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  • 1.
    Bergbauer, S.
    et al.
    University of Hawaii.
    Martel, S.J.
    University of Hawaii.
    Hieronymus, C.F.
    University of Hawaii.
    Thermal stress evolution in cooling pluton environments of different geometries1998In: Geophysical Research Letters, ISSN 0094-8276, E-ISSN 1944-8007, Vol. 25, no 5, 707-71- p.Article in journal (Refereed)
    Abstract [en]

    Thermoelastic displacement potentials and fast Fourier transforms can be combined to rapidly calculate the thermal stresses in 2-D for plutons that cool by conduction. First, temperature distributions over time are computed by solving the diffusion equation. Thermal stresses are then obtained using thermoelastic stress potentials. This method can be applied to a broad range of pluton geometries and initial conditions, and requires far less computation time than finite difference or finite element analyses. Results of 2-D analyses show that pluton geometry strongly influences the thermal stresses that occur in a cooling pluton. Thermal stresses of several tens of MPa arise during cooling and are highest at the corners or where the intrusion is thin. The most tensile stress is greater inside a pluton than in the host rock. Moreover, the orientation of the most tensile stress in a cooling pluton generally changes over time. This could result in multiple fracture sets, which would significantly affect the mechanical and hydraulic behavior of a pluton.

  • 2.
    Eken, Tuna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Shomali, Zaher Hossein
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Roberts, Roland
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Hieronymus, Christoph F.
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Bödvarsson, Reynir
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    S and P velocity heterogeneities within the upper mantle below the Baltic Shield2008In: Tectonophysics, ISSN 0040-1951, E-ISSN 1879-3266, Vol. 462, no 1-4, 109-124 p.Article in journal (Refereed)
    Abstract [en]

    Upper mantle structure beneath the Baltic (Fennoscandian) Shield is investigated using non-linear tomographic inversion of relative arrival-time residuals. 52 selected teleseismic earthquakes recorded by 45 broadband stations of the Swedish National Seismological Network (SNSN) provide 1532 good quality S-wave relative arrival times. SV and SH arrival-time residuals were initially analyzed independently, providing two separate models. These reveal several consistent major features, many of which are also consistent with P-wave results. Lateral velocity variations of ± 3–4% are observed to depths of at least 470 km. The correlation between the SH and SV models is investigated and shows a pattern of minor but significant differences down to around 150–200 km depth, below which the models are essentially similar. Direct cell by cell comparison of the model velocities reveals a similar pattern, with velocity differences between the models of up to 4%. Numerical tests show that differences in the two S-wave models can only be partially attributed to noise and limited resolution, and some features are attributed to the effect of large scale anisotropy. One of the significant and sharp discrepancies between the S models coincides with a presumed boundary between Archean and Proterozic domains, suggesting different anisotropic characteristics in the two regions.

  • 3.
    Hieronymus, C. F.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Goes, S.
    Department of Earth Science and Engineering, Imperial College, London, UK.
    Sargent, M.
    Max-Planck Institut für Astronomie, Heidelberg, Germany.
    Morra, G.
    Department of Earth Sciences, Institute of Geophysics, ETH Zürich, Zürich, Switzerland.
    A dynamical model for generating Eurasian lithospheric stress and strain rate fields: Effect of rheology and cratons2008In: Journal of Geophysical Research, ISSN 0148-0227, E-ISSN 2156-2202, Vol. 113, no B7, B07404- p.Article in journal (Refereed)
    Abstract [en]

    For most continents, stress models driven by plate boundary forces have successfully reproduced the main characteristics of the stress field. However, Eurasia has remained a challenge due to its large areas of intraplate deformation. We present a set of three-dimensional models of the upper mantle lithosphere system for a simplified geometry of the Eurasian plate where we try to match the first-order characteristics of the stress and strain rate fields simultaneously. For typical elastic, viscous, or plastic rheologies, high stress levels are required in order to produce realistic convergence rates between India and Asia. Our models show robustly that such stresses are transmitted throughout most of the plate, dominating locally generated stresses even in distal regions such as Europe in a manner that is not compatible with observations. Cratons with roots that extend deep into the mantle are unable to provide a significant stress-shielding effect unless the viscosity contrast between the asthenosphere and the underlying mantle is around 100 or greater. A damage rheology for the lithosphere with history-dependent behavior and material softening by a viscosity reduction of several orders of magnitude is shown to eliminate this conundrum. Continental convergence at high velocity but low stress is facilitated by the formation of long-lived shear zones similar to those observed north of the Himalayas. The low stress associated with the collision, together with the decoupling effect of the shear zones, causes the distal stress field in Europe to be controlled by the effects of the neighboring boundaries in agreement with observations.

  • 4.
    Hieronymus, C.F.
    et al.
    Danish Lithosphere Centre.
    Bercovici, D.
    University of Hawaii.
    A theoretical model of hotspot volcanism: Control on volcanic spacing and patterns via magma dynamics and lithospheric stresses2001In: Journal of Geophysical Research, ISSN 0148-0227, E-ISSN 2156-2202, Vol. 106, no B1, 683-702 p.Article in journal (Refereed)
    Abstract [en]

    Many linear island chains are thought to be the result of the steady motion of the lithospheric plates over stationary hotspots. The occurrence of discrete, nearly regularly spaced volcanoes, rather than continuous ridges, are assumed to be caused by the interaction of flexural stresses (due to the volcanic loads) with magma percolation. A parameter study is performed on a simple model that incorporates these effects in addition to dike wall erosion. It is demonstrated that the strength of the erosional feedback determines whether the model generates discrete volcanoes or a continuous ridge. The intervolcanic spacing depends not only on the elastic thickness of the lithosphere but also on the magma pressure at the base of the lithosphere. The size of the eruptive region of the individual volcanoes is controlled by the elastic response of the lithosphere to magma overpressurization. If an initial off-axis edifice is introduced, the model is able to preserve this asymmetry and produce an alternating series of volcanoes. A small initial perturbation grows over time, resulting in double lines or wider patterns depending on the width of the magma source region. Single lines of volcanoes therefore indicate very narrow magma source regions.

  • 5.
    Hieronymus, C.F.
    et al.
    Danish Lithosphere Centre.
    Bercovici, D.
    University of Hawaii.
    Discrete alternating hotspot islands formed by interaction of magma transport and lithospheric flexure1999In: Nature, ISSN 0028-0836, E-ISSN 1476-4687, Vol. 397, no 6720, 604-607 p.Article in journal (Refereed)
    Abstract [en]

    The large-scale geometry and age progression of many hotspot island chains, such as the Hawaiian-Emperor chain, are well explained by the steady movement of tectonic plates over stationary hotspots. But on a smaller scale, hotspot tracks are composed of discrete volcanic islands whose spacing correlates with lithospheric thickness(1). Moreover, the volcanic shields themselves are often not positioned along single lines, but in more complicated patterns, such as the dual line known as the Kea and Loa trends of the Hawaiian islands(2,3). Here we make use of the hypothesis that. island spacing is controlled by lithospheric flexure(1) to develop a simple nonlinear model coupling magma flow, which feeds volcanic growth, to the flexure caused by volcanic loads on the underlying plate. For a steady source of melt underneath a moving lithospheric plate, magma is found to reach the surface and build a chain of separate volcanic edifices with realistic spacing. If a volcano is introduced away from the axis of the chain, as might occur following a change in the direction of plate motion, the model perpetuates the asymmetry for long distances and times, thereby producing an alternating: series of edifices similar to that observed in the Kea and Loa trends of the Hawaiian island chain.

  • 6.
    Hieronymus, C.F.
    et al.
    Danish Lithosphere Centre.
    Bercovici, D.
    Yale University.
    Focusing of eruptions by fracture wall erosion2001In: Geophysical Research Letters, ISSN 0094-8276, E-ISSN 1944-8007, Vol. 28, no 9, 1823-1826 p.Article in journal (Refereed)
    Abstract [en]

    Lithospheric flexural stresses beneath volcanic loads are horizontally strongly compressive towards the top of the lithosphere. Thus, while magma transport through the brittle lithosphere occurs via fractures, the fracture paths under the volcanic center are predicted by stress trajectories to be horizontal and thus unable to supply melt to the volcanic edifice where eruptions are observed. Moreover, the magnitude of the compressive stresses under large loads would close down any vertical magma paths. Both problems may be resolved by additional stresses due to melting or thermomechanical erosion of fracture walls developing over the life-span of the volcano. Fractures form and close frequently in the seismogenic zone of the lithosphere, with each fracture eroding away a small amount of material. The total amount of material removed makes the stress field more tensile, thereby facilitating the long-lived and vertically oriented magma pathways necessary to build discrete volcanic structures.

  • 7.
    Hieronymus, C.F.
    et al.
    Danish Lithosphere Centre.
    Bercovici, D.
    University of Hawaii.
    Non-hotspot formation of volcanic chains: control of tectonic and flexural stresses on magma transport2000In: Earth and Planetary Science Letters, ISSN 0012-821X, E-ISSN 1385-013X, Vol. 181, no 4, 539-554 p.Article in journal (Refereed)
    Abstract [en]

    The South Pacific, in the vicinity of both the superswell and the East Pacific Rise, is repleat with volcanic chains that, unlike the Emperor-Hawaiian Chain, defy the hypothesis of formation via the relative motion of plates and hotspots. We propose two nearly identical models for the origin of near-axis and superswell chains, assuming that both regions are underlain by significant quantities of more or less uniformly distributed partial melt. Given an initial volcanic load or a local anomaly in the melt source region, volcanic chains form by magmatic hydrofracture at local tensile maxima of flexural and membrane stresses. Fracture wall erosion by magma flow provides a feedback which results in discrete edifices within the chains. The model predicts island chains aligned with a deviatorically tensile tectonic stress. Near the ridge, the elastic lithosphere is thin, and observations and theoretical considerations indicate a strong deviatorically tensile stress field perpendicular to the ridge axis. Under such conditions, the model results in parallel lines of volcanoes perpendicular to the spreading ridge. Later, interstitial volcanism within the individual chains reduces the average spacing and results in nearly continuous ridges. On the thicker lithosphere of the superswell, membrane stresses are negligible and the model produces chains of much more widely spaced volcanoes. A more isotropic stress field may result in broader chain-like patterns of volcanoes. In both cases, the chains represent self-propagating disturbances; the resulting age progressions are thus independent of plate velocity, but depend only on the dynamics of volcano formation and evolution.

  • 8.
    Hieronymus, Christoph
    Danish Lithosphere Centre, Ostervoldgade 10, L, Copenhagen K, 1350, Denmark.
    Control on seafloor spreading geometries by stress- and strain-induced lithospheric weakening2004In: Earth and Planetary Science Letters, ISSN 0012-821X, E-ISSN 1385-013X, Vol. 222, no 1, 177-189 p.Article in journal (Refereed)
    Abstract [en]

    Seafloor spreading typically occurs along ridge segments oriented at right angles to plate motion and offset by orthogonal transform faults. Few regions exhibit different patterns, such as the East Pacific Rise (EPR), which additionally displays overlapping spreading centres (OSCs) and microplates. We introduce a dynamical model using two independent, scalar types of damage in an elastic plate that generates most observed spreading geometries as natural failure modes, suggesting that the dynamics of the underlying mantle have only a minor influence on accretionary plate margins. The elastic modulus that is affected by the damage determines the type of localized deformation. Damage reducing the bulk modulus tends to result in tensile fractures, while a reduction in shear modulus leads to shear fractures. The damage source determines the fracture orientation. Material weakening in tension results in fractures perpendicular to the most tensile principal stress, while shear weakening results in two conjugate fractures at 45degrees relative to the applied stress. Strain or energy-dependent damage results in propagating, localized fractures. Stress-dependent damage tends to evolve into diffuse regions that may eventually focus into narrow zones. Starting from small perturbations with reduced elastic moduli as nucleation points, all ridge geometries start with ridge propagation caused by tensile energy reducing both elastic moduli by a model of damage caused by tensile energy reducing both moduli. Orthogonal transform faults develop in regions between offset segments if there is an additional reduction in shear modulus due to shear stress. The orthogonality of the transform faults does not derive from the local stress orientation but from the dynamics of damage focusing which causes the fault to converge towards an optimal geometry that concentrates nearly all deformation into damaged zones. OSCs form when the shear damage leading to transform faults is suppressed, while microplate formation requires additional reduction of the shear modulus by tensile energy. Oblique spreading at 45degrees. recently discovered along ultraslow spreading ridges, occurs when both moduli are weakened by shear energy. A parameter regime exists in which ridge-transform patterns develop at low applied tension, while microplates form at higher stresses. These results indicate that at least three different micromechanical processes operate with different evolution rates. OSCs and oblique spreading require different material properties.

  • 9.
    Hieronymus, Christoph F.
    Institute of Geophysics, ETH Zürich, Switzerland.
    Time-dependent strain localization in viscous media with state-dependent viscosity2006In: Physics of the Earth and Planetary Interiors, ISSN 0031-9201, E-ISSN 1872-7395, Vol. 157, no 3-4, 151-163 p.Article in journal (Refereed)
    Abstract [en]

    The temporal evolution of viscous rheologies with dependence on an additional state variable is examined. A localization measure is introduced that quantifies the change in the degree of localization in time. Three sample rheologies are analyzed in detail, each representative of a larger class of rheologies: (1) a grain-size dependent viscosity with grain growth and diminution, (2) shear heating with temperature-dependence according to the Arrhenius law, and (3) shear heating with temperature dependence in the Frank-Kamenetzky approximation. All three rheologies display stages of temporal increase and decrease of localization, depending on the initial conditions. This localization behavior is not discernible in plots of strain rate versus strain at constant driving stress which are the typical output of creep experiments. The grain-size dependence of olivine leads to effectively non-Newtonian behavior with a stress exponent of about 5. If the laws describing the grain-size evolution are applicable to the mantle, then the lower mantle and those parts of the upper mantle that are dominated by diffusion creep thus have a stronger stress-dependence than the depth range governed by dislocation creep, provided that the timescale of deformation is greater than 10^5 –10^6 years.

  • 10.
    Hieronymus, Christoph F.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Shomali, Zaher Hossein
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Pedersen, Laust B.
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    A dynamical model for generating sharp seismic velocity contrasts underneath continents: Application to the Sorgenfrei-Tornquist Zone2007In: Earth and Planetary Science Letters, ISSN 0012-821X, E-ISSN 1385-013X, Vol. 262, no 1-2, 77-91 p.Article in journal (Refereed)
    Abstract [en]

    New seismic velocity models based on teleseismic traveltime tomography show a sharp lithospheric boundary at the Sorgenfrei–Tornquist Zone (STZ) between 100 and 250 km depth with P-waves about 4% faster and S-waves 6% faster within the cratonic lithosphere to the north. Experiments and thermodynamic calculations indicate that seismic velocity differences in the shallow mantle down to the transition zone must be mostly of thermal origin as typical mantle rocks are characterized by similar velocities based on composition alone. We propose a dynamical model of convection in the upper mantle that is consistent with rheological data and that satisfies the seismic observations by maintaining an abrupt lateral temperature contrast over hundreds of Myrs. A step-like increase in lithospheric thickness from 100 to 250 km is assumed to have formed in a Triassic rifting event at the STZ (around 220 Ma) and is subsequently exposed to active convection below. A lithosphere that is distinct from the mantle in terms of temperature and composition remains stable against convective erosion. Heat advection to different depth beneath the thin and the thick lithosphere leads to a maximum horizontal contrast of 500 °C at 150 km depth over a lateral transition distance of 100 km, sufficient to generate 5% and 8% in maximum P- and S-wave velocity perturbation, respectively. A purely conductive model under the same conditions yields only Δvp ≈ 1% and Δvs ≈ 2%, while a lithospheric evolution simulation without a compositional effect on the rheology leads to significant thermo-mechanical erosion of the lithosphere giving Δvp ≈ 2% and Δvs ≈ 4%.

  • 11.
    Hieronymus, Christoph
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Goes, S.
    Complex cratonic seismic structure from thermal models of the lithosphere: effects of variations in deep radiogenic heating2010In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 180, no 3, 999-1012 p.Article in journal (Refereed)
    Abstract [en]

    Cratons are the long-term tectonically stable cores of the continents. Despite their thermal stability they display substantial seismic complexity with lateral and vertical lithospheric anomalies of up to several percent in both V(S) and V(P). Although some of these anomalies have been correlated with compositional variations, others are too large to be explained with any common mantle lithosphere compositions ranging from fertile peridotites to highly melt-depleted dunites, under the assumption that thermal perturbations are negligible. To test whether temperature anomalies could contribute to seismic complexity, we performed a set of 2-D thermal calculations for a range of cratonic tectonic models and converted them into seismic structure, accounting for variations in phase and elastic and anelastic response to pressure and temperature. With the long thermal equilibration time in cratonic settings, even relatively mild variations in concentrations of radioactive elements can leave long-lasting lithospheric thermal anomalies of 100-300 degrees C. Concentrations of radioactive elements decrease with increasing melt depletion ( or decreasing metasomatic refertilization), resulting in lower temperatures and increased seismic velocities. This thermal seismic effect enhances the intrinsic velocity-increasing compositional seismic signature of melt depletion. The joint thermochemical effects can leave cratonic seismic anomalies of up to 3-4.5 per cent in V(S) and up to 2.5-4 per cent in V(P), with gradients sometimes as sharp as a few kilometre in width. Thus the variations in major and minor element mantle lithosphere composition commonly seen in mantle samples can account for much of the variability in imaged seismic structure of cratonic lithosphere.

  • 12.
    Hieronymus, Christoph
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Goes, Saskia
    Department of Earth Science and Engineering, Imperial College London, London, UK.
    Complex cratonic seismic structure from thermal models of the lithosphere: effects of variations in deep radiogenic heating2010In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 180, no 3, 999-1012 p.Article in journal (Refereed)
    Abstract [en]

    Cratons are the long-term tectonically stable cores of the continents. Despite their thermal stability they display substantial seismic complexity with lateral and vertical lithospheric anomalies of up to several percent in both  VS and  VP . Although some of these anomalies have been correlated with compositional variations, others are too large to be explained with any common mantle lithosphere compositions ranging from fertile peridotites to highly melt-depleted dunites, under the assumption that thermal perturbations are negligible. To test whether temperature anomalies could contribute to seismic complexity, we performed a set of 2-D thermal calculations for a range of cratonic tectonic models and converted them into seismic structure, accounting for variations in phase and elastic and anelastic response to pressure and temperature. With the long thermal equilibration time in cratonic settings, even relatively mild variations in concentrations of radioactive elements can leave long-lasting lithospheric thermal anomalies of 100–300 °C. Concentrations of radioactive elements decrease with increasing melt depletion (or decreasing metasomatic refertilization), resulting in lower temperatures and increased seismic velocities. This thermal seismic effect enhances the intrinsic velocity-increasing compositional seismic signature of melt depletion. The joint thermochemical effects can leave cratonic seismic anomalies of up to 3–4.5 per cent in  VS and up to 2.5–4 per cent in  VP , with gradients sometimes as sharp as a few kilometre in width. Thus the variations in major and minor element mantle lithosphere composition commonly seen in mantle samples can account for much of the variability in imaged seismic structure of cratonic lithosphere.

  • 13.
    Krumbholz, Michael
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Solid Earth Geology.
    Hieronymus, Christoph
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Burchardt, Steffi
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Solid Earth Geology.
    Troll, Valentin
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Solid Earth Geology.
    Tanner, David
    Leibniz Institute of Applied Geophysics.
    Friese, Nadine
    Wintershall Norge AS.
    Weibull-distributed dyke thickness reflects probabilistic character of host-rock strength2014In: Nature Communications, ISSN 2041-1723, E-ISSN 2041-1723, Vol. 5, 3272- p.Article in journal (Refereed)
    Abstract [en]

    Magmatic sheet intrusions (dykes) constitute the main form of magma transport in the Earth’s crust. The size distribution of dykes is a crucial parameter that controls volcanic surface deformation and eruption rates and is required to realistically model volcano deformation for eruption forecasting. Here we present statistical analyses of 3,676 dyke thickness measurements from different tectonic settings and show that dyke thickness consistently follows the Weibull distribution. Known from materials science, power law-distributed flaws in brittle materials lead to Weibull-distributed failure stress. We therefore propose a dynamic model in which dyke thickness is determined by variable magma pressure that exploits differently sized host-rock weaknesses. The observed dyke thickness distributions are thus site-specific because rock strength, rather than magma viscosity and composition, exerts the dominant control on dyke emplacement. Fundamentally, the strength of geomaterials is scale-dependent and should be approximated by a probability distribution.

  • 14.
    Lund, Björn
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Schmidt, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Hieronymus, Christoph
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Stress evolution and fault stability during the Weichselian glacial cycle2009Report (Other academic)
  • 15.
    Schmidt, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Lund, Björn
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Hieronymus, Christoph
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Implementation of the glacial rebound pre-stress advection correction in general-purpose finite element analysis software: Springs versus foundations2012In: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 40, 97-106 p.Article in journal (Refereed)
    Abstract [en]

    When general-purpose finite element analysis software is used to model glacial isostatic adjustment (GIA), the first-order effect of prestress advection has to be accounted for by the user. We show here that the common use of elastic foundations at boundaries between materials of different densities will produce incorrect displacements, unless the boundary is perpendicular to the direction of gravity. This is due to the foundations always acting perpendicular to the surface to which they are attached, while the body force they represent always acts in the direction of gravity. If prestress advection is instead accounted for by the use of elastic spring elements in the direction of gravity, the representation will be correct. The use of springs adds a computation of the spring constants to the analysis. The spring constant for a particular node is defined by the product of the density contrast at the boundary, the gravitational acceleration, and the area supported by the node. To be consistent with the finite element formulation, the area is evaluated by integration of the nodal shape functions. We outline an algorithm for the calculation and include a Python script that integrates the shape functions over a bilinear quadrilateral element. For linear rectangular and triangular elements, the area supported by each node is equal to the element area divided the number of defining nodes, thereby simplifying the computation. This is, however, not true in the general nonrectangular case, and we demonstrate this with a simple 1-element model. The spring constant calculation is simple and performed in the preprocessing stage of the analysis. The time spent on the calculation is more than compensated for by a shorter analysis time, compared to that for a model with foundations. We illustrate the effects of using springs versus foundations with a simple two-dimensional GIA model of glacial loading, where the Earth model has an inclined boundary between the overlying elastic layer and the lower viscoelastic layer. Our example shows that the error introduced by the use of foundations is large enough to affect an analysis based on high-accuracy geodetic data.

  • 16.
    Schmidt, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Lund, Björn
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Hieronymus, Christoph
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Maclennan, John
    Department of Earth Sciences, University of Cambridge.
    Árnadóttir, Thora
    Nordic Volcanological Center, Institute of Earth Sciences, University of Iceland.
    Pagli, Carolina
    School of Earth and Environment, University of Leeds.
    Effects of present day deglaciation on melt production rates beneath Iceland2013In: Journal of Geophysical Research-Solid Earth, ISSN 2169-9313, Vol. 118, no 7, 3366-3379 p.Article in journal (Other academic)
    Abstract [en]

    Ongoing deglaciation in Iceland not only causes uplift at the surface but also increases magma production at depth due to decompression of the mantle. Here we study glacially induced decompression melting using 3-D models of glacial isostatic adjustment in Iceland since 1890. We find that the mean glacially induced pressure rate of change in the mantle increases melt production rates by 100–135%, or an additional 0.21–0.23 km3 of magma per year beneath Iceland. Approximately 50% of this melt is produced underneath central Iceland. The greatest volumetric increase is found directly beneath Iceland's largest ice cap, Vatnajökull, colocated with the most productive volcanoes. Our models of the effect of deglaciation on mantle melting predict a significantly larger volumetric response than previous models which only considered the effect of deglaciation of Vatnajökull, and only mantle melting directly below Vatnajökull. Although the ongoing deglaciation significantly increases the melt production rate, the increase in melt supply rate at the base of the lithosphere is delayed and depends on the melt ascent velocity through the mantle. Assuming that 25% of the melt reaches the surface, the upper limit on our deglaciation-induced melt estimates for central Iceland would be equivalent to an eruption the size of the 2010 Eyjafjallajökull summit eruption every seventh year.

  • 17.
    Vachon, Remi
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Hieronymus, Christoph F.
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, Geophysics.
    Effect of host-rock rheology on dyke shape, thickness and magma overpressure2017In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 208, no 3, 1414-1429 p.Article in journal (Refereed)
    Abstract [en]

    The size and thickness of dykes is of fundamental importance for volcano dynamics because dykes are the primary path for magma transport, and because large numbers of dykes often comprise a major proportion of the volcanic edifice and of the underlying crust. Standard elastic models predict dyke geometry to be elliptic in cross-section for constant overpressure and uniform host-rock properties, whereas observations show that dyke thickness is typically more nearly constant with a sharp taper at the ends. Moreover, the predicted overpressures required to inflate dykes in a purely elastic medium are often significantly higher (> 150 MPa and up to 2 GPa) than those estimated by other means (about 1-50 MPa). In this study, we use 2-D finite element models to test whether other host-rock rheologies lead to more realistic dyke shapes and overpressures. We examine three different rheologies, each of which is affected by the presence of the dyke itself: (1) elasticity with reduced moduli in regions of low pressure or tension; (2) elastoplasticity with plastic failure in the high-stress regions surrounding the dyke tips; (3) viscoelasticity with a viscosity decrease due to heating by the dyke. We use rheological parameters obtained from laboratory experiments whenever possible, and assume static conditions for the final dyke shape. We find that all three rheologies tend to make the dyke more rectangular relative to the elliptical dykes of the linearly elastic models. The change in shape is due to enhanced deformation in the high-stress zone surrounding the dyke tip. We also find that the overpressure required to inflate an initially thin dyke to a given thickness is reduced for all three rheologies. The greatest decrease in overpressure by a factor of about 0.1 is observed for the elastoplastic model, and for the viscoelastic model if the dyke intrudes into moderately pre-heated host-rock. We discuss our results with respect to dyke observations from Rum Island (Scotland) and use these as a guide to evaluate our models.

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