Articles | Volume 8, issue 6
https://doi.org/10.5194/se-8-1181-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/se-8-1181-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Method article
| 
24 Nov 2017
Method article |
| 24 Nov 2017
| 24 Nov 2017
Analytical solution for viscous incompressible Stokes flow in a spherical shell
Department of Earth Sciences, Utrecht University, Utrecht, the Netherlands
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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.
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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.
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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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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.
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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.
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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.
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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.
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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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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.
Anne Glerum, Cedric Thieulot, Menno Fraters, Constantijn Blom, and Wim Spakman
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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.
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
Cedric Thieulot and Wolfgang Bangerth
EGUsphere, https://doi.org/10.5194/egusphere-2024-1668, https://doi.org/10.5194/egusphere-2024-1668, 2024
Short summary
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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
Short summary
Short summary
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
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.
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.
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
Short summary
Short summary
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
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
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.
Anne Glerum, Cedric Thieulot, Menno Fraters, Constantijn Blom, and Wim Spakman
Solid Earth, 9, 267–294, https://doi.org/10.5194/se-9-267-2018, https://doi.org/10.5194/se-9-267-2018, 2018
Short summary
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.
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
Short summary
Short summary
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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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
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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.
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
Arrial, P.-A., Flyer, N., Wright, G. B., and Kellogg, L. H.: On the sensitivity of 3-D thermal convection codes to numerical discretization: a model intercomparison, Geosci. Model Dev., 7, 2065–2076, https://doi.org/10.5194/gmd-7-2065-2014, 2014.
Bangerth, W., Hartmann, R., and Kanschat, G.: deal.II – a general purpose object oriented finite element library, ACM T. Math. Software, 33, https://doi.org/10.1145/1268776.1268779, 2007.
Bangerth, W., Davydov, D., Heister, T., Heltai, L., Kanschat, G., Kronbichler, M., Maier, M., Turcksin, B., and Wells, D.: The deal.ii library, version 8.4, J. Numer. Math., 24, https://doi.org/10.1515/jnma-2016-1045, 2016.
Bangerth, W., Dannberg, J., Gassmöller, R., Heister, T., and others: ASPECT: Advanced Solver for Problems in Earth's ConvecTion, User Manual, https://doi.org/10.6084/m9.figshare.4865333, 2017.
Bercovici, D., Schubert, G., Glatzmaier, G., and Zebib, A.: Three-dimensional thermal convection in a spherical shell, J. Fluid Mech., 206, 75–104, 1989.
Blankenbach, B., Busse, F., Christensen, U., Cserepes, L., Gunkel, D., Hansen, U., Harder, H., Jarvis, G., Koch, M., Marquart, G., Moore, D., Olson, P., Schmeling, H., and Schnaubelt, T.: A benchmark comparison for mantle convection codes, Geophys. J. Int., 98, 23–38, 1989.
Blinova, I., Makeev, I., and Popov, I.: Benchmark solutions for Stokes flows in cyclindrical and spherical geometry, Bulletin of the Transilvania University of Brasov, 9, 58–63, 2016.
Bower, D., Gurnis, M., and Flament, N.: Assimilating lithosphere and slab history in 4-D Earth models, Phys. Earth. Planet. In., 238, 8–22, 2015.
Braess, D.: Finite Elements, Cambridge, UK, 2007.
Bull, A., Domeier, M., and Torsvik, T.: The effect of plate motion history on the longevity of deep mantle heterogeneities, Earth Planet. Sc. Lett., 401, 172–182, 2014.
Burstedde, C., Stadler, G., Alisic, L., Wilcox, L., Tan, E., Gurnis, M., and Ghattas, O.: Large-scale adaptive mantle convection simulation, Geophys. J. Int., 192, 889–906, 2013.
Busse, F.: Patterns of convection in spherical shells, J. Fluid Mech., 72, 67–85, 1975.
Busse, F. and Riahi, N.: Patterns of convection in spherical shells – Part 2, J. Fluid Mech., 123, 283–301, 1982.
Choblet, G., Čadek, O., Couturier, F., and Dumoulin, C.: OEDIPUS: a new tool to study the dynamics of planetary interiors, Geophy. J. Int., 170, 9–30, 2007.
Crameri, F. and Tackley, P.: Subduction initiation from a stagnant lid and global overturn: new insights from numerical models with a free surface, Progress in Earth and Planetary Science, 3, https://doi.org/10.1186/s40645-016-0103-8, 2016.
Dannberg, J. and Heister, T.: Compressible magma/mantle dynamics: 3-D, adaptive simulations in ASPECT, Geophy. J. Int., 207, 1343–1366, 2016.
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.
Elman, H.: Multigrid and Krylov subspace methods for the discrete Stokes equations, Int. J. Numer. Meth. Fl., 22, 755–770, 1996.
Glatzmaier, G.: Numerical simulations of mantle convection: Time-dependent, three-dimensional, compressible, spherical shell, Geophys. Astro. Fluid, 43, 223–264, 1988.
Hager, B. and O'Connell, R.: A simple global model of plate dynamics and mantle convection, J. Geophys. Res., 86, 4843–4867, 1981.
Heister, T., Dannberg, J., Gassmöller, R., and Bangerth, W.: High Accuracy Mantle Convection Simulation through Modern Numerical Methods. II: Realistic Models and Problems, Geophy. J. Int., 210, 833–851, 2017.
Iwase, Y.: Three-dimensional infinite Prandtl number convection in a spherical shell with temperature-dependent viscosity, J. Geomagn. Geoelectr., 48, 1499–1514, 1996.
Kageyama, A. and Sato, T.: “Yin-Yang grid”: An overset grid in spherical geometry, Geochem. Geophy. Geosys., 5, Q09005, https://doi.org/10.1029/2004GC000734, 2004.
Kronbichler, M., Heister, T., and Bangerth, W.: High accuracy mantle convection simulation through modern numerical methods , Geophy. J. Int., 191, 12–29, 2012.
Lavecchia, A., Thieulot, C., Beekman, F., Cloetingh, S., and Clark, S.: Lithosphere erosion and continental breakup: Interaction of extension, plume upwelling and melting, Earth Planet. Sc. Lett., 467, 89–98, 2017.
Lay, T. and Garnero, E.: Deep Mantle Seismic Modeling and Imaging, Annu. Rev. Earth Pl. Sc., 39, 91–123, 2011.
Machetel, P., Rabinowitz, M., and Bernardet, P.: Three-dimensional convection in spherical shells, Geophys. Astro. Fluid, 37, 57–84, 1986.
Popov, I. Yu., Lobanov, I. S., Popov, S. I., Popov, A. I., and Gerya, T. V.: Practical analytical solutions for benchmarking of 2-D and 3-D geodynamic Stokes problems with variable viscosity, Solid Earth, 5, 461–476, https://doi.org/10.5194/se-5-461-2014, 2014.
Ratcliff, J., Schubert, G., and Zebib, A.: Steady tetrahedral and cubic patterns of spherical shell convection with temperature-dependent viscosity, J. Geophys. Res., 101, 25473–25484, 1996.
Richards, M. and Hager, B.: Geoid anomalies in a dynamic Earth, J. Geophys. Res., 89, 5987–6002, 1984.
Richards, M., Yang, W.-S., Baumgardner, J., and Bunge, H.-P.: Role of a low-viscosity zone in stabilizing plate tectonics: Implications for comparative terrestrial planetology, Geochem. Geophys. Geosy., 2, 1026, https://doi.org/10.1029/2000GC000115,, 2001.
Schubert, G., Turcotte, D., and Olson, P.: Mantle Convection in the Earth and Planets, Cambridge University Press, Cambridge, UK, 2001.
Stemmer, K., Harder, H., and Hansen, U.: A new method to simulate convection with strongly temperature- and pressure-dependent viscosity in a spherical shell: Applications to the Earth's mantle, Phys. Earth Planet. In., 157, 223–249, 2006.
Tabata, M. and Suzuki, A.: A stabilized finite element method for the Rayleigh-Bénard equations with infinite Prandtl number in a spherical shell, Comput. Method. Appl. M., 190, 387–402, 2000.
Tackley, P.: Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the yin-yang grid, Phys. Earth Planet. In., 171, 7–18, 2008.
Tackley, P.: Dynamics and evolution of the deep mantle resulting from thermal, chemical, phase and melting effects, Earth-Sci. Rev., 110, 1–25, 2012.
Thieulot, C.: FANTOM: two- and three-dimensional numerical modelling of creeping flows for the solution of geological problems, Phys. Earth Planet. Int., 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.
Tosi, N. and Martinec, Z.: Semi-analytical solution for viscous Stokes flow in two eccentrically nested spheres, Geophys. J. Int., 170, 1015–1030, 2007.
Tosi, N., Stein, C., Noack, L., Huettig, C., Maierova, P., Samuel, H., Davies, D., Wilson, C., Kramer, S., Thieulot, C., Glerum, A., Fraters, M., Spakman, W., Rozel, A., and Tackley, P.: A community benchmark for viscoplastic thermal convection in a 2-D square box, Geochem. Geophy. Geosy., 16, 2175–2196, https://doi.org/10.1002/2015GC005807, 2015.
van Heck, H. J., Davies, J. H., Elliott, T., and Porcelli, D.: Global-scale modelling of melting and isotopic evolution of Earth's mantle: melting modules for TERRA, Geosci. Model Dev., 9, 1399–1411, https://doi.org/10.5194/gmd-9-1399-2016, 2016.
van Hinsbergen, D., Steinberger, B., Doubrovine, P., and Gassmöller, R.: Acceleration and deceleration of India–Asia convergence since the Cretaceous: Roles of mantle plumes and continental collision, J. Geophys. Res., 116, B06101, https://doi.org/10.1029/2010JB008051, 2011.
van Keken, P., Hauri, E., and Ballentine, C.: Mantle mixing: the generation, preservation and destruction of chemical heterogeneity, Annu. Rev. Earth Pl. Sc, 30, 493–525, 2002.
Yoshida, M. and Kageyama, A.: Application of the Yin-Yang grid to a thermal convection of a Boussinesq fluid with infinite Prandtl number in a three-dimensional spherical shell, Geophys. Res. Lett., 31, L12609, https://doi.org/10.1029/2004GL019970, 2004.
Zhang, S. and Christensen, U.: Some effects of lateral viscosity variations on geoid and surface velocities induced by density anomalies in the mantle, Geophy. J. Int., 114, 531–547, 1993.
Zhang, S. and Yuen, D.: The influences of lower mantle viscosity stratification on 3D spherical-shell mantle convection, Earth Planet. Sc. Lett., 132, 157–166, 1995.
Zhong, S.: Analytic solutions for Stokes' flow with lateral variations in viscosity, Geophys. J. Int., 124, 18–28, 1996.
Zhong, S., Zuber, M., Moresi, L., and Gurnis, M.: The role of temperature-dependent viscosity and surface plates in spherical shell models of mantle convection, J. Geophys. Res., 105, 11063–11082, 2000.
Zhong, S., McNamara, A., Tan, E., Moresi, L., and Gurnis, M.: A benchmark study on mantle convection in a 3-D spherical shell using CITCOMS, Geochem. Geophy. Geosy., 9, Q10017, https://doi.org/10.1029/2008GC002048, 2008.
Short summary
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.
I present a new family of analytical flow solutions to the incompressible Stokes equation in a...
