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The ensemble Kalman filter (EnKF) is a popular estimation technique in the geosciences. It is used as a numerical tool for state vector prognosis and parameter estimation. The EnKF can, for example, help to evaluate the geothermal potential of an aquifer. In such applications, the EnKF is often used with small or medium ensemble sizes. It is therefore of interest to characterize the EnKF behavior for these ensemble sizes. For seven ensemble sizes (50, 70, 100, 250, 500, 1,000, and 2,000) and seven EnKF variants (damped, iterative, local, hybrid, dual, normal score, and classical EnKF), we computed 1,000 synthetic parameter estimation experiments for two setups: a 2‐D tracer transport problem and a 2‐D flow problem with one injection well. For each model, the only difference among synthetic experiments was the generated set of random permeability fields. The 1,000 synthetic experiments allow to calculate the probability density function of the root‐mean‐square error (RMSE) of the characterization of the permeability field. Comparing mean RMSEs for different EnKF variants, ensemble sizes and flow/transport setups suggests that multiple synthetic experiments are needed for a solid performance comparison. In this work, 10 synthetic experiments were needed to correctly distinguish RMSE differences between EnKF variants smaller than 10%. For detecting RMSE differences smaller than 2%, 100 synthetic experiments were needed for ensemble sizes 50, 70, 100, and 250. The overall ranking of the EnKF variants is strongly dependent on the physical model setup and the ensemble size.

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.

Salt diapirs are commonly seen in the North Sea. Below the Zechstein Group exist possibly overpressured salt-anhydrite formations. One explanation as to the salt precipitation in areas with salt diapirs is that salt cementation is thermally driven and occurs strongly in places adjacent to salt diapirs. This paper assumes that the sealing effect of the cap rock above the salt formations is compromised and overpressured fluids, carrying dissolved minerals such as anhydrite (CaSO4) and salt mineral components (NaCl of halite), flow into the porous sedimentary layers above the salt formations. Additionally, a salt-diapir-like structure is assumed to be at one side of the model. The numerical flow and heat transport simulator SHEMAT-Suite was developed and applied to calculating the concentrations of species, and dissolution and precipitation amounts. Results show that the overpressured salt-anhydrite formations have higher pressure heads and the species elements sodium and chlorite are transported into porous sediment rocks through water influx (saturated brine). Halite can precipitate as brine with sodium and chlorite ions flows to the cooler environment. Salt cementation of reservoir rocks leads to decreasing porosity and permeability near salt domes, and cementation of reservoir formations decreases with growing distance to the salt diapir. The proposed approach in this paper can also be used to evaluate precipitation relevant to scaling problems in geothermal engineering.

We investigate the influence of hydrothermal circulation on cooling of oceanic lithosphere. We include hydrothermal convection in a 1-D lithosphere cooling model by using a scaling law which relates the Rayleigh to the Nusselt number. This law allows calculating an effective thermal conductivity accounting for the extra heat transport. Based on a global data set for bathymetry and surface heat flow for ocean floor ages between 0.7 and 160 Ma, we perform a joint inversion based on a downhill simplex algorithm to constrain characteristic parameters for hydrothermal cooling (beside the classical parameter mantle temperature, thickness of the lithosphere, and thermal expansivity of lithosphere rocks). Hydrothermal cooling parameters are crack aspect ratio which controls the hydrothermal penetrations depth, characteristic cementation time at which cracks become closed and hydrothermal circulation ceases, and sealing time when enough sedimentary cover on top of the lithosphere has accumulated to prevent hydrothermal fluid escaping into the ocean. Best fitting parameter sets predict mantle temperatures between 1350 and 1450°C and lithosphere thickness between 70 and 90 km and further suggest that (1) the fit to the data is strongly improved if hydrothermal cooling effects are considered, (2) hydrothermal cooling is important for up to 10 Ma old lithosphere and leads to a significant deviation from the 1/square root—law with an exponent closer to 1/3, (3) sedimentary sealing is completed for ~1.5 Ma old lithosphere, and (4) fitting of the data is improved for an apparently 1.4 times higher value of thermal expansivity which may account for effects of melt solidification.

We study the impact of spatially heterogeneous permeability on the formation and shape of hydrothermal porous flow convection in the Yarragadee Aquifer by modelling three simulation scenarios, each with differing permeability distributions. In all scenarios, the southern part of the model is characterised by convection rolls, while the north is dominated by a stable region of decreased temperatures at depth due to hydraulic interaction with shallower aquifers. This suggests that reservoir structure is a first-order controlling factor for the formation of the free convective system. The convective system adjusts to the spatially heterogeneous permeability distribution, yielding locally different convection patterns.

Modeling anisotropic flow in porous or fractured rock often assumes that the permeability tensor is diagonal, which means that its principle directions are always aligned with the coordinate axes. However, the permeability of a heterogeneous anisotropic medium usually is a full tensor. For overcoming this shortcoming, we use the mimetic finite difference method (mFD) for discretizing the flow equation in a hydrothermal reservoir simulation code, SHEMAT-Suite, which couples this equation with the heat transport equation. We verify SHEMAT-Suite-mFD against analytical solutions of pumping tests, using both diagonal and full permeability tensors. We compare results from three benchmarks for testing the capability of SHEMAT-Suite-mFD to handle anisotropic flow in porous and fractured media. The benchmarks include coupled flow and heat transport problems, three-dimensional problems and flow through a fractured porous medium with full equivalent permeability tensor. It shows firstly that the mimetic finite difference method can model anisotropic flow both in porous and in fractured media accurately and its results are better than those obtained by the multi-point flux approximation method in highly anisotropic models, secondly that the asymmetric permeability tensor can be included and leads to improved results compared the symmetric permeability tensor in the equivalent fracture models, and thirdly that the method can be easily implemented in existing finite volume or finite difference codes, which has been demonstrated successfully for SHEMAT-Suite.

During geothermal reservoir development, drilling deep boreholes turns out to be extremely expensive and risky. Thus, it is of great importance to work out the details of suitable borehole locations in advance. Here, given a set of existing boreholes, we demonstrate how a sophisticated numerical technique called optimal experimental design helps to find a location of an additional exploratory borehole that reduces risk and, ultimately, saves cost. More precisely, the approach minimizes the uncertainty when deducing the effective permeability of a buried reservoir layer from a temperature profile measured in this exploratory borehole. In this paper, we (1) outline the mathematical formulation in terms of an optimization problem, (2) describe the numerical implementation involving various software components, and (3) apply the method to a 3D numerical simulation model representing a real geothermal reservoir in northern Italy. Our results show that optimal experimental design is conceptually and computationally feasible for industrial-scale applications. For the particular reservoir and the estimation of permeability from temperature, the optimal location of the additional borehole coincides with regions of high flow rates and large deviations from the mean temperature of the reservoir layer in question. Finally, the presentation shows that, methodologically, the optimization method can be generalized from estimating permeability to finding any other reservoir properties.

The area of the 9.1-km-deep Continental Deep Drillhole (KTB) in Germany is used as a case study for a geothermal reservoir situated in folded and faulted metamorphic crystalline crust. The presented approach is based on the analysis of 3-D seismic reflection data combined with borehole data and hydrothermal numerical modelling. The KTB location exemplarily contains all elements that make seismic prospecting in crystalline environment often more difficult than in sedimentary units, basically complicated tectonics and fracturing and low-coherent strata. In a first step major rock units including two known nearly parallel fault zones are identified down to a depth of 12 km. These units form the basis of a gridded 3-D numerical model for investigating temperature and fluid flow. Conductive and advective heat transport takes place mainly in a metamorphic block composed of gneisses and metabasites that show considerable differences in thermal conductivity and heat production. Therefore, in a second step, the structure of this unit is investigated by seismic waveform modelling. The third step of interpretation consists of applying wavenumber filtering and log-Gabor-filtering for locating fractures. Since fracture networks are the major fluid pathways in the crystalline, we associate the fracture density distribution with distributions of relative porosity and permeability that can be calibrated by logging data and forward modelling of the temperature field. The resulting permeability distribution shows values between 10-16 and 10-19 m(-2) and does not correlate with particular rock units. Once thermohydraulic rock properties are attributed to the numerical model, the differential equations for heat and fluid transport in porous media are solved numerically based on a finite difference approach. The hydraulic potential caused by topography and a heat flux of 54 mW m(-2) were applied as boundary conditions at the top and bottom of the model. Fluid flow is generally slow and mainly occurring within the two fault zones. Thus, our model confirms the previous finding that diffusive heat transport is the dominant process at the KTB site. Fitting the observed temperature-depth profile requires a correction for palaeoclimate of about 4 K at 1 km depth. Modelled and observed temperature data fit well within 0.2 degrees C bounds. Whereas thermal conditions are suitable for geothermal energy production, hydraulic conditions are unfavourable without engineered stimulation.

We present a method to determine equivalent permeability of fractured porous media. Inspired by the previous flow-based upscaling methods, we use a multi-boundary integration approach to compute flow rates within fractures. We apply a recently developed multi-point flux approximation Finite Volume method for discrete fracture model simulation. The method is verified by upscaling an arbitrarily oriented fracture which is crossing a Cartesian grid. We demonstrate the method by applying it to a long fracture, a fracture network and the fracture network with different matrix permeabilities. The equivalent permeability tensors of a long fracture crossing Cartesian grids are symmetric, and have identical values. The application to the fracture network case with increasing matrix permeabilities shows that the matrix permeability influences more the diagonal terms of the equivalent permeability tensor than the off-diagonal terms, but the off-diagonal terms remain important to correctly assess the flow field.

We present a comprehensive statistical analysis of petrophysical properties of rocks of the northeastern Rhenish Massif and the Lower Rhine Embayment in Germany. Properties measured comprise thermal conductivity, specific heat capacity density, porosity, hydraulic permeability, and compressional wave velocity. This robust and statistically reliable data is generally useful for numerical modeling of heat transport processes and helps, in particular, reducing the risk of failure in projects of geothermal energy use. We measured the thermophysical properties of rocks from two geological settings: (1) predominantly little consolidated Tertiary rocks forming the young sedimentary cover of the Lower Rhine Embayment in the condition they arrived in the laboratory; (2) well consolidated Paleozoic rocks from the northeastern Rhenish Massif in both dry and saturated condition. We tested a total of 476 samples from different lithologies in both settings in a comprehensive laboratory program consisting of mineralogical analyses and various petro- and thermophysical measurements at ambient and elevated p-T-conditions. This yields relations between composition and thermophysical properties of different sedimentary rock types and allows distinguishing between effects due to rock matrix and structure. The results are used to prove petrophysical rock models and allow predicting thermal properties of distinct rock types for greater depth. The results show that the thermophysical properties of Paleozoic rocks are mainly controlled by their mineralogical compositions, while thermophysical characteristics of Tertiary rocks are the result of a superposition of properties of their mineral content and the water-filled pore volume.

SUMMARY Followingearlierstudies,wepresentforwardandinversesimulationsofheatandfluidtransport of the upper crust using a local 3-D model of the Kola area. We provide best estimates for palaeotemperatures and permeabilities, their errors and their dependencies. Our results allow discriminating between the two mentioned processes to a certain extent, partly resolving the non-uniqueness of the problem. We find clear indications for a significant contribution of advective heat transport, which, in turn, imply only slightly lower ground surface temperatures during the last glacial maximum relative to the present value. These findings are consistent with the general background knowledge of (i) the fracture zones and the corresponding fluid movements in the bedrock and (ii) the glacial history of the Kola area.

[1] Studying heat transfer processes in sedimentary crustal rocks requires the correct thermal conductivity of the respective rock type. Often a single value is used for a given rock type, obtained from the measurements on homogenous samples. We demonstrate how variations in rock layering and microfractures on the subcentimeter scale may influence thermal conductivity values at much larger scale. We obtain thermal conductivity images from lab measurements on two different, heterogeneous samples performed with an optical thermal conductivity scanner in two directions. We study different spatial averaging methods for parameterizing the structural heterogeneities and the associated variation of thermal conductivity within the samples. For each of these structural simplifications, we set up a numerical model for a numerical heat transfer experiment in order to determine effective thermal conductivity values in two directions. We compare these values and the mean thermal conductivities obtained from different mixing laws and find that, in heterogeneous rocks, effective and mean thermal conductivity may differ substantially. This may cause significant errors in reservoir-scale simulations of heat transfer with associated severe consequences for estimated heat flow and temperatures.

We analyze the likelihood of success for heat production strategies in a sandstone reservoir in the north-eastern German basin in a depth of about 2 km by simulating both double and single well configurations. For this test case study we use an exploited oil and gas field. We combine seismic interpretation, numerical modeling, and stochastic estimation of rock properties to predict the transient temperature and pressure variations and their uncertainties in a geothermal reservoir. We demonstrate the essential necessity in geothermal reservoir modeling to account for heterogeneity of rock properties. We use 3D seismic data and stratigraphy data from about 100 wells at 1500 m – 2500 m depth for setting up a 3D stratigraphic model. Rock properties are assigned to this model by a Monte Carlo approach using Sequential Gaussian Simulation. Using 3D inversion of temperature data obtained in the wells we estimate a specific heat flow of 77.7 mW m −2 ± 1.2 mW m −2 at 6 km depth, in agreement with a temperature of 87.1 °C ± 1.8 K in the Rhaetian sandstone target layer at a depth of ∼2 km. For different types of potential geothermal well installations inside the Rhaetian sandstone layer the probability of success is just 1.6%.

European Geosciences Union General Assembly 2017, EGU Division Energy, Resources & Environment (ERE) / Edited by Sonja Martens, Christopher Juhlin, Suzanne Hangx, Michael Kühn European Geosciences Union General Assembly 2017, ERE, Vienna, Austria, 23 Apr 2017 - 28 Apr 2017; Amsterdam [u.a.] : Elsevier, Energy Procedia, 125, 318-326 (2017). doi:10.1016/j.egypro.2017.08.206, Published by Elsevier, Amsterdam [u.a.]

In this study, we identify a suite of fluid flow pathways and estimate permeability distribution for the engineered geothermal reservoir at the European enhanced geothermal system test site at Soultz-sous-Forets, France. The work is based on the 2005 hydraulic connectivity experiment between the injection borehole GPK3 and the production boreholes GPK2 and GPK4. We use a massive Monte Carlo approach, together with a geostatistically based assignment of permeability distributions using a stochastic technique, in order to investigate the observed tracer concentration curves. By applying different fitting criteria, 49 single models were selected, providing a good fit to the observation data from a model ensemble of 10,000 realizations. These models are classified in three groups with different flow geometries and permeability distributions, and were analyzed for their Darcy velocities. This approach allows the limits for possible permeability distributions and geometries of the stimulated zones to be quantitatively approximated.

A major consequence of the interaction of a plume with an oceanic ridge is the enhanced melt production and associated crust generation. In the case of Iceland crustal thickness as large as 20 to 40 km has been reported. Crustal seismic velocities are high, and have to be explained by thermal or chemical effects. In the first part of the paper we address the question whether extraction of melt out of the plume beneath a slowly spreading ridge and deposition of extracted basalt volumes at the surface produces a dynamic feedback mechanism on mantle melting. To study this question we solve the convection equations for a ridge centred plume with non-Newtonian rheology including melting, melt extraction associated with deposition of cold crust at the surface of the model, and using a simplified approach for compaction. The assumption of cold crust is justified if the thickness of each deposited basaltic layer is less than roughly 1 km. Depending on the buoyancy flux of the plume, crustal thicknesses between 10 and 40 km are modelled, showing characteristic dipping structures resembling the rift-ward dipping basaltic layers of East- and Western Iceland. Comparing the resulting crustal thickness and magma generation rate with models in which the dynamic effect of crust deposition has been suppressed indicates, that melt generation beneath a slowly spreading ridge is considerably damped by the dynamic feedback mechanism if the plume buoyancy flux exceeds 400 to 600 kg/s. Based on the observed crustal thickness of Iceland our models predict a plume buoyancy flux of 1140 kg/s. In the second part we study the accretion of the Icelandic crust by a thermo-mechanical model in more detail based on the Navier–Stokes-, the heat transport and the mass conservation equations including volumetric sources. Hot (1200 °C) molten crustal material is injected into the newly forming crust with a constant rate at different crustal source regions: a) deep, widespread emplacement of dykes and sills including crustal underplating, b) magma chambers at shallow to mid-crustal level, and c) surface extrusions and intrusions in fissure swarms at shallow depth connected to volcanic centres. We identify the material from the different source regions by a marker approach. Varying the relative dominance of these source regions, characteristic crustal structures evolve, showing shallow dipping upper crustal layers with dip angles between 10 and 15°. The thermal structure of the crust varies between cold crust (shallow-source region dominating) and hot crust (deep-source region dominating). We use observations of maximum depth of seismicity to constrain the depth of the 650 °C isotherm and seismological inferences on the lower crust to constrain temperatures in that region. The best agreement with our models is achieved for crust formation dominated by deep dykes and underplating with a considerable influence of magma chamber accretion.

Granitoid intrusions are the primary heat source of many deep geothermal reservoirs in Tuscany. The depth and shape of these plutons, characterised in this study by a prominent seismic reflector (the K horizon), may vary significantly within the spatial scale of interest. In an exploration field, simulations reveal the mechanisms by which such a heat source influences temperature distribution. A simple analysis quantifies the sensitivity of potentially measurable indicators (i.e. vertical temperature profiles and surface heat flow) to variations in depth, temperature, and shape of the heat source within given ranges of uncertainty., Geothermal Energy, 4, ISSN:2195-9706

New satellite technology to measure changes in the Earth’s gravity field gives new possibilities to detect layers of low viscosity inside the Earth. We used density models for the Earth mantle based on slab history as well as on tomography and fitted the viscosity by comparison of predicted gravity to the new CHAMP gravity model. We first confirm that the fit to the observed geoid is insensitive to the presence of a low viscosity anomaly in the upper mantle as long as the layer is thin (not, vert, similar 200 km) and the viscosity reduction is less than two orders of magnitude. Then we investigated the temporal change in geoid by comparing two stages of slablet sinking based on subduction history or by advection of tomography derived densities and compared the spectra of the geoid change for cases with and without a low viscosity layer, but about equal fit to the observed geoid. The presence of a low viscosity layer causes relaxation at smaller wavelength and thus leads to a spectrum with relatively stronger power in higher modes and a peak around degrees 5 and 6. Comparing the spectra to the expected degree resolution for GRACE data for a 5 years mission duration shows a weak possibility to detect changes in the Earth’s gravity field due to large scale mantle circulation, provided that other causes of geoid changes can be taken into account with sufficient accuracy. A discrimination between the two viscosity cases, however, demands a new generation of gravity field observing satellites.

The dynamic and melting processes of a ridge-centred plume have been investigated in a companion paper by Ruedas et al. (hereafter referred to as Paper I) in a set of 3-D numerical fluid dynamic models with varying plume excess temperatures and melt extraction thresholds. In Paper I, the modelled thickness of the generated crust has been compared to observations of the Icelandic crust. Using the results of those plume models magnetotelluric (MT) transfer functions and seismic velocity anomalies are predicted in this paper. Together with Paper I, a dynamically consistent set of geophysical observables of a ridge-centred plume is presented and applied to Iceland. Temperature, partial melting and the connectivity of the melt phase influence the electrical conductivity of crust and mantle rocks. The temperature and melt fraction of our plume models are used to calculate 3-D conductivity models for MT modelling. For the melt geometry ellipsoidal inclusions with appropriate aspect ratios were assumed to control melt connectivity. The resulting transfer functions are compared to each other and to models not including a plume to separate signals from the ridge and the plume. They may be applied to observed MT measurements. If the plume head contains only 1 per cent of melt, the plume signal cannot be distinguished from the ridge signal, at least 3 per cent melt is needed for such distinction. The other predicted observables calculated from the different numerical models are seismic velocity anomalies. The temperature-induced VP and VS anomalies were estimated including anharmonic and anelastic effects as well as the water induced increase of dislocation mobility that lowers seismic velocities. Realistic melt geometries, as observed in laboratory experiments, were used to calculate the effect of partial melts on the seismic velocities. VS anomaly distributions are synthesized from the different plume models and compared to seismic observations. To reconcile seismic anomalies of the plume head and plume stem, a wet plume stem overlain by a partially molten, dehydrated plume head is favoured. The combined interpretation of available observations, crustal thicknesses (Paper I) and seismic results, with our dynamic plume models (Paper I) leads to a favoured plume model with 135 K excess temperature and a vertical velocity of approximately 13 cm yr−1 at 200 km depth, with 1 per cent melt extraction threshold, and a melting zone of approximately 500 km width and 100 km depth extent., This research was supported by the Deutsche Forschungsgemeinschaft, grants Schm 872/6-1 and Schm 872/6-2. We wish to thank Wolfgang Jacoby for helpful and inspiring discussions, Thomas J. Shankland and an anonymous referee for valuable comments and constructive criticism.

SUMMARY The North Atlantic around Iceland is characterized by a large geoid high and an anomalous shallow ocean floor; both observations are presumably due to upwelling of hot material in the mantle. We extracted this region from a global tomography data set to study the structure of the mantle in more detail. The tomography data reveal a confined low-velocity structure from the core–mantle boundary (CMB) to the upper mantle, stretching from a location at the CMB below southwest Greenland towards the upper mantle in a strongly eastward inclination. In the present study we compare the observed gravity potential field in the North Atlantic with a modelled field based on mantle temperature variations estimated from tomography. Seismic traveltime residuals are converted to temperature variations assuming a linear relation between seismic velocity and density and a pressure-dependent thermal expansivity. We found a maximum excess temperature in the plume conduit at the CMB of ∼250 °C, weakly decreasing towards the phase transition zone (PTZ). In the PTZ a temperature rise of ∼50–70 °C is found, which is in agreement with the latent heat release by the olivine phase transitions. The 3-D temperature field is then used as the driving force for viscous flow in a Cartesian convection model. The model dimensions are chosen four times as large as the tomographic section to allow resolution for long wavelengths and convective return flow. For a number of constant viscosity and temperature- and depth-dependent viscosity cases the dynamic topography, gravity anomaly and geoid undulations are calculated and compared with the EGM96 potential field coefficients in the wavelength range of 400 to 4000 km. The observation data were also corrected for ocean lithosphere cooling and isostatic compensation of continental crust. The best agreement between observation and modelled data (78 per cent fit for geoid and 47 per cent for gravity) is obtained for a temperature-dependent viscosity of about one order of magnitude for 500 °C temperature variation and an increase of viscosity with depth by no more than a factor of 50 from the upper to the lower mantle. The generally good spatial agreement supports the tomographic model, at least for the upper mantle, and indicates that the East Greenland margin as well as the outer Faroer Ridge are dynamically supported. Low-density material west of the Kolbeinsey Ridge might be linked to low-density anomalies below the Greenland Shield. The presence of lower mantle anomalies causes a large-scale geoid high of ∼3 to 5 m in agreement with observations, but our approach cannot further constrain the spatial distribution of anomalies in the lower mantle.

SUMMARY In this study and a companion paper, numerical models of convection and melt generation in a ridge-centred plume system are developed for plumes with different temperature anomalies ΔTP and varying fractions of retained melt ϕex. The produced melt in excess of the retention threshold is used to generate ridge and plume crust respectively, whose thickness is found to be sensitive to changes in ΔTP and ϕex. Comparison of calculated crustal thicknesses with observations from mid-oceanic ridges and from Iceland confirms earlier findings that ΔTP of the Iceland plume in the upper mantle is about 150–200 K and that the Icelandic crust is thick. It also suggests that the retained melt fraction in partially molten mantle is at most 1 per cent. In the preferred model, plume melting occurs between ca. 25 and 110 km depth, at up to ∼250 km from the spreading centre. The temperature and melt fraction fields from the numerical models are used as input for the derivation of seismic velocity anomalies and magnetotelluric response functions in the companion paper. Furthermore, the models reveal that the high temperatures of plumes result in a superlinear increase of crustal thickness with plume excess temperature through the combined effects of enhanced melting, active upwelling and the extent and geometry of the melting zone.

SUMMARY In most mantle convection studies with variable thermal expansivity only the pressure dependence is considered. Here we investigate the effect of temperature- and/or pressure-dependent thermal expansivity α on the distribution of buoyancy forces in mantle convection. Thermal expansivity is calculated for the dominant upper-mantle mineral, forsterite, and a map of its dependence on T and p is given. By studying simple 2-D steady-state constant-viscosity convection and comparing cases with constant α, α( p), α(T ) and α(p, T) we find that at mantle temperatures the pressure dependence of α is important. For the lithosphere the dependence of α on temperature dominates, since the temperature dependence of α is much stronger in the low-pressure regime. Also dynamic topography changes considerably (up to 15 per cent) if α is T- and p-dependent compared with a constant or only p-dependent case. Scaling laws for the Nusselt number and the rms velocity are obtained. They differ from the constant-α case by at most 12 per cent if an effective Rayleigh number based on the spatial average of α is used.

European Geosciences Union General Assembly 2015 - Division Energy, Resources and Environment, EGU 2015 / Edited by Maria Ask, Suzanne Hangx, Viktor Bruckman and Michael Kühn European Geosciences Union General Assembly 2015, EGU 2015, Vienna, Austria, 12 Apr 2015 - 17 Apr 2015; Amsterdam [u.a.] : Elsevier, Energy procedia 76, 321-330 (2015). doi:10.1016/j.egypro.2015.07.869, Published by Elsevier, Amsterdam [u.a.]

SUMMARY The North Atlantic between the Charlie–Gibbs and Senja Fracture Zones shows a number of oceanic plateaux, continental fragments and unusual mid-oceanic ridges, the Reykjanes Ridges and the Iceland Plateau being the most prominent ones. While rifted continental fragments and marginal volcanic plateaux have been formed during the initial formation process of the North Atlantic, others, such as the Reykjanes Ridge and plume-related plateaux such as Iceland and possibly also Jan Mayen, are still under development. By studying the ratio of geoid to topography in the long-wavelength range for these regions of elevated topography and comparing the results with theoretical models of crustal loading and subsurface thermal uplift we can show that the Rockall Bank and the Voring Plateau are compensated by a thick crust alone, while the Iceland Plateau, the outer Faeroe Plateau and the Jan Mayen Block have a strong component of deeply situated mass anomalies. The admittance, the spectral ratio of geoid to topography, for a number of profiles across the Reykjanes Ridge clearly indicates a decreas ei n compensation depth with distance from Iceland. This strengthens the argument for a mass flux from the Iceland Plume into the Reykjanes Ridge.

Stresses in the lithosphere are one indication of processes in the Earth interior: here we present a calculation of largescale lithospheric stresses caused by global mantle circulation. The mantle flow field is calculated based on density structures inferred from global seismic tomography. Predicted principal stress directions are compared to interpolations based on observed stresses. Agreement between predictions and observations is often good in regions where lithospheric stresses and mantle tomography are well constrained. Predicted magnitudes of scalar stress anomalies vary more strongly than predicted stress directions for various tomographic models. Hotspots preferentially occur in regions where calculated stress anomalies are tensile or slightly compressive. Results do not strongly depend on radial mantle viscosity structure, lithospheric rheology (viscous or elastic) or plate motion model. The model also predicts the directions of motion well for most plates; misfits in the predicted magnitudes can be explained qualitatively. Stress anomalies due to causes within the lithosphere (oceanic cooling with age, variations in crustal thickness, topography isostatically compensated at subcrustal levels) are also computed. Predicted stress directions in the absence of mantle flow can explain observations almost as well as mantle flow. Nevertheless, current models of mantle flow are largely in accord with interpolations of observed principal stress directions and the observed plate motions. fl 2001 Elsevier Science B.V. All rights reserved.

Summary The convective flow pattern beneath the oceanic lithosphere is strongly influenced by the movement of the lithospheric plate on top. Assuming upper mantle convection, the wavelengths, geometric structure and time of onset for ridge-perpendicular rolls as functions of the Rayleigh number and the plate velocity have been investigated by numerical modelling. The related gravity anomalies have been estimated and compared to observations from the SE Pacific, which show ridge-perpendicular anomalies with wavelengths of 150–220 km and amplitudes of about 10 mGal. For constant viscosity, the type of secondary circulation perpendicular to the diverging ridge depends on the relation between imposed plate velocity, vs, and maximum velocity in the free-convection case, vHfree. If vs is less than vHfree the flow is dominated by off-ridge up- and downwellings; if vs is about 10 times larger than vHfree the flow remains 2-D. If vs is between these extrema, a chain of ridge plumes develops from the lower thermal boundary layer with adjacent ridge-perpendicular walls that lead to roll-like circulation (‘Richter rolls’) throughout the model box. The wavelength of these rolls is a function of the Rayleigh number and the plate velocity. For parameters realistic for the Earth, rolls with considerable amplitude first develop after more than 50 Myr with wavelengths of at least 250 km. For temperature- and pressure- (depth-) dependent viscosity, the wavelengths of the evolving rolls are determined by the Rayleigh number related to the maximum viscosity in the interior of the convecting system (and not to the average viscosity). For models with a strong decrease in viscosity to values of about 1019 Pa s in a 100-km-wide asthenospheric channel below the lithosphere, ridge-perpendicular rolls, which only fill the low-viscosity layer, appear after a few million years. After a transitional stage of some tens of millions of years rolls in the whole upper mantle also evolve. The asthenospheric rolls develop from instabilities of the upper thermal boundary layer and have wavelengths of about 220–280 km. The time needed for alignment of these rolls to the direction of plate movement is a few million years and the distance from the ridge to the point of onset of the rolls is about 200–500 km; both are functions of the plate velocity. While the formation time for rolls in the whole upper mantle is quite large and their existence is related largely to two-layered convection, this type of flow might not be very relevant for the Earth, although it has been used to account for 3-D structures at oceanic ridges. To explain the observed gravity anomalies in the SE Pacific, roll-like circulation in a low-viscosity asthenospheric layer is the preferred candidate, where the modelled amplitudes and wavelengths of gravity anomalies fit the observations.

Geochemical observations of ocean island basalts show a broad variety in the chemical composition of trace elements. These observations cannot be explained by different temperature and pressure conditions at the melt production region only but also demand differences in the parental material at the base of the lithosphere. Here, we add a new explanation for this finding based on the different interaction of small and large plumes with the spinel–perovskite phase boundary (SPB) in the Earth’s mantle. We assume that mantle plumes detaching from the core–mantle boundary (CMB) are of variable size and excess temperature. While rising through the lower mantle, they form an approximately spherical plume head. When arriving at the SPB, they are retained from further rise depending on their size and excess temperature. We have investigated the interaction of a plume with the SPB using a numerical approach for viscous flow. To focus particularly on this interaction, we simply modelled the initial plume as a hot volume of variable cross-section and excess temperature. Volumes with a radius exceeding about 150 km and an excess temperature of more than 100°C rapidly cross the SPB. With decreasing size and increasing excess temperature, volumes are retarded at the SPB and those with a radius smaller than about 80 km stagnate entirely below the SPB. These results are roughly independent of the particular rheology or two-dimensional versus three-dimensional geometry. In the present study, we investigated the degree of thermal entrainment of material at the SPB for strongly retarded plumes. We estimate the amount of chemical mixing by tracking passive markers from the original plume volume and the regions around the SPB to the base of the lithosphere. The amount of entrainment of material from close to the SPB depends on the retardation time and the thermal growth of the plume head at the SPB. Plume heads which reach the base of the lithosphere after a retardation time of more than 50 Ma might entrain (in the numerical model) large amounts of material from the SBP but they may not be characteristic for the Earth, since they might be distorted by large scale mantle flow. However, even if we limit the retardation time to reach the base of the lithosphere to 50 Ma, plumes, originally composed of material from the CMB and the adjacent lower mantle, might easily entrain up to 15% of their volume of material originating from the SPB.

At a depth of ∼660 km in the Earth's mantle the spinel-perovskite phase boundary is a prominent barrier for mantle convection. This is due to the negative Clapeyron slope of the phase equilibrium curve which leads to an elevation of the phase boundary within hot upwellings causing negative buoyancy forces. We have investigated the conditions for rising plumes either to penetrate and pass the spinel-perovskite phase boundary or to stick and spread below it by studying the fundamental physics of this process. The plume heads were simply modeled as hot three-dimensional (3-D) spheres or 2-D cylinders. A simple calculation balancing the positive thermal and the negative phase bouyancy forces leads to a better parameterization using two dimensionless quantities. In addition to the phase buoyancy parameter, we defined a deflection parameter, relating the elevation of the phase boundary to the plume head radius to account for the geometrical shape of a plume head. This parameterization is further tested with numerical models that include the effects of thermal diffusion, latent heat, the olivine-spinel phase boundary at a depth of 410 km, and temperature and/or phase-dependent viscosity structure. For laboratory estimates of the slope (-3 MPa/K) and density increase at the spinel-perovskite phase boundary (250 kg/m 3 ) our models predict that plumes with excess temperatures of 50°-600°C will stick at the top of the lower mantle if their head radii are less than ∼100 km. Plumes will penetrate into the upper mantle if plume head radii exceed 100 km. While the style of plume penetration or spreading at the top of the lower mantle strongly depends on the viscosity structure, the conditions for penetration do not. All rising hot volumes with nonpenetrating conditions stick at the top of the lower mantle and spread laterally, independent of their viscosity structure. For weakly nonpenetrating conditions, heat diffusion increases the radius of the hot volume and leads to penetration during a secondary stage. For strongly nonpenetrating conditions, spreading at the top of the lower mantle drives a mechanically coupled counterflow in the upper mantle, which is stable for a very long time. For volumes with an excess temperature of more than 350°C heat diffusion across the phase boundary will eventually inhibit this counterflow and stabilize a thermally coupled flow which might entrain some material of the hot volume. However, our results suggest that the spinel-perovskite phase boundary is unlikely to inhibit the penetration of mantle plumes of the size thought to have generated many flood basalt provinces and hotspot chains.

SUMMARY Interpretation of satellite altimetry data as well as ship bathymetry data revealed strongly elongated anomalies roughly perpendicular to the mid-ocean ridges in the Indian and east Pacific oceans. A spectral analysis of gravity altimetry data along profiles parallel to the East Pacific Rise indicated wavelengths of about 150‐180 km close to the ridge and about 250 km further away. A simple model of Rayleigh‐Taylor instabilities developing at the base of the cooling lithosphere is discussed and applied to the data. By considering thermal diVusion and comparing Rayleigh‐Taylor growth rates to the velocity of the thermal front in the cooling lithosphere, we are able to explain the observed anomalies by instabilities developing below the lithosphere in a layer with a viscosity of about 1019 Pa s above an asthenospheric layer with a viscosity reduction of 2‐3 orders of magnitude.

[1] We present an estimation of the permeability fields of the reservoir at the Enhanced Geothermal System (EGS) at Soultz-sous-Forets, France, based on the data assimilation technique Ensemble Kalman Filter (EnKF). To this end, we assimilate data from a tracer circulation experiment performed in 2005. Using a 3-D numerical simulation of fluid transport and chemical tracer dispersion, we advance the tracer in time and control the concentration. With the EnKF we obtain reliable fits for concentration data recorded in both existing production boreholes, GPK2 and GPK4. As an alternative to discrete fracture networks, our heterogeneous equivalent porous medium approach thus can also characterize the hydraulically fractured zone of the engineered geothermal system. We present best estimates for permeabilities (10−14 m2–10−12 m2for the fracture zone) and the corresponding uncertainty which is about one order of magnitude. After comparing our results to results from a massive Monte Carlo and from a gradient-based Bayesian approach, it becomes clear that only the EnKF of this three approaches is able to fit concentrations at GPK2 and GPK4 simultaneously. Based on the EnKF estimates obtained, a long-term performance prediction including an uncertainty analysis for the reservoir (as it was in 2005) yields no thermal breakthrough in the system within at least 50 years of operation. Our study demonstrates the efficiency of the EnKF when estimating the permeability distribution in an EGS reservoir even with sparse data available.

Geothermal energy is a clean, globally available and nearly inexhaustible energy resource. However, the necessary deep drill holes demand financial investments on the order of a few tens of millions of Euros, without guarantee that the required flow rates and temperature of the produced fluids allow an economical use. This exploration risk often turns into a major show-stopper for a commercial use of geothermal energy. Improved methods for estimating the distribution of subsurface hydraulic and thermal properties will result in a reduced exploration risk. Therefore, reliable estimates of these properties are mandatory for the economic and technical planning and operation of a geothermal installation. Not in the least, this comprises quantifying the uncertainty of these estimates at an early stage of reservoir exploration and continuous updates and modifications as reservoir development progresses.

The evolution of the lithosphere is mainly controlled by time-dependent forces due to (1) plate tectonic processes and (2) sublithospheric mantle flow. Plate tectonic processes like continental collision may provide strong thermal disturbances and, after completion, may trigger secondary convection beneath the lithosphere. Without such mantle flows lateral variations of temperature (and associated variations of lithospheric thickness hL or seismic velocities) will equilibrate after time scales which are considerably shorter than the geologic ages of several provinces in Europe. We will discuss the role of sublithospheric mantle flows on the evolution of the lithosphere and the asthenosphere and compare the results with observations from the European lithosphere. Steady-state convection models with a rheology based on laboratory data on lherzolite show, that there exists a simple relationship between mantle heat flow and hL. However, steady state may be reached only after transition times of the order of 1 Ga. During such times, hL shows strong lateral variations. If such variations were inherited from plate tectonic events, the role of sublithospheric convection would be to prolong their lifetime considerably. At higher heat flows, sublithospheric mantle convection becomes strongly time-dependent with a time scale of 25–50 Ma. On this time scale, variations of hL are small. Altogether, we observe no strong direct correlation between upwelling mantle flows and thin lithosphere. In some cases the correlation is even reversed. On the other hand, the presence or absence of a partially molten asthenosphere may be strongly affected by sublithospheric convection, and may show strong lateral variations as well. These variations in space and time can be correlated with the laterally heterogeneous LVZ, with seismic tomography data and with intraplate volcanism in Europe. Mantle convection, mantle diapirs, and variations in thickness of the lithosphere may exert forces on the lithosphere and crust. They will lead to bending of the lithosphere, changes in surface topography and thinning or thickening of the crust, induced by lateral flows within the lower crust. Depending on the time scale of loading and unloading of the lithosphere and the relaxation time associated with lower crustal flows characteristic relations between Moho depth and surface topography are predicted. Comparison with observed correlations between Moho depth, surface topography and lithospheric thickness of European crustal age provinces show some trends in agreement with the proposed crustal deformation model.

Small-scale convection beneath continental lithosphere is likely to initiate viscous flow in the ductile lower crust. Positive lithospheric bending will develop above upwelling mantle flow leading to a lateral squeezing out of crustal material from elevated areas which results in significant crustal thickness variations in its final stage. This process was studied with a finite element approach for viscous material for a number of different viscosity contrasts between lower crust and lithospheric mantle. Significant Moho undulations of the order of at least 5 km within a time period of about 50 m.y. can only be reached if the lower crustal viscosity is less than 1021 Pa s or if the lithospheric mantle viscosity is less than 1024 Pa s. The maximum topography is a function of the viscosity contrast and is generally of the order of a few hundreds of meters with a relaxation time between 5 and 103 m.y., strongly dependent on the crustal viscosity. In conclusion, this process might be important to explain crustal thinning and thickening of the order of about 10 km in areas of enhanced thermal gradient.

SUMMARY Geoid height anomalies around the Iceland hotspot in an area extending between 50"W to 14"E and 45"N to 72"N have been investigated to search for evidence of an upper mantle thermal anomaly. After removing wavelengths longer than 3800 km, the effect of the cooling lithosphere was eliminated by low-pass filtering of age data and applying the boundary model. The effects of the various platforms and swells in the North Atlantic were removed by an Airy model, since the geoid-to-topography ratio is lower than 1.5 m km-' for all areas of elevated topography independent of their origin. The residual geoid shows a large positive anomaly with a steep constant slope towards a location (north)west of Iceland beneath Greenland. The amplitude of the anomaly can be estimated to at least 8m. The geoid-to-topography ratio reaches a value of 7mkm-' which is in good agreement with a plume-related anomaly.

The effect of sublithospheric convection on the thickness and structure of the continental lithosphere is studied in numerical models assuming different rheologies (Newtonian, non-Newtonian, and temperature and pressure dependent), heat fluxes, and heating modes (bottom versus internal heating). The stagnant regions near the top of the models are identified with the lithosphere. We distinguish a seismic and thermal lithosphere (controlled by temperature), an elastic lithosphere (controlled by viscosity), and a mechanical lithosphere (controlled by strain rate). Strong lateral thickness undulations with a thick lithosphere above the downwelling regions and a thin lithosphere above the upwelling regions develop. The thickness of the elastic lithosphere is about two-thirds of the mechanical lithosphere, while the ratio of the elastic to the thermal lithosphere varies between 0.4 and 0.8. The time dependence of some models (with internal heating and a surface heat flow of 20 mW/m2) is characterized by long periods (of the order of 1 Ga) close to steady state and short periods (100 Ma) of changing cell patterns and lithospheric thicknesses. Models showing thick lithospheric roots suggest that the mantle beneath some old shields may be associated with cold, slowly downwelling convective flow rather than being firmly attached to the lithosphere. The missing gravity and topography signals from such regions can be explained by elastic bending of the lithosphere and by dynamic adjustment of the Moho. Observed lithospheric thickness variations in Europe and their minimum to maximum spacing agree well with the models, suggesting sublithospheric convection to be the cause. Compared to other observed features, thickness undulations of the lithosphere seem to provide the strongest indications for sublithospherical convection. Relatively low viscosities in the lower crust may lead to a long-term decoupling of surface topography from Moho topography and mantle dynamics. The Moho depth is capable of adjusting to mantle stresses within relaxation times of the order of 100 Ma, while surface topography may flatten out. Such a mechanism may be important in regions with a deep Moho such as Fennoscandia or with a shallow Moho such as the Pannonian Basin, neither region showing a pronounced surface topography.

Currently the North Atlantic ridge is overriding the Iceland plume. Due to several ridge jumps the plume has been virtually ridge-centred since 20–25 Ma giving rise to extensive melting and crust formation. This review gives an overview over the results of the geophysical and, to minor extent, the geochemical research on the general structure of the Icelandic crust and the mantle beneath Iceland. In the first part, results mostly from topography/bathymetry, gravity, seismics/seismology, magnetotellurics, and geodynamical numerical modelling are summarised. They support the main conclusion that the Icelandic crust is up to ca. 40 km thick, whereby the lower crust and the uppermost mantle have an anomalously small density contrast and a gradual transition rather than a well-defined Moho. The interpretation of a good electrical conductor at 10–15 km depth as a molten layer is irreconcilable with a thick crust, so that alternative explanations have to be sought for this still enigmatic feature. In the second part, results from different branches of seismology, geochemistry, and numerical modelling on the Iceland plume arc reviewed and discussed. For the upper mantle, combining seismological models, geodynamical models and crustal thickness data suggests that the plume has a radius of 100–120 km and an excess temperature of 150–200 K, while the structure of the plume head is less well known. The volume flux is likely to be 5–6 km3/a, and numerical modelling indicates that water and its loss upon melting have a substantial impact on melt production and on the dynamics and distribution of segregating melt. Geochemical studies indicate that the plume source is quite heterogeneous and very probably contains material from the lower mantle. An origin of the plume somewhere in the lower mantle is also supported by several seismological findings, but evidence is not unambiguous yet and has still to be improved.

The long wavelength geoid height undulations are the result of density variations inside the Earth and the dynamic response of the viscous mantle due to the buoyancy forces resulting in dynamic topography, plus the contribution of isostatic topography due to crustal and lithospheric structure. The dynamic topography is a function of the effective stress transmission inside the earth and is linked to the viscosity of the mantle. We solve the equation of motion for a viscous Earth's mantle assuming an incompressible 6-layer shell model and determine the dynamic response function for geoid, dynamic topography, and (poloidal) surface velocity. The internal density distribution can be estimated from seismic tomography, but since density variations might be of thermal and chemical nature, the s-wave velocity to density conversion factor, Rρ\νs, varies throughout the mantle. Based on CHAMP gravity field coefficients and four new seismic s-wave tomography models we search for ranges of radial profiles of viscosity and Rρ\νSubscript>s, resulting in a correlation to better than 0.85 to the long wavelength hydrostatic geoid, and to a fit better than 0.6 for gravity, dynamic topography and (poloidal) plate velocity. For purely thermal origin Rρ\νs should be between 0.2 and 0.4. Successful models however, show a small or even negative value for Rρ\νSubscript>s, between 100 and 300 km depth and a low value of ∼ .1 between 700 and 1200 km, but is otherwise roughly constant with values of ∼ .28. The viscosity is slightly reduced in the asthenosphere and even stronger decreased in the mantle transition zone between 410 and 670 km. Resolution for both, viscosity and conversion factor, is poor below the transition zone down to ∼ 1500 km, but well confined in deeper parts of the mantle, where a viscosity between 30 to 40 1021 Pa s and a conversion factor of 0.28 to 0.32 is found.

[1] The Lofoten-Vesteralen continental margin in Norway shows pronounced elongated positive and negative gravity anomalies. The source of these anomalies cannot be explained by the flat bathymetry, but can be explained by the crustal density anomalies that are observed. We propose a boudinage mechanism to explain the generation of these density anomalies and respective crustal layer undulations. Free-air gravity anomalies have been derived using ERS-1 and Geosat altimetry data and have been validated by comparison with shipborne data. Structural models of the margin are available from extensive seismic surveys, which have been used to carry out a gravity inversion to cross-validate the observed gravity anomalies with seismic data. The crustal structure data reveal two wavelengths of crustal undulations. The first is related to crustal blocks separated by listric faults, and the second wavelength is related to an undulated Moho. The undulations were likely generated during the opening of the North Atlantic, 56 Myr ago, and were particularly formed during the transition phase between rifting and spreading. The dominating wavelengths of the undulations are 46 and 109 km, respectively. To explain the evolution of crustal undulations in an extensional stress regime, we use a two-dimensional finite element model. A viscoelastoplastic power law rheology is used to study the growth of instabilities developing in a three-layer lithosphere. Prescribed random vertical undulations show wavelength-dependent growth under extension, and the dominating wavelengths are 18–65 and 129 km, respectively. These results are in good agreement with the gravity observations and provide a strong indication that the proposed boudinage mechanism influences the evolution of the passive margin segment.

In Fennoscandia the lithospheric structure is unusual compared to Phanerozoic Europe. All available data show that even though the topography is low, the crustal depth is in some places well below 50km and the lithospheric thickness has been estimated to be about 200 km. This structure leads to a density distribution that can be expected to have an impact on the potential field anomalies. The key parameter, however, is the compensating mass balance inside the lithosphere. Seismic profiling generally indicates high lower crustal density, but does not reveal high-density mass distributions inside the crust or in the uppermost part of the lithosphere needed to locally balance the Moho depth undulations. It can be expected that small-balancing density contrasts are distributed to rather great depth. From a geophysical point of view, taking a compensation depth of 30 or 50km (inside the crust) to be responsible for all compensation is not realistic. In general, for a better understanding of the compensating mass distribution, one has to take into account the topography and the internal structure of the crust and the lithosphere. The important raw data set for the study by Nord & Sjoberg is a Moho map for Fennoscandia. The problem here is that any Moho map is based on a very limited number of seismic reflection or refraction profiles. The exact Moho depth for each profile can only be estimated with an accuracy of about 2 to 5 km in limited parts along the profile. Thus it is easy to imagine that any Moho depth map can only give a rough estimate on the real variations of the crust-mantle boundary and is critically dependent on the imagination of the person who draws the isolines or on the algorithm of the applied computer program. In Fennoscandia in particular, areas exist where no or very few data are available. This is true for most of the continent-ocean transition for SW Norway, for the southern Baltic Sea, and for the entire SE part of the area of investigation. Nord & Sjoberg used a Moho depth map from Luosto (1990), which differs in some way from maps published

Summary The effect of subcontinental upper mantle convection on topography, gravity and geoid undulation is studied with special regard to the effective elastic thickness of the continental lithosphere (hel). We designed a numerical model of the upper mantle-lithosphere system consisting of a constant viscosity fluid overlayed by a partly elastic plate. the boundary tractions (stresses) at the top of the convecting mantle model were applied to the lithosphere model for which we used the thin plate approximation. the total thickness of the lithosphere was kept constant to 150 km while the elastic thickness was varied between 0 and 150 km. the aspect ratio of the convecting mantle was varied between 0.7 and 3 and the Rayleigh number between 104 and 106. Our calculations demonstrate the effect of a thick elastic lithosphere on the surface observables: peak to peak averaged amplitude of topography, geoid undulation and gravity are strongly reduced and their spectra are low pass filtered. For an aspect ratio less than 1 and a very thick elastic lithosphere topography tends to zero and while geoid undulation and gravity may even become negative above the up welling plume. the spectral relation of geoid or gravity to topography (admittance) is nearly unaffected for hie

The medium wavelength geoid (wavelengths The result of this study demonstrate that crustal thickness variations are important for the interpretation of the Fennoscandian geoid or gravity. However, submoho deviatoric stresses might become very high (about 200 MPa) if the entire anomaly is assumed to be supported by lateral density variations at less than 80 km depth. This implies that the pronounced negative anomaly is additionally maintained by dynamical flow inside the mantle.

Different types of geodynamically active regions like mountain belts, hot spots, or areas of salt tectonics are characterized by diapirism. One key for the reconstruction of the dynamic history of such structures is the progressive strain, which can sometimes be determined from field observations. Successful interpretation of such observations requires a quantitative model of the finite strain in and around a rising diapir. A constant viscosity fluid sphere of radius R rising through another isoviscous fluid is assumed to approximate the buoyant motion of a diapir. Known analytical solutions for the velocity fields are used to numerically evaluate the finite deformation in and around the sphere. Regions of very high strains are found in a tube with a radius 1 2 R behind the sphere and in a shell of thickness of 0.1R around the sphere. The following three-dimensional strain regimes can be identified: In the half space above the sphere down to its equator finite strains are oblate. Behind the sphere they progressively change to plane strain. In the diapiric source region they are prolate. Viscous drag at the sphere's surface leads to an internal circulation with one overturn after 10R of rise, if the sphere has a relatively low viscosity. Finite strains within the fluid sphere show a continuous increase with superimposed cyclic straining and unstraining. After several body radii of rise, the strains become highly inhomogeneous inside the sphere except along the vertical axis and just inside the sphere's surface, where strong prolate and oblate strains are observed, respectively. Finite strain determinations in a falling ball experiment (Cruden, 1988) are compared with the theoretical results. At horizontal distances of a few body radii from the fall axis, the effect of confining container walls is clearly seen in the experimental strain data. The results are compared briefly with available strain data from the field which seem to be significantly lower than predicted. Proposed explanations include a short memory of the rock fabric, and a lack of recognition of the strain concentration which would be expected for a temperature-dependent rheology. It might also be possible that few natural diapirs rise more than a few radii in the solid state.

Summary We have carried out a comparison study for a set of benchmark problems which are relevant for convection in the Earth's mantle. The cases comprise steady isoviscous convection, variable viscosity convection and time-dependent convection with internal heating. We compare Nusselt numbers, velocity, temperature, heat-flow, topography and geoid data. Among the applied codes are finite-difference, finite-element and spectral methods. In a synthesis we give best estimates of the ‘true’ solutions and ranges of uncertainty. We recommend these data for the validation of convection codes in the future.

Information on the permeability at depth is important for the exploitation of geothermal reservoirs. The Ensemble Kalman Filter (EnKF) is tool for property estimation if temporal observations are available. Observations can be temperature, hydraulic head during pumping tests, and chemical concentrations from tracer experiments at a few boreholes. The EnKF is a recursive Bayesian method incorporating observations in a Monte-Carlo-ensemble of reservoir simulations considering probability distributions. We present in synthetic test cases the application of the EnKF for estimating permeability and demonstrate its use for exploration planning. We apply the method to the 2005-tracer experiment of the Soultz-sous-Forets geothermal reservoir.

Directions of maximum horizontal stress SH derived from borehole breakouts are presented. For seven boreholes in the Central and Viking graben we found a clear preference of EW direction of SH, nearly perpendicular to the graben axes. EW directions were also estimated at four locations close to the Voering plateau and in the north Norwegian margin. Occurrence of breakouts in a borehole are not related to lithology, but salt inclusions change the SH-direction in adjacent layers.