Articles | Volume 9, issue 5
https://doi.org/10.5194/se-9-1169-2018
© Author(s) 2018. 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-9-1169-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
GHOST: Geoscientific Hollow Sphere Tessellation
Department of Earth Sciences, Faculty of Geosciences, Utrecht University, Utrecht, the Netherlands
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Erik van der Wiel, Cedric Thieulot, and Douwe J. J. van Hinsbergen
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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
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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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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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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.
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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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B. Hillebrand, C. Thieulot, T. Geenen, A. P. van den Berg, and W. Spakman
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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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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 us to quantify mixing in models. The entropy may be used to analyse the mixed state of the mantle as a whole and may also be useful to validate numerical models against anomalies in the mantle that are obtained from seismology and geochemistry.
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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
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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.
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.
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.
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
Short summary
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.
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
Related subject area
Subject area: Core and mantle structure and dynamics | Editorial team: Geodesy, gravity, and geomagnetism | Discipline: Geodynamics
Earth's core variability from magnetic and gravity field observations
Magma ascent mechanisms in the transition regime from solitary porosity waves to diapirism
Pragmatic solvers for 3D Stokes and elasticity problems with heterogeneous coefficients: evaluating modern incomplete LDLT preconditioners
Anita Thea Saraswati, Olivier de Viron, and Mioara Mandea
Solid Earth, 14, 1267–1287, https://doi.org/10.5194/se-14-1267-2023, https://doi.org/10.5194/se-14-1267-2023, 2023
Short summary
Short summary
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.
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
Short summary
Short summary
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.
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
Short summary
Short summary
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.
Cited articles
Alisic, L., Gurnis, M., Stadler, G., Burstedde, C., and Ghattas, O.: Multi-scale dynamics and rheology of mantle flow with plates, J. Geophys. Res., 117, B10402, https://doi.org/10.1029/2012JB009234, 2012.
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.
Baumgardner, J.: Three-Dimensional treatment of convective flow in the Earth's mantle, J. Stat. Phys., 39, 501–511, 1985.
Baumgardner, J. and Frederickson, P.: Isocahedral discretisation of the two-sphere, SIAM J. Numer. Anal., 22, 1107–1115, 1985.
Becker, T.: On the effect of temperature and strain-rate dependent viscosity on global mantle flow, net rotation, and plate-driving forces, Geophy. J. Int., 167, 943–957, 2006.
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.
Bull, A., McNamara, A., Becker, T., and Ritsema, J.: Global scale models of the mantle flow field predicted by synthetic tomography models, Phys. Earth. Planet. In., 182, 129–138, 2010.
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.
Bunge, H.-P., Richards, M., and Baumgardner, J.: Effect of depth-dependent viscosity on the planform of mantle convection, Nature, 379, 436–438, 1996.
Bunge, H.-P., Richards, M., and Baumgardner, J.: A sensitivity study of three-dimensional spherical mantle convection at 108 Rayleigh number: Effects of depth-dependent viscosity, heating mode, and endothermic phase change, J. Geophys. Res., 102, 11991–12007, 1997.
Bunge, H.-P., Richards, M., Lithgow-Bertelloni, C., Baumgardner, J., Grand, S., and Romanowicz, B.: Time scales and heterogeneous structure in geodynamic Earth models, Science, 280, 91–95, 1998.
Burstedde, C., Stadler, G., Alisic, L., Wilcox, L., Tan, E., Gurnis, M., and Ghattas, O.: Large-scale adaptive mantle convection simulation, Geophy. J. Int., 192, 889–906, 2013.
Busse, F.: Patterns of convection in spherical shells, J. Fluid Mech., 72, 67–85, 1975.
Choblet, G., Cadek, O., F.Couturier, and Dumoulin, C.: OEDIPUS: a new tool to study the dynamics of planetary interiors, Geophy. J. Int., 170, 9–30, 2007.
Christensen, U. and Harder, H.: 3-D convection with variable viscosity, Geophy. J. Int., 104, 213–226, 1991.
Crameri, F. and Tackley, P.: Spontaneous development of arcuate single-sided subduction in global 3-D mantle convection models with a free surface, J. Geophys. Res., 119, https://doi.org/10.1002/2014JB010939, 2014.
Crameri, F. and Tackley, P.: Subduction initiation from a stagnant lid and global overturn: new insights from numerical models with a free surface, Prog. Earth Planet. Sci., 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.
Dziewonski, A. and Anderson, D.: Preliminary reference Earth model, Phys. Earth. Planet. In., 25, 297–356, 1981.
Gerya, T. and Yuen, D.: Robust characteristics method for modelling multiphase visco-elasto-plastic thermo-mechanical problems, Phys. Earth. Planet. In., 163, 83–105, 2007.
Grandy, J.: Efficient Computation of Volume of Hexahedral Cells, Tech. Rep. UCRL-ID-128886, Lawrence Livermore National Laboratory, 1997.
Hall, R. and Spakman, W.: Mantle structure and tectonic history of SE Asia, Tectonophysics, 658, 14–45, 2015.
Hernlund, J. W. and Tackley, P. J.: Three-dimensional spherical shell convection at infinite Prandtl number using the “cubed sphere” method, Proceedings Second MIT Conference on Compurational Fluid and Solid Mechanics June 17–20 2003, Elsevier, 2003.
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.
Hüttig, C. and Stemmer, K.: The spiral grid: A new approach to discretize the sphere and its application to mantle convection, Geochem. Geophy. Geosy., 9, https://doi.org/10.1002/2014JB010939, 2008.
Kageyama, A. and Sato, T.: “Yin-Yang grid”: An overset grid in spherical geometry, Geochem. Geophy. Geosy., 5, Q09005, https://doi.org/10.1029/2004GC000734, 2004.
Kameyama, M., Kageyamab, A., and Sato, T.: Multigrid-based simulation code for mantle convection in spherical shell using Yin-Yang grid, Phys. Earth. Planet. In., 171, 19–32, 2008.
Kronbichler, M., Heister, T., and Bangerth, W.: High accuracy mantle convection simulation through modern numerical methods, Geophy. J. Int., 191, 12–29, 2012.
McNamara, A. and Zhong, S.: Thermochemical structures within a spherical mantle: Superplumes or piles?, J. Geophys. Res., 109, B07402, https://doi.org/10.1029/2003JB002847, 2004.
Oldham, D., Davies, J., and Phillips, T.: Generic polyhedron grid generation for solving partial differential equations on spherical surfaces, Comput. Geosci., 39, 11–17, 2012.
Pasyanos, M., Masters, T., Laske, G., and Ma, Z.: LITHO1.0: An updated crust and lithospheric model of the Earth, J. Geophys. Res., 119, B07402, https://doi.org/10.1002/2013JB010626, 2014.
Putman, W. and Lin, S.-J.: Finite-Volume transport on various cubed-sphere grids, J. Comp. Phys., 227, 55–78, 2007.
Ritsema, J., Deuss, A., van Heijst, H., and Woodhouse, J.: S40rts: a degree-40 shear- velocity model for the mantle from new rayleigh wave dispersio n, teleseismic traveltime and normal-mode splitting function measurements, Geophy. J. Int., 184, 1223–1236, 2011.
Ronchi, C., Iacono, R., and Paolucci, P.: The ”Cubed Sphere”: A New Method for the Solution of Partial Differential Equations in Spherical Geometry, J. Comp. Phys., 124, 93–114, 1996.
Sadourny, R.: Conservative Finite-Difference Approximations of the Primitive Equations on Quasi-Uniform Spherical Grids, Mon. Weather Rev., 100, 136–144, 1972.
Schubert, G., Turcotte, D., and Olson, P.: Mantle Convection in the Earth and Planets, Cambridge University Press, 2001.
Steinberger, B. and Calderwood, A.: Models of large-scale viscous flow in the Earth's mantle with constraints from mineral physics and surface observations, Geophy. J. Int., 167, 1461–1481, 2006.
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.: Mathematical modeling and numerical simulation of Earth's mantle convection, Mathematical modeling and numerical simulation in continuum mechanics, Lect. Notes Comp. Sci., 19, 219–231, 2002.
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.: Analytical solution for viscous incompressible Stokes flow in a spherical shell, Solid Earth, 8, 1181–1191, https://doi.org/10.5194/se-8-1181-2017, 2017.
Turcotte, D. and Schubert, G.: Geodynamics, 2nd edition, Cambridge, 2012.
van der Meer, D., van Hinsbergen, D., and Spakman, W.: Atlas of the Underworld: slab remnants in the mantle, their sinking history, and a new outlook on lower mantle viscosity, Tectonophysics, 723, 309–448, https://doi.org/10.1016/j.tecto.2017.10.004, 2017.
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 Keken, P., Hauri, E., and Ballentine, C.: Mantle mixing: the generation, preservation and destruction of chemical heterogeneity, Annu. Rev. Earth Sci., 30, 493–525, 2002.
Weller, M. and Lenardic, A.: The energetics and convective vigor of mixed-mode heating: Velocity scalings and implications for the tectonics of exoplanets, Geophys. Res. Lett., 43, https://doi.org/10.1002/2016GL069927, 2016.
Weller, M., Lenardic, A., and Moore, W.: Scaling relationships and physics for mixed heating convection in planetary interiors: Isoviscous spherical shells, J. Geophys. Res., 121, https://doi.org/10.1002/2016JB013247, 2016.
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.
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 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.
I present the GHOST (Geoscientific Hollow Sphere Tessellation) software which allows for the...