to specify the relationship between the existence and development of the ice sheet and regional climatic and tectonic conditions; (b) to study the influence of variations in surface temperature, mass balance, and geothermal flux (as functions of coordinates and time) on the evolution of the thickness of the ice sheet. Hence the principal requirements for modelling are: 1.The model must be evolutionary; in particular, various stationary stages should be derived from it (rather than postulated).2.The model must be non-isothermal because temperature variations amount to some tens of degrees.3.Two-dimensionality of the model is essential if we are to use it for making realistic forecasts.4.Conditions at the boundary between land ice and the sea, which are the basic factors controlling the location of the margin of the ice sheet, should be taken into account.5.Finally, the model must be acceptable for digital analysis by computer.Contemporary mathematical models of the dynamics of the Antarctic and Greenland ice sheets are too simplified and do not fulfil these requirements. Our mathematical model of the evolution of the Antarctic ice sheet is based on temperature parameterization. The parameterization correctly describes the distribution of temperature and its dependence on surface temperature, advection of ice, geothermal flux, and heat losses. The problem reduces to Cauchy’s problem for a non-linear parabolic partial differential equation with three-step dependence of ice temperature on depth. A linear viscous flow law is assumed. Tests treat the whole problem of the thermo-hydromechanics of the ice sheet. The ice sheet is assumed to be bounded by a grounding line or ice wall where the ice is in hydrostatic equilibrium with the sea. In this case, the problem reduces to a non-linear parabolic partial differential equation with a complicated boundary condition at the moving edge. A digital representation of the model is presented first. Tests demonstrated the possibility of using an explicit three-layered scheme. Calculations for the East Antarctic ice sheet indicated that the ice margin should retreat slightly under contemporary climatic conditions (which corresponds to the field evidence). In future the boundary should tend towards a stationary state. A forecast of the behaviour of the ice sheet is derived. The East Antarctic ice sheet is found to be stable during various changes in climatic factors. The calculated hydromechanical characteristics of the ice sheet agree with the observed field data.

Modelling the Evolution of the East Antarctic Ice Sheet: Problems and Perspectives (Abstract)

Modelling the thermodynamics of a large ice sheet is in essence a problem of the deformation of a non-isothermal and relatively thin viscous layer. Reasons for forecasting the behaviour of a large ice sheet are: (a) to specify the relationship between the existence and development of the ice sheet and regional climatic and tectonic conditions; (b) to study the influence of variations in surface temperature, mass balance, and geothermal flux (as functions of coordinates and time) on the evolution of the thickness of the ice sheet. Hence the principal requirements for modelling are: 1. The model must be evolutionary; in particular, various stationary stages should be derived from it (rather than postulated). 2. The model must be non-isothermal because temperature variations amount to some tens of degrees. 3. Two-dimensionality of the model is essential if we are to use it for making realistic forecasts. 4. Conditions at the boundary between land ice and the sea, which are the basic factors controlling the location of the margin of the ice sheet, should be taken into account. 5. Finally, the model must be acceptable for digital analysis by computer. Contemporary mathematical models of the dynamics of the Antarctic and Greenland ice sheets are too simplified and do not fulfil these requirements. Our mathematical model of the evolution of the Antarctic ice sheet is based on temperature parameterization. The parameterization correctly describes the distribution of temperature and its dependence on surface temperature, advection of ice, geothermal flux, and heat losses. The problem reduces to Cauchy’s problem for a non-linear parabolic partial differential equation with three-step dependence of ice temperature on depth. A linear viscous flow law is assumed. Tests treat the whole problem of the thermo-hydromechanics of the ice sheet. The ice sheet is assumed to be bounded by a grounding line or ice wall where the ice is in hydrostatic equilibrium with the sea. In this case, the problem reduces to a non-linear parabolic partial differential equation with a complicated boundary condition at the moving edge. A digital representation of the model is presented first. Tests demonstrated the possibility of using an explicit three-layered scheme. Calculations for the East Antarctic ice sheet indicated that the ice margin should retreat slightly under contemporary climatic conditions (which corresponds to the field evidence). In future the boundary should tend towards a stationary state. A forecast of the behaviour of the ice sheet is derived. The East Antarctic ice sheet is found to be stable during various changes in climatic factors. The calculated hydromechanical characteristics of the ice sheet agree with the observed field data.

A thermal balance model of the formation of sedimentary-exhalative lead-zinc deposits

A finite-difference, thermal balance model of hydrothermal circulation in a sedimentary basin is used to test quantitatively whether large-sized lead-zinc deposits can result from a system such as that postulated by Russell (1978), consisting of a one-pass convection cell within fractures that advance downward into basement rocks. The only heat source is the conductive geothermal flux, and the fluid is a single hypersaline brine recharged from an overlying sea.The buoyancy-driven flow system consists of downward percolation throughout the whole region, which is modeled as a porous medium, and rapid, localized upflow, which is modeled as turbulent pipe flow. The upflow may be located anywhere within the basin where there is a zone of high permeability. A flow equation is derived which equates the buoyancy force to the frictional losses in the recharge and discharge. Heat exchange is calculated between fluid and rock within the porous medium, which is treated as a one-dimensional vertical array of horizontal slices.Downward penetration of the fault system is controlled by an arbitrary cracking temperature, so that the fluid temperature cannot rise above a maximum value (200 degrees -250 degrees C) based on fluid inclusion data.The model determines the mass flow rate and fluid temperature. From this, the mass of Pb + Zn + Fe sulfide which the system could supply is estimated, using a metal solubility-temperature relationship derived from brine analyses.Results show that this system is capable of forming the very largest Pb-Zn deposits, provided that the metals are available to the system. For example, nearly 20 million metric tons of sulfide could be generated in 50,000 years either by circulation penetrating to a 10-km depth in rocks with a geothermal gradient of 30 degrees C km (super -1) or by circulation to a 6-km depth if the geothermal gradient is 60 degrees C km (super -1) . The model was extended to simulate repeated pulses of circulation and showed that thermal reequilibration of the rock to near the ambient gradient takes on the order of 10 6 years after which time heat extraction can be repeated.

Coupled thermomechanical response of an axisymmetric cold ice sheet

This study proposes a detailed model for ice sheets having a radially symmetric geometry. Governing relations are derived from first principles of physics, and the interactive effects of mechanical and thermal energy are taken into account. The resulting model is a nonlinear partial differential equation relating the temperature, velocity, and stress fields. Boundary conditions of accumulation rate, geothermal flux, sliding laws, and surface temperatures having been specified, and the model determines a steady state response in terms of ice sheet profile and internal temperatures, velocities, and stresses. We describe the computational methodology for numerically determining solutions from which one can assess the credibility of the model itself, and to the extent that it is credible, examine effects such as perturbing of external temperatures, accumulation rates, and so forth. Piloting examples illustrate this.