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Hieronymus, Christoph F.ORCID iD iconorcid.org/0000-0003-4005-9990
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Publications (10 of 21) Show all publications
Bazargan, M., Hieronymus, C. F. & Vachon, R. (2019). Evolution of the statistical distribution of crystal orientations in time- and space-varying viscous flows. Geophysical Journal International, 218(2), 773-786
Open this publication in new window or tab >>Evolution of the statistical distribution of crystal orientations in time- and space-varying viscous flows
2019 (English)In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 218, no 2, p. 773-786Article in journal (Refereed) Published
Abstract [en]

Magmas and other viscously deforming fluids in the Earth frequently contain embedded crystals or other solid inclusions. These inclusions generally rotate about their own axis and, under certain conditions, align themselves in a direction dictated by the details of the flow. This rotational behaviour has been studied extensively for homogeneous flows. Here, we couple the crystal rotation dynamics with the fluid mechanical Navier-Stokes equations for the large-scale flow, thus allowing the analysis of crystal rotations in settings that are variable in both space and time. The solution is valid provided that the intercrystal spacing is sufficiently large to preclude interaction between crystals. Additionally, we derive an evolution equation for the probability density function (PDF) of crystal orientations based on the fundamental concept of conservation of generic properties in continuum mechanics. The resulting system of equations is extensively tested against previous analytical and numerical solutions. Given the focus on method validation, we limit the fluid mechanics to simple systems with analytical solutions for the velocity field. Even for the simple examples computed, all of which are characterized by fluid flow that is constant in time, the crystal orientation patterns are spatially complex and change in time. Pressure-driven flow in a channel results in coherent bands of crystal orientations with band thickness decreasing towards the channel walls. In corner flow constrained by two mutually perpendicular walls, the pattern of crystal orientations does not exhibit any significant similarity with the flow field. Given that there is no local one-to-one correspondence between the flow and the PDF pattern, a combined and larger-scale solution of the two systems is generally required. The simple flow examples shown demonstrate the viability of this new approach. Application to more complex flow geometries which may commonly occur in nature is deferred to future studies.

National Category
Geophysics
Identifiers
urn:nbn:se:uu:diva-363054 (URN)10.1093/gji/ggz174 (DOI)000474771100004 ()
Note

Title in dissertation list of papers: Evolution of the statistical distribution of crystal orientations in spatially variable viscous flows

Available from: 2018-10-11 Created: 2018-10-11 Last updated: 2019-08-14Bibliographically approved
Vachon, R. & Hieronymus, C. F. (2018). Mechanical energy balance and fracture toughness for dykes in elastoplastic host rock..
Open this publication in new window or tab >>Mechanical energy balance and fracture toughness for dykes in elastoplastic host rock.
2018 (English)In: Article in journal (Refereed) Submitted
National Category
Geophysics
Identifiers
urn:nbn:se:uu:diva-363229 (URN)
Available from: 2018-10-15 Created: 2018-10-15 Last updated: 2018-10-15
Vachon, R. & Hieronymus, C. F. (2017). Effect of host-rock rheology on dyke shape, thickness and magma overpressure. Geophysical Journal International, 208(3), 1414-1429
Open this publication in new window or tab >>Effect of host-rock rheology on dyke shape, thickness and magma overpressure
2017 (English)In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 208, no 3, p. 1414-1429Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Oxford University Press, 2017
Keywords
Numerical solutions, Plasticity, diffusion, and creep, Elasticity and anelasticity, Mechanics, theory, and modelling, Rheology: crust and lithosphere, Physics of magma and magma bodies
National Category
Geophysics
Identifiers
urn:nbn:se:uu:diva-360834 (URN)10.1093/gji/ggw448 (DOI)000396818900012 ()
Available from: 2018-09-18 Created: 2018-09-18 Last updated: 2019-02-27Bibliographically approved
Krumbholz, M., Hieronymus, C., Burchardt, S., Troll, V., Tanner, D. & Friese, N. (2014). Weibull-distributed dyke thickness reflects probabilistic character of host-rock strength. Nature Communications, 5, 3272
Open this publication in new window or tab >>Weibull-distributed dyke thickness reflects probabilistic character of host-rock strength
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2014 (English)In: Nature Communications, ISSN 2041-1723, E-ISSN 2041-1723, Vol. 5, p. 3272-Article in journal (Refereed) Published
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.

Keywords
dykes, Weibull distribution, volcano tectonics
National Category
Geosciences, Multidisciplinary
Research subject
Geophysics with specialization in Solid Earth Physics; Earth Science with specialization in Mineral Chemistry, Petrology and Tectonics
Identifiers
urn:nbn:se:uu:diva-218648 (URN)10.1038/ncomms4272 (DOI)000332667600019 ()
Available from: 2014-02-13 Created: 2014-02-13 Last updated: 2017-12-06Bibliographically approved
Schmidt, P., Lund, B., Hieronymus, C., Maclennan, J., Árnadóttir, T. & Pagli, C. (2013). Effects of present day deglaciation on melt production rates beneath Iceland. Journal of Geophysical Research-Solid Earth, 118(7), 3366-3379
Open this publication in new window or tab >>Effects of present day deglaciation on melt production rates beneath Iceland
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2013 (English)In: Journal of Geophysical Research-Solid Earth, ISSN 2169-9313, Vol. 118, no 7, p. 3366-3379Article in journal (Other academic) Published
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.

Place, publisher, year, edition, pages
American Geophysical Union (AGU), 2013
Keywords
decompression melting, GIA, Iceland, mantle melting, volcanism, deglaciation
National Category
Geophysics
Identifiers
urn:nbn:se:uu:diva-169788 (URN)10.1002/jgrb.50273 (DOI)000324952300008 ()
Available from: 2012-03-06 Created: 2012-03-06 Last updated: 2013-11-04Bibliographically approved
Schmidt, P., Lund, B. & Hieronymus, C. (2012). Implementation of the glacial rebound pre-stress advection correction in general-purpose finite element analysis software: Springs versus foundations. Computers & Geosciences, 40, 97-106
Open this publication in new window or tab >>Implementation of the glacial rebound pre-stress advection correction in general-purpose finite element analysis software: Springs versus foundations
2012 (English)In: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 40, p. 97-106Article in journal (Refereed) Published
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.

National Category
Geophysics
Research subject
Geophysics with specialization in Solid Earth Physics
Identifiers
urn:nbn:se:uu:diva-159553 (URN)10.1016/j.cageo.2011.07.017 (DOI)000301624600009 ()
Available from: 2011-10-04 Created: 2011-10-04 Last updated: 2017-12-08Bibliographically approved
Hieronymus, C. & Goes, S. (2010). Complex cratonic seismic structure from thermal models of the lithosphere: effects of variations in deep radiogenic heating. Geophysical Journal International, 180(3), 999-1012
Open this publication in new window or tab >>Complex cratonic seismic structure from thermal models of the lithosphere: effects of variations in deep radiogenic heating
2010 (English)In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 180, no 3, p. 999-1012Article in journal (Refereed) Published
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.

Keywords
Composition of the mantle, Seismic tomography, Cratons, Heat generation and transport
National Category
Geophysics
Research subject
Geophysics with specialization in Solid Earth Physics
Identifiers
urn:nbn:se:uu:diva-162531 (URN)10.1111/j.1365-246X.2009.04478.x (DOI)
Available from: 2011-11-30 Created: 2011-11-30 Last updated: 2017-12-08Bibliographically approved
Hieronymus, C. & Goes, S. (2010). Complex cratonic seismic structure from thermal models of the lithosphere: effects of variations in deep radiogenic heating. Geophysical Journal International, 180(3), 999-1012
Open this publication in new window or tab >>Complex cratonic seismic structure from thermal models of the lithosphere: effects of variations in deep radiogenic heating
2010 (English)In: Geophysical Journal International, ISSN 0956-540X, E-ISSN 1365-246X, Vol. 180, no 3, p. 999-1012Article in journal (Refereed) Published
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.

Keywords
Composition of the mantle, Seismic tomography, Cratons, Heat generation and transport
National Category
Earth and Related Environmental Sciences
Research subject
Geophysics with specialization in Solid Earth Physics
Identifiers
urn:nbn:se:uu:diva-114500 (URN)10.1111/j.1365-246X.2009.04478.x (DOI)000274712100004 ()
Available from: 2010-02-16 Created: 2010-02-16 Last updated: 2017-12-12Bibliographically approved
Lund, B., Schmidt, P. & Hieronymus, C. (2009). Stress evolution and fault stability during the Weichselian glacial cycle. Swedish Nuclear Fuel and Waste Management Co
Open this publication in new window or tab >>Stress evolution and fault stability during the Weichselian glacial cycle
2009 (English)Report (Other academic)
Place, publisher, year, edition, pages
Swedish Nuclear Fuel and Waste Management Co, 2009. p. 106
Series
SKB Technical Report, ISSN 1404-0344 ; TR-09-15
National Category
Earth and Related Environmental Sciences
Identifiers
urn:nbn:se:uu:diva-138199 (URN)
Available from: 2010-12-16 Created: 2010-12-16 Last updated: 2015-09-25
Hieronymus, C. F., Goes, S., Sargent, M. & Morra, G. (2008). A dynamical model for generating Eurasian lithospheric stress and strain rate fields: Effect of rheology and cratons. Journal of Geophysical Research, 113(B7), B07404
Open this publication in new window or tab >>A dynamical model for generating Eurasian lithospheric stress and strain rate fields: Effect of rheology and cratons
2008 (English)In: Journal of Geophysical Research, ISSN 0148-0227, E-ISSN 2156-2202, Vol. 113, no B7, p. B07404-Article in journal (Refereed) Published
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.

National Category
Earth and Related Environmental Sciences
Identifiers
urn:nbn:se:uu:diva-109963 (URN)10.1029/2007JB004953 (DOI)000257747000001 ()
Available from: 2009-11-02 Created: 2009-11-02 Last updated: 2017-12-12Bibliographically approved
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ORCID iD: ORCID iD iconorcid.org/0000-0003-4005-9990

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