Articles | Volume 9, issue 2
https://doi.org/10.5194/se-9-267-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/se-9-267-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Method article
| 
19 Mar 2018
Method article |
| 19 Mar 2018
Nonlinear viscoplasticity in ASPECT: benchmarking and applications to subduction
Earth Sciences, Utrecht University, Utrecht, the Netherlands
Geodynamic Modelling, GFZ German Research Centre for Geosciences, Potsdam, Germany
Cedric Thieulot
Earth Sciences, Utrecht University, Utrecht, the Netherlands
Menno Fraters
Earth Sciences, Utrecht University, Utrecht, the Netherlands
Constantijn Blom
Earth Sciences, Utrecht University, Utrecht, the Netherlands
Wim Spakman
Earth Sciences, Utrecht University, Utrecht, the Netherlands
Centre of Earth Evolution and Dynamics (CEED), University of Oslo, 0316 Oslo, Norway
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Frank Zwaan, Tiago Alves, Patricia Cadenas, Mohamed Gouiza, Jordan Phethean, Sascha Brune, and Anne Glerum
EGUsphere, https://doi.org/10.5194/egusphere-2023-2548, https://doi.org/10.5194/egusphere-2023-2548, 2023
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Rifting and the break-up of continents is a key aspect of Earth’s plate tectonic system. A thorough understanding of the geological processes involved in rifting, as well as of the associated natural hazards and resources, is of great importance in the context of the energy transition. Here, we provide a coherent overview of rift processes and the links with hazards and resources, and we assess future challenges and opportunities for (collaboration between) researchers, government, and industry.
Anne Cathelijn Glerum, Sascha Brune, Joseph Michael Magnall, Philipp Weis, and Sarah A. Gleeson
EGUsphere, https://doi.org/10.5194/egusphere-2023-2518, https://doi.org/10.5194/egusphere-2023-2518, 2023
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Known high-value lead-zinc deposits formed in sedimentary basins created when tectonic plates rifted apart. We use computer simulations of rifting and the associated erosion and deposition of sediments to understand why they formed in some basins, but not in others. We find that conditions for deposit formation can briefly occur in both narrow and wide rifts for at most 3 My. Our models predict that the largest and the most deposits form in narrow margins of plates that rift asymmetrically.
Timothy Chris Schmid, Sascha Brune, Anne Glerum, and Guido Schreurs
Solid Earth, 14, 389–407, https://doi.org/10.5194/se-14-389-2023, https://doi.org/10.5194/se-14-389-2023, 2023
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Continental rifts form by linkage of individual rift segments and disturb the regional stress field. We use analog and numerical models of such rift segment interactions to investigate the linkage of deformation and stresses and subsequent stress deflections from the regional stress pattern. This local stress re-orientation eventually causes rift deflection when multiple rift segments compete for linkage with opposingly propagating segments and may explain rift deflection as observed in nature.
Iris van Zelst, Fabio Crameri, Adina E. Pusok, Anne Glerum, Juliane Dannberg, and Cedric Thieulot
Solid Earth, 13, 583–637, https://doi.org/10.5194/se-13-583-2022, https://doi.org/10.5194/se-13-583-2022, 2022
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Geodynamic modelling provides a powerful tool to investigate processes in the Earth’s crust, mantle, and core that are not directly observable. In this review, we present a comprehensive yet concise overview of the modelling process with an emphasis on best practices. We also highlight synergies with related fields, such as seismology and geology. Hence, this review is the perfect starting point for anyone wishing to (re)gain a solid understanding of geodynamic modelling as a whole.
Cedric Thieulot and Wolfgang Bangerth
EGUsphere, https://doi.org/10.5194/egusphere-2024-1668, https://doi.org/10.5194/egusphere-2024-1668, 2024
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One of the main numerical methods in geodynamics is the finite-element method. Many types of elements have been used in the past decades in hundreds of publications. They usually fall under two categories: quadrilaterals and triangles. For the first time we compare results obtained with the most used elements of each type on a series of geodynamical benchmarks and draw conclusions as to which are the best ones and which are to be preferably avoided.
Rene Gassmöller, Juliane Dannberg, Wolfgang Bangerth, Elbridge Gerry Puckett, and Cedric Thieulot
Geosci. Model Dev., 17, 4115–4134, https://doi.org/10.5194/gmd-17-4115-2024, https://doi.org/10.5194/gmd-17-4115-2024, 2024
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Numerical models that use simulated particles are a powerful tool for investigating flow in the interior of the Earth, but the accuracy of these models is not fully understood. Here we present two new benchmarks that allow measurement of model accuracy. We then document that better accuracy matters for applications like convection beneath an oceanic plate. Our benchmarks and methods are freely available to help the community develop better models.
Erik van der Wiel, Cedric Thieulot, and Douwe van Hinsbergen
EGUsphere, https://doi.org/10.31223/X56971, https://doi.org/10.31223/X56971, 2023
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Geodynamic models of mantle convection provide a powerful tool to study the structure and composition of the Earth’s mantle. Comparing such models with other datasets is difficult. We explore the use of 'configurational entropy', which allows to quantify mixing in models. The entropy may be used to analyze the mixed state of the mantle as a whole and may also be useful to validate numerical models against anomalies in the mantle that obtained from seismology and geochemistry.
Frank Zwaan, Tiago Alves, Patricia Cadenas, Mohamed Gouiza, Jordan Phethean, Sascha Brune, and Anne Glerum
EGUsphere, https://doi.org/10.5194/egusphere-2023-2548, https://doi.org/10.5194/egusphere-2023-2548, 2023
Short summary
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Rifting and the break-up of continents is a key aspect of Earth’s plate tectonic system. A thorough understanding of the geological processes involved in rifting, as well as of the associated natural hazards and resources, is of great importance in the context of the energy transition. Here, we provide a coherent overview of rift processes and the links with hazards and resources, and we assess future challenges and opportunities for (collaboration between) researchers, government, and industry.
Anne Cathelijn Glerum, Sascha Brune, Joseph Michael Magnall, Philipp Weis, and Sarah A. Gleeson
EGUsphere, https://doi.org/10.5194/egusphere-2023-2518, https://doi.org/10.5194/egusphere-2023-2518, 2023
Short summary
Short summary
Known high-value lead-zinc deposits formed in sedimentary basins created when tectonic plates rifted apart. We use computer simulations of rifting and the associated erosion and deposition of sediments to understand why they formed in some basins, but not in others. We find that conditions for deposit formation can briefly occur in both narrow and wide rifts for at most 3 My. Our models predict that the largest and the most deposits form in narrow margins of plates that rift asymmetrically.
Iris van Zelst, Cedric Thieulot, and Timothy J. Craig
Solid Earth, 14, 683–707, https://doi.org/10.5194/se-14-683-2023, https://doi.org/10.5194/se-14-683-2023, 2023
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A common simplification in subduction zone models is the use of constant thermal parameters, while experiments have shown that they vary with temperature. We test various formulations of temperature-dependent thermal parameters and show that they change the thermal structure of the subducting slab. We recommend that modelling studies of the thermal structure of subduction zones take the temperature dependence of thermal parameters into account, especially when providing insights into seismicity.
Timothy Chris Schmid, Sascha Brune, Anne Glerum, and Guido Schreurs
Solid Earth, 14, 389–407, https://doi.org/10.5194/se-14-389-2023, https://doi.org/10.5194/se-14-389-2023, 2023
Short summary
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Continental rifts form by linkage of individual rift segments and disturb the regional stress field. We use analog and numerical models of such rift segment interactions to investigate the linkage of deformation and stresses and subsequent stress deflections from the regional stress pattern. This local stress re-orientation eventually causes rift deflection when multiple rift segments compete for linkage with opposingly propagating segments and may explain rift deflection as observed in nature.
Barend Cornelis Root, Josef Sebera, Wolfgang Szwillus, Cedric Thieulot, Zdeněk Martinec, and Javier Fullea
Solid Earth, 13, 849–873, https://doi.org/10.5194/se-13-849-2022, https://doi.org/10.5194/se-13-849-2022, 2022
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Several alternative gravity modelling techniques and associated numerical codes with their own advantages and limitations are available for the solid Earth community. With upcoming state-of-the-art lithosphere density models and accurate global gravity field data sets, it is vital to understand the differences of the various approaches. In this paper, we discuss the four widely used techniques: spherical harmonics, tesseroid integration, triangle integration, and hexahedral integration.
Iris van Zelst, Fabio Crameri, Adina E. Pusok, Anne Glerum, Juliane Dannberg, and Cedric Thieulot
Solid Earth, 13, 583–637, https://doi.org/10.5194/se-13-583-2022, https://doi.org/10.5194/se-13-583-2022, 2022
Short summary
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Geodynamic modelling provides a powerful tool to investigate processes in the Earth’s crust, mantle, and core that are not directly observable. In this review, we present a comprehensive yet concise overview of the modelling process with an emphasis on best practices. We also highlight synergies with related fields, such as seismology and geology. Hence, this review is the perfect starting point for anyone wishing to (re)gain a solid understanding of geodynamic modelling as a whole.
Cedric Thieulot and Wolfgang Bangerth
Solid Earth, 13, 229–249, https://doi.org/10.5194/se-13-229-2022, https://doi.org/10.5194/se-13-229-2022, 2022
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One of the main numerical methods to solve the mass, momentum, and energy conservation equations in geodynamics is the finite-element method. Four main types of elements have been used in the past decades in hundreds of publications. For the first time we compare results obtained with these four elements on a series of geodynamical benchmarks and applications and draw conclusions as to which are the best ones and which are to be preferably avoided.
Melchior Schuh-Senlis, Cedric Thieulot, Paul Cupillard, and Guillaume Caumon
Solid Earth, 11, 1909–1930, https://doi.org/10.5194/se-11-1909-2020, https://doi.org/10.5194/se-11-1909-2020, 2020
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This paper presents a numerical method for restoring models of the subsurface to a previous state in their deformation history, acting as a numerical time machine for geological structures. The method relies on the assumption that rock layers can be modeled as highly viscous fluids. It shows promising results on simple setups, including models with faults and non-flat topography. While issues still remain, this could open a way to add more physics to reverse time structural modeling.
Menno Fraters, Cedric Thieulot, Arie van den Berg, and Wim Spakman
Solid Earth, 10, 1785–1807, https://doi.org/10.5194/se-10-1785-2019, https://doi.org/10.5194/se-10-1785-2019, 2019
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Three-dimensional numerical modelling of geodynamic processes may benefit strongly from using realistic 3-D starting models that approximate, e.g. natural subduction settings in the geological past or at present. To this end, we developed the Geodynamic World Builder (GWB), which enables relatively straightforward parameterization of complex 3-D geometric structures associated with geodynamic processes. The GWB is an open-source community code designed to easily interface with geodynamic codes.
Cedric Thieulot
Solid Earth, 9, 1169–1177, https://doi.org/10.5194/se-9-1169-2018, https://doi.org/10.5194/se-9-1169-2018, 2018
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I present the GHOST (Geoscientific Hollow Sphere Tessellation) software which allows for the fast generation of computational meshes in hollow sphere geometries counting up to a hundred million cells. Each mesh is composed of concentric spherical shells made of quadrilaterals or triangles. I focus here on three commonly used meshes used in the geodynamics/geophysics community and further benchmark the gravity and gravitational potential procedures in the simple case of a constant density.
Alexis Plunder, Cédric Thieulot, and Douwe J. J. van Hinsbergen
Solid Earth, 9, 759–776, https://doi.org/10.5194/se-9-759-2018, https://doi.org/10.5194/se-9-759-2018, 2018
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Short summary
The thermal state of the Earth's crust determines how it reacts to tectonic forces and to fluid flow responsible for ore formation. We hypothesize that the angle between plate motion and convergent boundaries determines the thermal regime of subduction zones (where a plate goes under another one). Computer models and a geological reconstruction of Turkey were used to validate this hypothesis.
This research was done to validate a hypothesis made on the basis of nonquantitative field data.
Cedric Thieulot
Solid Earth, 8, 1181–1191, https://doi.org/10.5194/se-8-1181-2017, https://doi.org/10.5194/se-8-1181-2017, 2017
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I present a new family of analytical flow solutions to the incompressible Stokes equation in a spherical shell. The velocity is tangential to both inner and outer boundaries, the viscosity is radial, and the solution has been designed so that the expressions for velocity, pressure, and body force are simple to implement in (geodynamics) codes. This forms the basis of a numerical benchmark for convection codes, and I have implemented it in two finite-element codes.
B. Hillebrand, C. Thieulot, T. Geenen, A. P. van den Berg, and W. Spakman
Solid Earth, 5, 1087–1098, https://doi.org/10.5194/se-5-1087-2014, https://doi.org/10.5194/se-5-1087-2014, 2014
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Our paper demonstrates that the level set method is a viable method for material tracking in multi-material flow models. The different benchmarks illustate several advantages that the level set method provides over tracer-based methods. We therefore conclude that the level set method is well suited for geodynamical modeling.
C. Thieulot
Solid Earth Discuss., https://doi.org/10.5194/sed-6-1949-2014, https://doi.org/10.5194/sed-6-1949-2014, 2014
Revised manuscript has not been submitted
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To understand core dynamics, insight from several possible observables is needed. By applying several separation methods, we show spatiotemporal variabilities in the magnetic and gravity fields related to the core dynamics. A 7-year oscillation is found in all conducted analyses. The results in the magnetic field reflect the core processes and the variabilities in the gravity field exhibit new findings that might be an interesting input to build an enhanced model of the Earth’s core.
Erik van der Wiel, Cedric Thieulot, and Douwe van Hinsbergen
EGUsphere, https://doi.org/10.31223/X56971, https://doi.org/10.31223/X56971, 2023
Short summary
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Geodynamic models of mantle convection provide a powerful tool to study the structure and composition of the Earth’s mantle. Comparing such models with other datasets is difficult. We explore the use of 'configurational entropy', which allows to quantify mixing in models. The entropy may be used to analyze the mixed state of the mantle as a whole and may also be useful to validate numerical models against anomalies in the mantle that obtained from seismology and geochemistry.
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EGUsphere, https://doi.org/10.5194/egusphere-2023-2736, https://doi.org/10.5194/egusphere-2023-2736, 2023
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Continental terranes have various rheological strengths due to the differences on their ages, compositions and structures. We applied four assumed rheological models to three terranes in a collisional model, and obtained four styles of lithosphere deformation pattern of collision, subduction, thickening/delamination, and replacement. These simulation patterns are seen in observed lithosphere deformation patterns and structures in East Asia.
Mengxue Liu, Dinghui Yang, and Rui Qi
Solid Earth, 14, 1155–1168, https://doi.org/10.5194/se-14-1155-2023, https://doi.org/10.5194/se-14-1155-2023, 2023
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The continuous subduction mainly occurs with a relatively cold overriding lithosphere (Tmoho ≤ 450 °C), while slab break-off dominates when the model has a relatively hot procontinental Moho temparature (Tmoho ≥ 500 °C). Hr is more prone to facilitating the deformation of the lithospheric upper part than altering the collision mode. The lithospheric thermal structure may have played a significant role in the development of Himalayan–Tibetan orogenic lateral heterogeneity.
Juliette Grosset, Stéphane Mazzotti, and Philippe Vernant
Solid Earth, 14, 1067–1081, https://doi.org/10.5194/se-14-1067-2023, https://doi.org/10.5194/se-14-1067-2023, 2023
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In glaciated regions, induced lithosphere deformation is proposed as a key process contributing to fault activity and seismicity. We study the impact of this effect on fault activity in the Western Alps. We show that the response to the last glaciation explains a major part of the geodetic strain rates but does not drive or promote the observed seismicity. Thus, seismic hazard studies in the Western Alps require detailed modeling of the glacial isostatic adjustment (GIA) transient impact.
Duo Zhang and Huw Davies
EGUsphere, https://doi.org/10.5194/egusphere-2023-1791, https://doi.org/10.5194/egusphere-2023-1791, 2023
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We numerically model the influence of an arc on back-arc extension. The arc is simulated by emplacing a hot region in the overriding plate. We investigate how plate ages and properties of the hot region affect back-arc extension and present regime diagrams of the nature of back-arc extension for these models. We find that back-arc extension not only at the hot region but surprisingly also away from it, and a hot region facilitates extension of the overriding plate.
Ananya P. Mukherjee and Animesh Mandal
EGUsphere, https://doi.org/10.5194/egusphere-2023-1389, https://doi.org/10.5194/egusphere-2023-1389, 2023
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Global gravity data is used to develop 2D models and Moho depth map (from 3D gravity inversion) to depict the crustal structure beneath the region covered by Proterozoic sedimentary basins, south of Bundelkhand craton in central India. The observed thick, mafic underplated layer above Moho points to the existence of Proterozoic plume activity. Thus, the study offers insights into the geodynamic processes that led to the formation the basins thereby about the crustal configuration of this region.
Iris van Zelst, Cedric Thieulot, and Timothy J. Craig
Solid Earth, 14, 683–707, https://doi.org/10.5194/se-14-683-2023, https://doi.org/10.5194/se-14-683-2023, 2023
Short summary
Short summary
A common simplification in subduction zone models is the use of constant thermal parameters, while experiments have shown that they vary with temperature. We test various formulations of temperature-dependent thermal parameters and show that they change the thermal structure of the subducting slab. We recommend that modelling studies of the thermal structure of subduction zones take the temperature dependence of thermal parameters into account, especially when providing insights into seismicity.
Fengping Pang, Jie Liao, Maxim D. Ballmer, and Lun Li
Solid Earth, 14, 353–368, https://doi.org/10.5194/se-14-353-2023, https://doi.org/10.5194/se-14-353-2023, 2023
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Plume–ridge interaction is an intriguing geological process in plate tectonics. In this paper, we address the respective role of ridgeward vs. plate-drag plume flow in 2D thermomechanical models and compare the results with a compilation of observations on Earth. From a geophysical and geochemical analysis of Earth plumes and in combination with the model results, we propose that the absence of plumes interacting with ridges in the Pacific is largely caused by the presence of plate drag.
Guoqiang Yan, Benjamin Busch, Robert Egert, Morteza Esmaeilpour, Kai Stricker, and Thomas Kohl
Solid Earth, 14, 293–310, https://doi.org/10.5194/se-14-293-2023, https://doi.org/10.5194/se-14-293-2023, 2023
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The physical processes leading to the kilometre-scale thermal anomaly in faulted tight sandstones are numerically investigated. The fluid-flow pathways, heat-transfer types and interactions among different convective and advective flow modes are systematically identified. The methodologies and results can be applied to interpret hydrothermal convection-related geological phenomena and to draw implications for future petroleum and geothermal exploration and exploitation in analogous settings.
David Hindle and Olivier Besson
Solid Earth, 14, 197–212, https://doi.org/10.5194/se-14-197-2023, https://doi.org/10.5194/se-14-197-2023, 2023
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By making a change to the way we solve the flexure equation that describes how the Earth's outer layer bends when it is subjected to loading by ice sheets or mountains, we develop new ways of using an old method from geodynamics. This lets us study the Earth's outer layer by measuring a parameter called the elastic thickness, effectively how stiff and springy the outer layer is when it gets loaded and also how the Earth's outer layer gets broken around its edges and in its interior.
Joshua Martin Guerrero, Frédéric Deschamps, Yang Li, Wen-Pin Hsieh, and Paul James Tackley
Solid Earth, 14, 119–135, https://doi.org/10.5194/se-14-119-2023, https://doi.org/10.5194/se-14-119-2023, 2023
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The mantle thermal conductivity's dependencies on temperature, pressure, and composition are often suppressed in numerical models. We examine the effect of these dependencies on the long-term evolution of lower-mantle thermochemical structure. We propose that depth-dependent conductivities derived from mantle minerals, along with moderate temperature and compositional correction, emulate the Earth's mean lowermost-mantle conductivity values and produce a stable two-pile configuration.
Antonio Manjón-Cabeza Córdoba and Maxim D. Ballmer
Solid Earth, 13, 1585–1605, https://doi.org/10.5194/se-13-1585-2022, https://doi.org/10.5194/se-13-1585-2022, 2022
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The origin of many volcanic archipelagos on the Earth remains uncertain. By using 3D modelling of mantle flow and melting, we investigate the interaction between the convective mantle near the continental–oceanic transition and rising hot plumes. We believe that this phenomenon is the origin behind some archipelagos, in particular the Canary Islands. Analysing our results, we reconcile observations that were previously enigmatic, such as the complex patterns of volcanism in the Canaries.
Adina E. Pusok, Dave R. Stegman, and Madeleine Kerr
Solid Earth, 13, 1455–1473, https://doi.org/10.5194/se-13-1455-2022, https://doi.org/10.5194/se-13-1455-2022, 2022
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Sediments play an important role in global volatile and tectonic cycles, yet their effect on subduction dynamics is poorly resolved. In this study, we investigate how sediment properties influence subduction dynamics and obtain accretionary or erosive-style margins. Results show that even a thin layer of sediments can exert a profound influence on the emergent regional-scale subduction dynamics.
Laure Chevalier and Harro Schmeling
Solid Earth, 13, 1045–1063, https://doi.org/10.5194/se-13-1045-2022, https://doi.org/10.5194/se-13-1045-2022, 2022
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Fluid flow through rock occurs in many geological settings on different scales, at different temperature conditions and with different flow velocities. Fluid is either in local thermal equilibrium with the host rock or not. We explore the parameters of porous flow and give scaling laws. These allow us to decide whether porous flows are in thermal equilibrium or not. Applied to magmatic systems, moving melts in channels or dikes moderately to strongly deviate from thermal equilibrium.
Iris van Zelst, Fabio Crameri, Adina E. Pusok, Anne Glerum, Juliane Dannberg, and Cedric Thieulot
Solid Earth, 13, 583–637, https://doi.org/10.5194/se-13-583-2022, https://doi.org/10.5194/se-13-583-2022, 2022
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Geodynamic modelling provides a powerful tool to investigate processes in the Earth’s crust, mantle, and core that are not directly observable. In this review, we present a comprehensive yet concise overview of the modelling process with an emphasis on best practices. We also highlight synergies with related fields, such as seismology and geology. Hence, this review is the perfect starting point for anyone wishing to (re)gain a solid understanding of geodynamic modelling as a whole.
Igor Ognev, Jörg Ebbing, and Peter Haas
Solid Earth, 13, 431–448, https://doi.org/10.5194/se-13-431-2022, https://doi.org/10.5194/se-13-431-2022, 2022
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We present a new 3D crustal model of Volgo–Uralia, an eastern segment of the East European craton. We built this model by processing the satellite gravity data and using prior crustal thickness estimation from regional seismic studies to constrain the results. The modelling revealed a high-density body on the top of the mantle and otherwise reflected the main known features of the Volgo–Uralian crustal architecture. We plan to use the obtained model for further geothermal analysis of the region.
Cedric Thieulot and Wolfgang Bangerth
Solid Earth, 13, 229–249, https://doi.org/10.5194/se-13-229-2022, https://doi.org/10.5194/se-13-229-2022, 2022
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One of the main numerical methods to solve the mass, momentum, and energy conservation equations in geodynamics is the finite-element method. Four main types of elements have been used in the past decades in hundreds of publications. For the first time we compare results obtained with these four elements on a series of geodynamical benchmarks and applications and draw conclusions as to which are the best ones and which are to be preferably avoided.
Jean Furstoss, Carole Petit, Clément Ganino, Marc Bernacki, and Daniel Pino-Muñoz
Solid Earth, 12, 2369–2385, https://doi.org/10.5194/se-12-2369-2021, https://doi.org/10.5194/se-12-2369-2021, 2021
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In the first part of this article, we present a new methodology that we have developed to model the deformation and the microstructural evolutions of olivine rocks, which make up the main part of the Earth upper mantle. In a second part, using this methodology we show that microstructural features such as small grain sizes and preferential grain orientations can localize strain at the same intensity and can act together to produce an even stronger strain localization.
Duan Li, Jinsong Du, Chao Chen, Qing Liang, and Shida Sun
Solid Earth Discuss., https://doi.org/10.5194/se-2021-117, https://doi.org/10.5194/se-2021-117, 2021
Revised manuscript not accepted
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Oceanic magnetic anomalies are generally carried out using only few survey lines and thus there are many areas with data gaps. Traditional interpolation methods based on the morphological characteristics of data are not suitable for data with large gaps. The use of dual-layer equivalent-source techniques may improve the interpolation of magnetic anomaly fields in areas with sparse data which gives a good consideration to the extension of the magnetic lineation feature.
Anna Johanna Pia Gülcher, Maxim Dionys Ballmer, and Paul James Tackley
Solid Earth, 12, 2087–2107, https://doi.org/10.5194/se-12-2087-2021, https://doi.org/10.5194/se-12-2087-2021, 2021
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The lower mantle extends from 660–2890 km depth, making up > 50 % of the Earth’s volume. Its composition and structure, however, remain poorly understood. In this study, we investigate several hypotheses with computer simulations of mantle convection that include different materials: recycled, dense rocks and ancient, strong rocks. We propose a new integrated style of mantle convection including
piles,
blobs, and
streaksthat agrees with various observations of the deep Earth.
Lorenzo G. Candioti, Thibault Duretz, Evangelos Moulas, and Stefan M. Schmalholz
Solid Earth, 12, 1749–1775, https://doi.org/10.5194/se-12-1749-2021, https://doi.org/10.5194/se-12-1749-2021, 2021
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We quantify the relative importance of forces driving the dynamics of mountain building using two-dimensional computer simulations of long-term coupled lithosphere–upper-mantle deformation. Buoyancy forces can be as high as shear forces induced by far-field plate motion and should be considered when studying the formation of mountain ranges. The strength of rocks flooring the oceans and the density structure of the crust control deep rock cycling and the topographic elevation of orogens.
Olivier de Viron, Michel Van Camp, Alexia Grabkowiak, and Ana M. G. Ferreira
Solid Earth, 12, 1601–1634, https://doi.org/10.5194/se-12-1601-2021, https://doi.org/10.5194/se-12-1601-2021, 2021
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As the travel time of seismic waves depends on the Earth's interior properties, seismic tomography uses it to infer the distribution of velocity anomalies, similarly to what is done in medical tomography. We propose analysing the outputs of those models using varimax principal component analysis, which results in a compressed objective representation of the model, helping analysis and comparison.
Janik Dohmen and Harro Schmeling
Solid Earth, 12, 1549–1561, https://doi.org/10.5194/se-12-1549-2021, https://doi.org/10.5194/se-12-1549-2021, 2021
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In partially molten regions within the Earth, the melt is able to move separately from the surrounding rocks. This allows for the emergence of so-called solitary porosity waves, driven by compaction and decompaction due to the melt with higher buoyancy. Our numerical models can predict whether a partially molten region will ascend dominated by solitary waves or diapirism. Even in diapiris-dominated regions, solitary waves will build up and ascend as a swarm when the ascend time is long enough.
Xin Zhong, Marcin Dabrowski, and Bjørn Jamtveit
Solid Earth, 12, 817–833, https://doi.org/10.5194/se-12-817-2021, https://doi.org/10.5194/se-12-817-2021, 2021
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Elastic thermobarometry is an useful tool to recover paleo-pressure and temperature. Here, we provide an analytical model based on the Eshelby solution to calculate the residual stress and strain preserved in a mineral inclusion exhumed from depth. The method applies to ellipsoidal, anisotropic inclusions in infinite isotropic hosts. A finite-element method is also used for a facet effect. Volumetrically averaged stress is shown to be a good proxy for the overall heterogeneous stress stage.
Maximilian Lowe, Jörg Ebbing, Amr El-Sharkawy, and Thomas Meier
Solid Earth, 12, 691–711, https://doi.org/10.5194/se-12-691-2021, https://doi.org/10.5194/se-12-691-2021, 2021
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This study estimates the gravitational contribution from subcrustal density heterogeneities interpreted as subducting lithosphere beneath the Alps to the gravity field. We showed that those heterogeneities contribute up to 40 mGal of gravitational signal. Such density variations are often not accounted for in Alpine lithospheric models. We demonstrate that future studies should account for subcrustal density variations to provide a meaningful representation of the complex geodynamic Alpine area.
Antonio Manjón-Cabeza Córdoba and Maxim D. Ballmer
Solid Earth, 12, 613–632, https://doi.org/10.5194/se-12-613-2021, https://doi.org/10.5194/se-12-613-2021, 2021
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The study of intraplate volcanism can inform us about underlying mantle dynamic processes and thermal and/or compositional anomalies. Here, we investigated numerical models of mantle flow and melting of edge-driven convection (EDC), a potential origin for intraplate volcanism. Our most important conclusion is that EDC can only produce moderate amounts of mantle melting. By itself, EDC is insufficient to support the formation of voluminous island-building volcanism over several millions of years.
Davide Tadiello and Carla Braitenberg
Solid Earth, 12, 539–561, https://doi.org/10.5194/se-12-539-2021, https://doi.org/10.5194/se-12-539-2021, 2021
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We present an innovative approach to estimate a lithosphere density distribution model based on seismic tomography and gravity data. In the studied area, the model shows that magmatic events have increased density in the middle to lower crust, which explains the observed positive gravity anomaly. We interpret the densification through crustal intrusion and magmatic underplating. The proposed method has been tested in the Alps but can be applied to other geological contexts.
Daniela Paz Bolrão, Maxim D. Ballmer, Adrien Morison, Antoine B. Rozel, Patrick Sanan, Stéphane Labrosse, and Paul J. Tackley
Solid Earth, 12, 421–437, https://doi.org/10.5194/se-12-421-2021, https://doi.org/10.5194/se-12-421-2021, 2021
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We use numerical models to investigate the thermo-chemical evolution of a solid mantle during a magma ocean stage. When applied to the Earth, our study shows that the solid mantle and a magma ocean tend toward chemical equilibration before crystallisation of this magma ocean. Our findings suggest that a very strong chemical stratification of the solid mantle is unlikely to occur (as predicted by previous studies), which may explain why the Earth’s mantle is rather homogeneous in composition.
Ángela María Gómez-García, Eline Le Breton, Magdalena Scheck-Wenderoth, Gaspar Monsalve, and Denis Anikiev
Solid Earth, 12, 275–298, https://doi.org/10.5194/se-12-275-2021, https://doi.org/10.5194/se-12-275-2021, 2021
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The Earth’s crust beneath the Caribbean Sea formed at about 90 Ma due to large magmatic activity of a mantle plume, which brought molten material up from the deep Earth. By integrating diverse geophysical datasets, we image for the first time two fossil magmatic conduits beneath the Caribbean. The location of these conduits at 90 Ma does not correspond with the present-day Galápagos plume. Either this mantle plume migrated in time or these conduits were formed above another unknown plume.
Lorenzo G. Candioti, Stefan M. Schmalholz, and Thibault Duretz
Solid Earth, 11, 2327–2357, https://doi.org/10.5194/se-11-2327-2020, https://doi.org/10.5194/se-11-2327-2020, 2020
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With computer simulations, we study the interplay between thermo-mechanical processes in the lithosphere and the underlying upper mantle during a long-term (> 100 Myr) tectonic cycle of extension–cooling–convergence. The intensity of mantle convection is important for (i) subduction initiation, (ii) the development of single- or double-slab subduction zones, and (iii) the forces necessary to initiate subduction. Our models are applicable to the opening and closure of the western Alpine Tethys.
Patrick Sanan, Dave A. May, Matthias Bollhöfer, and Olaf Schenk
Solid Earth, 11, 2031–2045, https://doi.org/10.5194/se-11-2031-2020, https://doi.org/10.5194/se-11-2031-2020, 2020
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Mantle and lithospheric dynamics, elasticity, subsurface flow, and other fields involve solving indefinite linear systems. Tools include direct solvers (robust, easy to use, expensive) and advanced iterative solvers (complex, problem-sensitive). We show that a third option, ILDL preconditioners, requires less memory than direct solvers but is easy to use, as applied to 3D problems with parameter jumps. With included software, we hope to allow researchers to solve previously infeasible problems.
Philipp Eichheimer, Marcel Thielmann, Wakana Fujita, Gregor J. Golabek, Michihiko Nakamura, Satoshi Okumura, Takayuki Nakatani, and Maximilian O. Kottwitz
Solid Earth, 11, 1079–1095, https://doi.org/10.5194/se-11-1079-2020, https://doi.org/10.5194/se-11-1079-2020, 2020
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To describe permeability, a key parameter controlling fluid flows in the Earth’s subsurface, an accurate determination of permeability on the pore scale is necessary. For this reason, we sinter artificial glass bead samples with various
porosities, determining the microstructure and permeability using both
experimental and numerical approaches. Based on this we provide
parameterizations of permeability, which can be used as input parameters for
large-scale numerical models.
Mark D. Lindsay, Sandra Occhipinti, Crystal Laflamme, Alan Aitken, and Lara Ramos
Solid Earth, 11, 1053–1077, https://doi.org/10.5194/se-11-1053-2020, https://doi.org/10.5194/se-11-1053-2020, 2020
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Integrated interpretation of multiple datasets is a key skill required for better understanding the composition and configuration of the Earth's crust. Geophysical and 3D geological modelling are used here to aid the interpretation process in investigating anomalous and cryptic geophysical signatures which suggest a more complex structure and history of a Palaeoproterozoic basin in Western Australia.
Tomáš Fischer, Josef Vlček, and Martin Lanzendörfer
Solid Earth, 11, 983–998, https://doi.org/10.5194/se-11-983-2020, https://doi.org/10.5194/se-11-983-2020, 2020
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Data on CO2 degassing help understanding the relations of the gas flow on geodynamic processes. Long-term gas flow measurements in rough field conditions present a challenge due to technical problems. We describe methods used for CO2 flow monitoring in West-Bohemia/Vogtland, which is typical for high CO2 flow, and present a new robust method based on pressure measurements in a water column. The results of 10 years of CO2 flow measurements and their relation to seismic activity are discussed.
Jana Schierjott, Antoine Rozel, and Paul Tackley
Solid Earth, 11, 959–982, https://doi.org/10.5194/se-11-959-2020, https://doi.org/10.5194/se-11-959-2020, 2020
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We investigate the size of mineral grains of Earth's rocks in computer models of the whole Earth. This is relevant because grain size affects the stiffness (large grains are stiffer) and deformation of the Earth's mantle. We see that mineral grains grow inside stable non-deforming regions of the Earth. However, these regions are less stiff than expected. On the other hand, we find that grain size diminishes during deformation events such as when surface material comes down into the Earth.
Irene Pérez-Cáceres, David Jesús Martínez Poyatos, Olivier Vidal, Olivier Beyssac, Fernando Nieto, José Fernando Simancas, Antonio Azor, and Franck Bourdelle
Solid Earth, 11, 469–488, https://doi.org/10.5194/se-11-469-2020, https://doi.org/10.5194/se-11-469-2020, 2020
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The metamorphism of the Pulo do Lobo unit (SW Iberian Massif) is described in this paper. To this end, three different and complementary methodologies have been applied. The new results reported here contribute to the knowledge of the metamorphic conditions of the Pulo do Lobo unit in relation to its deformation. Furthermore, the results are compared in order to assess the reliability of the different methods applied.
Ömer F. Bodur and Patrice F. Rey
Solid Earth, 10, 2167–2178, https://doi.org/10.5194/se-10-2167-2019, https://doi.org/10.5194/se-10-2167-2019, 2019
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Convection in the deep Earth dynamically changes the elevation of plates. Amplitudes of those vertical motions predicted from numerical models are significantly higher than observations. We find that at small wavelengths (< 1000 km) this misfit can be due to the oversimplification in viscosity of rocks. By a suite of numerical experiments, we show that considering the non–Newtonian rheology of the mantle results in predictions in amplitude of dynamic topography consistent with observations.
Janik Dohmen, Harro Schmeling, and Jan Philipp Kruse
Solid Earth, 10, 2103–2113, https://doi.org/10.5194/se-10-2103-2019, https://doi.org/10.5194/se-10-2103-2019, 2019
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In source regions of magmatic systems the temperature is above solidus and melt ascent is assumed to occur predominantly by two-phase flow. This two-phase flow allows for the emergence of solitary porosity waves. By now most solutions of these waves used strongly simplified viscosity laws, while in our laws the viscosity decreases rapidly for small melt fractions. The results show that for higher background porosities the phase velocities and the width of the wave are significantly decreased.
Cameron Spooner, Magdalena Scheck-Wenderoth, Hans-Jürgen Götze, Jörg Ebbing, György Hetényi, and the AlpArray Working Group
Solid Earth, 10, 2073–2088, https://doi.org/10.5194/se-10-2073-2019, https://doi.org/10.5194/se-10-2073-2019, 2019
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By utilising both the observed gravity field of the Alps and their forelands and indications from deep seismic surveys, we were able to produce a 3-D structural model of the region that indicates the distribution of densities within the lithosphere. We found that the present-day Adriatic crust is both thinner and denser than the European crust and that the properties of Alpine crust are strongly linked to their provenance.
Philipp Eichheimer, Marcel Thielmann, Anton Popov, Gregor J. Golabek, Wakana Fujita, Maximilian O. Kottwitz, and Boris J. P. Kaus
Solid Earth, 10, 1717–1731, https://doi.org/10.5194/se-10-1717-2019, https://doi.org/10.5194/se-10-1717-2019, 2019
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Prediction of rock permeability is of crucial importance for several research areas in geoscience. In this study, we enhance the finite difference code LaMEM to compute fluid flow on the pore scale using Newtonian and non-Newtonian rheologies. The accuracy of the code is demonstrated using several analytical solutions as well as experimental data. Our results show good agreement with analytical solutions and recent numerical studies.
Ershad Gholamrezaie, Magdalena Scheck-Wenderoth, Judith Bott, Oliver Heidbach, and Manfred R. Strecker
Solid Earth, 10, 785–807, https://doi.org/10.5194/se-10-785-2019, https://doi.org/10.5194/se-10-785-2019, 2019
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Based on geophysical data integration and 3-D gravity modeling, we show that significant density heterogeneities are expressed as two large high-density bodies in the crust below the Sea of Marmara. The location of these bodies correlates spatially with the bends of the main Marmara fault, indicating that rheological contrasts in the crust may influence the fault kinematics. Our findings may have implications for seismic hazard and risk assessments in the Marmara region.
Sascha Brune, Simon E. Williams, and R. Dietmar Müller
Solid Earth, 9, 1187–1206, https://doi.org/10.5194/se-9-1187-2018, https://doi.org/10.5194/se-9-1187-2018, 2018
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Fragmentation of continents often involves obliquely rifting segments that feature a complex three-dimensional structural evolution. Here we show that more than ~ 70 % of Earth’s rifted margins exceeded an obliquity of 20° demonstrating that oblique rifting should be considered the rule, not the exception. This highlights the importance of three-dimensional approaches in modelling, surveying, and interpretation of those rift segments where oblique rifting is the dominant mode of deformation.
Cited articles
Andrews, E. R. and Billen, M. I.: Rheologic controls on the dynamics of slab detachment, Tectonophysics, 464, 60–69, 2009.
Androvicova, A., Cizkova, H., and van den Berg, A. P.: The effects of rheological decoupling on slab deformation in the Earth's upper mantle, Stud. Geophys. Geod., 57, 460–481, https://doi.org/10.1007/s11200-012-0259-7, 2013.
Arndt, D., Bangerth, W., Davydov, D., Heister, T., Heltai, L., Kronbichler, M., Maier, M., Pelteret, J.-P., Turcksin, B., and Wells, D.: The deal.II Library, Version 8.5, J. Numer. Math., 24, 135–141, https://doi.org/10.1515/jnma-2016-1045, 2017.
Bangerth, W., Hartmann, R., and Kanschat, G.: deal.II – a general purpose object oriented finite element library, ACM Trans. Math. Softw., 33, 24/1–24/27, 2007.
Bangerth, W., Dannberg, J., Gassmöller, R., Heister, T., et al.: ASPECT: Advanced Solver for Problems in Earth's ConvecTion, User manual, Computational Infrastructure in Geodynamics, https://doi.org/10.6084/m9.figshare.4865333, 2017a.
Bangerth, W., Dannberg, J., Gassmöller, R., Heister, T., et al.: ASPECT v1.5.0 [software], Computational Infrastructure for Geodynamics, https://doi.org/10.5281/zenodo.344623, 2017b.
Baumgardner, J. R.: Three-dimensional treatment of convective flow in the earth's mantle, J. Stat. Phys., 39, 501–511, 1985.
Braun, J.: Three-dimensional numerical simulations of crustal-scale wrenching using a non-linear failure criterion, J. Struct. Geol., 16, 1173–1186, 1994.
Braun, J. and Beaumont, C.: Three-dimensional numerical experiments of strain partitioning at oblique plate boundaries: Implications for contrasting tectonic styles in the southern Coast Ranges, California, and central South Island, New Zealand, J. Geophys. Res.-Solid Earth, 100, 18059–19074, https://doi.org/10.1029/95JB01683, 1995.
Braun, J., Thieulot, C., Fullsack, P., DeKool, M., Beaumont, C., and Huismans, R. S: DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems, Phys. Earth Planet. In., 171, 76–91, https://doi.org/10.1016/j.pepi.2008.05.003, 2008.
Buiter, S. J. H.: A review of brittle compressional wedge models, Tectonophysics, 530–531, 1–17, 2012.
Buiter, S. J. H., Babeyko, A. Y., Ellis, S., Gerya, T. V., Kaus, B. J. P., Kellner, A., Schreurs, G., and Yamada, Y.: The numerical sandbox: comparison of model results for a shortening and an extension experiment, in: Analogue and Numerical Modelling of Crustal-Scale Processes, edited by: Buiter, S. J. H. and Schreurs, G., vol. 253, pp. 29–64, Geological Society, London, Special Publications, 2006.
Burkett, E. R. and Billen, M. I.: Dynamics and implications of slab detachment due to ridge-trench collision, J. Geophys. Res., 114, B12402, https://doi.org/10.1029/2009JB006402, 2009.
Burkett, E. R. and Billen, M. I.: Three-dimensionality of slab detachment due to ridge-trench collision: Laterally simultaneous boudinage versus tear propagation, Geochem. Geophy. Geosy., 11, Q11012, https://doi.org/10.1029/2010GC003286, 2010.
Burov, E.: Rheology and strength of the lithosphere, Mar. Petrol. Geol., 28, 1402–1443, https://doi.org/10.1016/j.marpetgeo.2011.05.008, 2011.
Burstedde, C., Ghattas, O., Gurnis, M., Stadler, G., Tan, E., Tu, T., Wilcox, L. C., and Zhong, S.: Scalable Adaptive Mantle Convection Simulation on Petascale Supercomputers, in: 2008 SC – International Conference for High Performance Computing, Networking, Storage and Analysis, IEEE, 1–15, https://doi.org/10.1109/SC.2008.5214248, 2008.
Burstedde, C., Wilcox, L., and Ghattas, O.: p4est: Scalable algorithms for parallel adaptive mesh refinement on forests of octrees, SIAM Journal on Scientific Computing, 33, 1103–1133, 2011.
Capitanio, F. A. and Faccenda, M.: Complex mantle flow around heterogeneous subducting oceanic plates, Earth Planet. Sci. Lett., 353–354, 29–37, 2012.
Capitanio, F. A. and Replumaz, A.: Subduction and slab breakoff controls on Asian indentation tectonics and Himalayan western syntaxis formation, Geochem. Geophy. Geosy., 353–354, 29–37, https://doi.org/10.1016/j.epsl.2012.07.042, 2013.
Chertova, M. V., Geenen, T., van den Berg, A., and Spakman, W.: Using open sidewalls for modelling self-consistent lithosphere subduction dynamics, Solid Earth, 3, 313–326, https://doi.org/10.5194/se-3-313-2012, 2012.
Chertova, M. V., Spakman, W., Geenen, T., van den Berg, A. P., and van Hinsbergen, D. J. J.: Underpinning tectonic reconstructions of the western Mediterranean region with dynamic slab evolution from 3-D numerical modeling, J. Geophys. Res.-Solid Earth, 119, 5876–5902, https://doi.org/10.1002/2014JB011150, 2014a.
Chertova, M. V., Spakman, W., van den Berg, A. P., and van Hinsbergen, D. J. J.: Absolute plate motions and regional subduction evolution, Geochem. Geophy. Geosy., 15, 3780–3792, https://doi.org/10.1002/2014GC005494, 2014b.
Choi, E. and Petersen, K. D.: Making Coulomb angle-oriented shear bands in numerical tectonic models, Tectonophysics, 657, 94–101, https://doi.org/10.1016/j.tecto.2015.06.026, 2015.
Christensen, U. R. and Yuen, D. A.: Layered convection induced by phase transitions, J. Geophys. Res., 90, 10291–10300, 1985.
Christiansen, E. and Pedersen, O. S.: Automatic mesh refinement in limit analysis, Int. J. Numer. Meth. Eng., 6, 1331–1346, https://doi.org/10.1002/1097-0207(20010228)50:6<1331::AID-NME46>3.0.CO;2-S, 2001.
Cizkova, H., van den Berg, A. P., Spakman, W., and Matyska, C.: The viscosity of the Earth's lower mantle inferred from sinking speed of subducted lithosphere, Phys. Earth Planet. In., 200–201, 56–62, 2012.
Crameri, F. and Tackley, P. J.: Spontaneous development of arcuate single-sided subduction in global 3-D mantle convection models with a free surface, J. Geophys. Res.-Solid Earth, 119, 5921–5942, https://doi.org/10.1002/2014JB010939, 2014.
Crameri, F., Schmeling, H. A., Golabek, G. J., Duretz, T., Orendt, R., Buiter, S. J. H., May, D. A., Kaus, B., Gerya, T. V., and Tackley, P. J.: A comparison of numerical surface topography calculations in geodynamic modelling: an evaluation of the `sticky air' method, Geophys. J. Int., 189, 38–54, 2012.
Dabrowski, M., Krotkiewski, M., and Schmid, D.: MILAMIN: MATLAB-based finite element method solver for large problems, Geochem. Geophy. Geosy., 9, Q04030, https://doi.org/10.1029/2007GC001719, 2008.
Dannberg, J. and Heister, T.: Compressible magma/mantle dynamics: 3d, adaptive simulations in ASPECT, Geophys. J. Int., 207, 1343–1366, https://doi.org/10.1093/gji/ggw329, 2016.
Davies, D. R., Wilson, C. R., and Kramer, S. C.: Fluidity: a fully unstructured anisotropic adaptive mesh computational modeling framework for geodynamics, Geochem. Geophy. Geosy., 120, Q06001, https://doi.org/10.1029/2011GC003551, 2011.
Davies, D. R., Davies, J. H., Bollada, P. C., Hassan, O., Morgan, K., and Nithiarasu, P.: A hierarchical mesh refinement technique for global 3-D spherical mantle convection modelling, Geosci. Model Dev., 6, 1095–1107, https://doi.org/10.5194/gmd-6-1095-2013, 2013.
Davis, R. O. and Selvadurai, A. P. S.: Plasticity and Geomechanics, Cambridge University Press, 2002.
de Souza Neto, E. A., Peric, D., and Owen, D. R. J.: Computational methods for plasticity, John Wiley & Sons, Ltd, 2008.
Deubelbeiss, Y. and Kaus, B.: Comparison of Eulerian and Lagrangian numerical techniques for the Stokes equations in the presence of stronly varying viscosity, Phys. Earth Planet. In., 171, 92–111, 2008.
Donea, J. and Huerta, A.: Finite element methods for flow problems, John Wiley & Sons, Ltd, https://doi.org/10.1002/0470013826, 2003.
Duretz, T., Gerya, T. V., and May, D. A.: Numerical modelling of spontaneous slab breakoff and subsequent topographic response, Tectonophysics, 502, 244–256, https://doi.org/10.1016/j.tecto.2010.05.024, 2011.
Duretz, T., Schmalholz, S. M., and Gerya, T. V.: The dynamics of slab detachment, Geochem. Geophy. Geosy., 13, Q03020, https://doi.org/10.1029/2011GC004024, 2012.
Duretz, T., Gerya, T. V., and Spakman, W.: Slab detachment in laterally varying subduction zones: 3-D numerical modeling, Geophys. Res. Lett., 41, 1951–1956, 2014.
Farrington, R. J., Moresi, L. N., and Capitanio, F. A.: The role of viscoelasticity in subducting plates, Geochem. Geophy. Geosy., 15, 4291–4304, 2014.
Fleck, N. and Hutchinson, J.: A reformulation of strain gradient plasticity, J. Mech. Phys. Solids, 49, 2245–2271, https://doi.org/10.1016/S0022-5096(01)00049-7, 2001.
Fourel, L., Goes, S., and Morra, G.: The role of elasticity in slab bending, Geochem. Geophy. Geosy., 15, 4507–4525, 2014.
Fraters, M., Bangerth, W., Thieulot, C., and Spakman, W.: Newton Solver Stabilization for Stokes Solvers in Geodynamic Problems, Geophys. Res. Abstr., 19, EGU2017-13556, 2017.
Garel, F., Goes, S., Davies, D. R., Davies, J. H., Kramer, S. C., and Wilson, C. R.: Interaction of subducted slabs with the mantle transition-zone: a regime diagram from 2-D thermo-mechanical models with a mobile trench and an overriding plate, Geochem. Geophy. Geosy., 15, 1739–1765, https://doi.org/10.1002/2014GC005257, 2014.
Gassmöller, R., Heien, E., Puckett, E. G., and Bangerth, W.: Flexible and scalable particle-in-cell methods for massively parallel computations, ArXiv e-prints, available at: https://arxiv.org/abs/1612.03369, 2016.
Gerbault, M., Poliakov, A. N. B., and Daignieres, M.: Prediction of faulting from the theories of elasticity and plasticity: what are the limits?, J. Struct. Geol., 20, 301–330, 1998.
Gerya, T. V.: Introduction to Numerical Geodynamic Modelling, Cambridge University Press, 2010.
Gerya, T. V. and Yuen, D. A.: Robust characteristics method for modelling multiphase visco-elasto-plastic thermo-mechanical problems, Phys. Earth Planet. In., 163, 83–105, 2007.
Gerya, T. V., Yuen, D. A., and Maresh, W. V.: Thermomechanical modelling of slab detachment, Earth Planet. Sci. Lett., 226, 101–116, 2004.
Gerya, T. V., May, D. A., and Duretz, T.: An adaptive staggered grid finite difference method for modeling geodynamic Stokes flows with strongly variable viscosity, Geochem. Geophy. Geosy., 14, 4, https://doi.org/10.1002/ggge.20078, 2013.
Glerum, A.: Source code, input files and postprocessing scripts, available at: https://doi.org/10.5281/zenodo.852654, August 2017.
Gourvenec, S., Randolph, M., and Kingsnorth, O.: Undrained bearing capacity of square and rectangular footings, Int. J. Geomechanics, 6, 147–157, https://doi.org/10.1061/(ASCE)1532-3641(2006)6:3(147), 2006.
Guermond, J.-L., Pasquetti, R., and Popov, B.: Entropy viscosity method for nonlinear conservation laws, J. Comput. Phys., 230, 4248–4267, 2011.
He, Y., Puckett, E. G., and Billen, M. I.: A discontinuous Galerkin method with a bound preserving limiter for the advection of non-diffusive fields in solid Earth geodynamics, Phys. Earth Planet. In., 263, 23–37, https://doi.org/10.1016/j.pepi.2016.12.001, 2017.
Heister, T., Dannberg, J., Gassmöller, R., and Bangerth, W.: High accuracy mantle convection simulation through modern numerical methods – II: realistic models and problems, Geophys. J. Int., 210, 833–851, https://doi.org/10.1093/gji/ggx195, 2017.
Heroux, M. A. and Willenbring, J. M.: A new overview of the Trilinos Project, Scientific Programming, 20, 83–88, https://doi.org/10.3233/SPR-2012-0355, 2012.
Heroux, M. A., Bartlett, R. A., Howle, V. E., Hoekstra, R. J., Hu, J. J., Kolda, T. G., Lehoucq, R. B., Long, K. R., Pawlowski, R. P., Phipps, E. T., Salinger, A. G., Thornquist, H. K., Tuminaro, R. S., Willenbring, J. M., Williams, A., and Stanley, K. S.: An overview of the Trilinos project, ACM Trans. Math. Softw., 31, 397–423, 2005.
Hillebrand, B., Thieulot, C., Geenen, T., van den Berg, A. P., and Spakman, W.: Using the level set method in geodynamical modeling of multi-material flows and Earth's free surface, Solid Earth, 5, 1087–1098, https://doi.org/10.5194/se-5-1087-2014, 2014.
Hirth, G. and Kohlstedt, D.: Rheology of the upper mantle and the mantle wedge: a view from the experimentalists, in: Inside the Subduction Factory, edited by: Eiler, J., vol. 183 of Geophysical Monograph, American Geophysical Union, 2003.
Huh, H., Lee, C. H., and Yang, W. H.: A general algorithm for plastic flow simulation by finite element limit analysis, Int. J. Solids Struct., 36, 1193–1207, 1999.
Ismail-Zadeh, A. and Tackley, P. J.: Computational Methods for Geodynamics, Cambridge University Press, 2010.
Kachanov, L. M.: Fundamentals of the Theory of Plasticity, Dover Publications, Inc., 2004.
Karato, S.: Deformation of Earth Materials: An Introduction to the Rheology of Solid Earth, Cambridge University Press, 2008.
Karato, S. and Wu, P.: Rheology of the Upper Mantle: A Synthesis, Science, 260, 771–778, 1993.
Kaus, B.: Factors that control the angle of shear bands in geodynamic numerical models of brittle deformation, Tectonophysics, 484, 36–47, 2010.
Kaus, B., Mühlhaus, H.-B., and May, D. A.: A stabilization algorithm for geodynamic numerical simulations with a free surface, Phys. Earth Planet. In., 181, 12–20, https://doi.org/10.1016/j.pepi.2010.04.007, 2010.
Kaus, B. J. P., Popov, A. A., Baumann, T. S., Püsök, A. E., Bauville, A., Fernandez, N., and Collignon, M.: Forward and inverse modelling of lithospheric deformation on geological timescales, no. 8 in NIC Series, Forschungszentrum Jülich GmbH, 2016.
Kronbichler, M., Heister, T., and Bangerth, W.: High accuracy mantle convection simulation through modern numerical methods, Geophys. J. Int., 191, 12–29, 2012.
Lee, J., Salgado, R., and Kim, S.: Bearing capacity of circular footings under surcharge using state-dependent finite element analysis, Comput. Geotech., 32, 445–457, 2005.
Lemiale, V., Mühlhaus, H.-B., Moresi, L., and Stafford, J.: Shear banding analysis of plastic models formulated for incompressible viscous flows, Phys. Earth Planet. In., 171, 177–186, 2008.
Lliboutry, L. A.: Very slow flow of fluids: Basics of modeling in geodynamics and glaciology, chap. The rigid-plastic model, pp. 393–401, Martinus Nijhoff Publishers, 1987.
Malatesta, C., Gerya, T. V., Crispini, L., Federico, L., and Capponi, G.: Oblique subduction modelling indicates along-trench tectonic transport of sediments, Nature Communications, 4, 2456, https://doi.org/10.1038/ncomms3456, 2013.
Mason, W. G., Moresi, L., Betss, P., and Miller, M. S.: Three-dimensional numerical models of the influence of a buoyant oceanic plateau on subduction zones, Tectonophysics, 483, 71–79, 2010.
May, D. A., Brown, J., and Le Pourhiet, L.: A scalable, matrix-free multigrid precondition for finite element discretizations of heterogeneous Stokes flow, Comput. Methods Appl. M., 290, 496–523, 2015.
Moresi, L., Zhong, S., and Gurnis, M.: The accuracy of finite element solutions of Stokes' flow with strongly varying viscosity, Phys. Earth Planet. In., 97, 83–94, 1996.
Moresi, L., Quenette, S., Lemiale, V., Mériaux, C., Appelbe, B., and Mühlhaus, H.-B.: Computational approaches to studying non-linear dynamics of the crust and mantle, Phys. Earth Planet. In., 163, 69–82, 2007.
Popov, A. A. and Sobolev, S. V.: SLIM3D: a tool for the three-dimensional thermomechanical modeling of the lithospheric deformation with elasto-visco-plastic rheology, Phys. Earth Planet. In., 171, 55–75, https://doi.org/10.1016/j.pepi.2008.03.007, 2008.
Ranalli, G.: Rheology of the Earth, Chapman and Hall, London, 1995.
Rose, I., Buffett, B. A., and Heister, T.: Stability and accuracy of free surface time integration in viscous flows, Phys. Earth Planet. In., 262, 90–100, 2017.
Rudi, J., Malossi, A. C. I., Isaac, T., Stadler, G., Gurnis, M., Staar, P. W. J., Ineichen, Y., Bekas, C., Curioni, A., and Ghattas, O.: An Extreme-scale Implicit Solver for Complex PDEs: Highly Heterogeneous Flow in Earth's Mantle, in: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC '15, pp. 5:1–5:12, ACM, New York, NY, USA, https://doi.org/10.1145/2807591.2807675, 2015.
Schellart, W. P. and Moresi, L.: A new driving mechanism for backarc extension and backarc shortening through slab sinking induced toroidal and poloidal mantle flow: Results from dynamic subduction models with an overriding plate, J. Geophys. Res., 118, 1–28, 2013.
Schellart, W. P., Freeman, J., Stegman, D. R., Moresi, L., and May, D.: Evolution and diversity of subduction zones controlled by slab width, Nature Lett., 446, 308–311, https://doi.org/10.1038/nature05615, 2007.
Schmalholz, S. M.: A simple analytical solution for slab detachment, Earth Planet. Sci. Lett., 304, 45–54, 2011.
Schmeling, H. A., Babeyko, A. Y., Enns, A., Faccenna, C., Funiciello, F., Gerya, T., Golabek, G. J., Grigull, S., Kaus, B. J. P., Morra, G., Schmalholz, S. M., and van Hunen, J.: A benchmark comparison of spontaneous subduction models-Towards a free surface, Phys. Earth Planet. In., 171, 198–223, 2008.
Schreurs, G., Buiter, S. J. H., Boutelier, D., Corti, G., Costa, E., Cruden, A. R., Daniel, J.-M., Hoth, S., Koyi, H. A., Kukowski, N., Lohrmann, J., Ravaglia, A., Schlische, R. W., Withjack, M. O., Yamada, Y., Cavozzi, C., Del Ventisette, C., Brady, J. A. E., Hoffmann-Rothe, A., Mengus, J.-M., Montanari, D., and Nilforoushan, F.: Analogue benchmarks of shortening and extension experiments, in: Analogue and Numerical Modelling of Crustal-Scale Processes, edited by: Buiter, S. J. H. and Schreurs, G., Geological Society, London, Special Publications, 253, 1–27, https://doi.org/10.1144/GSL.SP.2006.253.01.01, 2006.
Schubert, G., Turcotte, D. L., and Olson, P.: Mantle Convection in the Earth and Planets, Cambridge University Press, 2001.
Spiegelman, M., May, D. A., and Wilson, C. R.: On the solvability of incompressible Stokes with viscoplastic rheologies in geodynamics, Geochem. Geophy. Geosy., 17, 2213–2238, https://doi.org/10.1002/2015GC006228, 2016.
Stegman, D. R., Freeman, J., Schellart, W. P., Moresi, L., and May, D. A.: Influence of trench width on subduction hinge retreat rates in 3-D models of slab rollback, Geochem. Geophy. Geosy., 7, Q03012, https://doi.org/10.1029/2005GC001056, 2006.
Stegman, D. R., Schellart, W. P., and Freeman, J.: Competing influences of plate width and far-field boundary conditions on trench migration and morphology of subducted slabs in the upper mantle, Tectonophysics, 483, 46–57, 2010.
Sternai, P., Jolivet, L., Menant, A., and Gerya, T. V.: Driving the upper plate surface deformation by slab rollback and mantle flow, Earth Planet. Sci. Lett., 405, 110–118, 2014.
Thieulot, C.: FANTOM: Two- and three-dimensional numerical modelling of creeping flows for the solution of geological problems, Phys. Earth Planet. In., 188, 47–68, 2011.
Thieulot, C.: ELEFANT: a user-friendly multipurpose geodynamics code, Solid Earth Discuss., https://doi.org/10.5194/sed-6-1949-2014, in review, 2014.
Thieulot, C., Fullsack, P., and Braun, J.: Adaptive octree-based finite element analysis of two- and three-dimensional indentation problems, J. Geophys. Res., 113, B12207, https://doi.org/10.1029/2008JB005591, 2008.
Tosi, N., Stein, C., Noack, L., Hüttig, C., Maierova, P., Samual, H., Davies, D. R., Wilson, C. R., Kramer, S. C., Thieulot, C., Glerum, A., Fraters, M., Spakman, W., Rozel, A., and Tackley, P. J.: A community benchmark for viscoplastic thermal convection in a 2-D square box, Geochem. Geophy. Geosy., 16, 2175–2196, 2015.
van den Berg, A., van Keken, P., and Yuen, D. A.: The effects of a composite non-Newtonian and Newtonian rheology on mantle convection, Geophys. J. Int., 115, 62–78, 1993.
van Hunen, J. and Allen, M. B.: Continental collision and slab break-off: A comparison of 3-D numerical models with observations, Earth Planet. Sci. Lett., 302, 27–37, 2011.
Vermeer, P. A.: The orientation of shear bands in bi-axial tests, Géotechnique, 40, 223–236, 1990.
von Tscharner, M., Schmalholz, S. M., and Duretz, T.: Three-dimensional necking during viscous slab detachment, Geophys. Res. Lett., 41, 4194–4200, 2014.
Willett, S. D.: Dynamic and kinematic growth and change of a Coulomb wedge, in: Thrust tectonics, edited by: McClay, K. R., pp. 19–32, Chapman and Hall, New York, 1992.
Wilson, C. R., Spiegelman, M., and van Keken, P. E.: TerraFERMA: The Transparent Finite Element Rapid Model Assembler for multiphysics problems in Earth sciences, Geochem. Geophy. Geosy., 18, 769–810, https://doi.org/10.1002/2016GC006702, 2017.
Wortel, M. J. R. and Spakman, W.: Subduction and slab detachment in the Mediterranean-Carpathian region, Science, 290, 1910, https://doi.org/10.1126/science.290.5498.1910, 2000.
Yamato, P., Husson, L., Braun, J., Loiselet, C., and Thieulot, C.: Influence of surrounding plates on 3D subduction dynamics, Geophys. Res. Lett., 36, L07303, https://doi.org/10.1029/2008GL036942, 2009.
Yu, X. and Tin-Loi, F.: A simple mixed finite element for static limit analyis, Computers and Structures, 84, 1906–1917, 2006.
Zhang, S. and O'Neill, C.: The early geodynamic evolution of Mars-type planets, Icarus, 265, 187–208, https://doi.org/10.1016/j.icarus.2015.10.019, 2016.
Zhong, S.: Constraints on thermochemical convection of the mantle from plume heat flux, plume excess temperature, and upper mantle temperature, J. Geophys. Res., 111, B04409, https://doi.org/10.1029/2005JB003972, 2006.
Zienkiewicz, O. C., Huang, M., and Pastor, M.: Localization problems in plasticity using finite elements with adaptive remeshing, Numerical and Analytical Methods in Geomechanics, 19, 127–148, 1995.
Short summary
A nonlinear viscoplastic rheology is implemented and benchmarked in the ASPECT software, allowing for the modeling of lithospheric deformation. We showcase the new functionality with a four-dimensional model of thermomechanically coupled subduction.
A nonlinear viscoplastic rheology is implemented and benchmarked in the ASPECT software,...
