Articles | Volume 15, issue 7
https://doi.org/10.5194/se-15-861-2024
© Author(s) 2024. 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-15-861-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Quantifying mantle mixing through configurational entropy
Erik van der Wiel
CORRESPONDING AUTHOR
Department of Earth Sciences, Utrecht University, Princetonlaan 8A, 3584 CB Utrecht, the Netherlands
Cedric Thieulot
Department of Earth Sciences, Utrecht University, Princetonlaan 8A, 3584 CB Utrecht, the Netherlands
Douwe J. J. van Hinsbergen
Department of Earth Sciences, Utrecht University, Princetonlaan 8A, 3584 CB Utrecht, the Netherlands
Related authors
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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.
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.
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
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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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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.
Derya Gürer, Douwe J. J. van Hinsbergen, Murat Özkaptan, Iverna Creton, Mathijs R. Koymans, Antonio Cascella, and Cornelis G. Langereis
Solid Earth, 9, 295–322, https://doi.org/10.5194/se-9-295-2018, https://doi.org/10.5194/se-9-295-2018, 2018
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Central and Eastern Anatolia (present-day Turkey) accommodated Africa–Eurasia convergence in Cenozoic times. As a result, the region underwent distributed deformation and rotation. We provide a paleomagnetic dataset from sedimentary basins and assess the timing and amount of rotations. The obtained rotation patterns together with known fault zones suggest that south-central Turkey represents a coherently counterclockwise-rotating domain.
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
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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.
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.
Michiel Baatsen, Douwe J. J. van Hinsbergen, Anna S. von der Heydt, Henk A. Dijkstra, Appy Sluijs, Hemmo A. Abels, and Peter K. Bijl
Clim. Past, 12, 1635–1644, https://doi.org/10.5194/cp-12-1635-2016, https://doi.org/10.5194/cp-12-1635-2016, 2016
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One of the major difficulties in modelling palaeoclimate is constricting the boundary conditions, causing significant discrepancies between different studies. Here, a new method is presented to automate much of the process of generating the necessary geographical reconstructions. The latter can be made using various rotational frameworks and topography/bathymetry input, allowing for easy inter-comparisons and the incorporation of the latest insights from geoscientific research.
G. Hoareau, B. Bomou, D. J. J. van Hinsbergen, N. Carry, D. Marquer, Y. Donnadieu, G. Le Hir, B. Vrielynck, and A.-V. Walter-Simonnet
Clim. Past, 11, 1751–1767, https://doi.org/10.5194/cp-11-1751-2015, https://doi.org/10.5194/cp-11-1751-2015, 2015
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The impact of Neo-Tethys closure on early Cenozoic warming has been tested. First, the volume of subducted sediments and the amount of CO2 emitted along the northern Tethys margin has been calculated. Second, corresponding pCO2 have been tested using the GEOCLIM model. Despite high CO2 production, maximum pCO2 values (750ppm) do not reach values inferred from proxies. Other cited sources of excess CO2 such as the NAIP are also below fluxes required by GEOCLIM to fit with proxy data.
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
D. J. J. van Hinsbergen, M. Mensink, C. G. Langereis, M. Maffione, L. Spalluto, M. Tropeano, and L. Sabato
Solid Earth, 5, 611–629, https://doi.org/10.5194/se-5-611-2014, https://doi.org/10.5194/se-5-611-2014, 2014
Related subject area
Subject area: Core and mantle structure and dynamics | Editorial team: Geodynamics and quantitative modelling | Discipline: Geodynamics
ECOMAN: an open-source package for geodynamic and seismological modelling of mechanical anisotropy
On the impact of true polar wander on heat flux patterns at the core–mantle boundary
Modeling liquid transport in the Earth's mantle as two-phase flow: effect of an enforced positive porosity on liquid flow and mass conservation
Transport mechanisms of hydrothermal convection in faulted tight sandstones
Influence of heterogeneous thermal conductivity on the long-term evolution of the lower-mantle thermochemical structure: implications for primordial reservoirs
On the choice of finite element for applications in geodynamics
Coupled dynamics and evolution of primordial and recycled heterogeneity in Earth's lower mantle
Comparing global seismic tomography models using varimax principal component analysis
Manuele Faccenda, Brandon P. VanderBeek, Albert de Montserrat, Jianfeng Yang, Francesco Rappisi, and Neil Ribe
Solid Earth, 15, 1241–1264, https://doi.org/10.5194/se-15-1241-2024, https://doi.org/10.5194/se-15-1241-2024, 2024
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The Earth's internal dynamics and structure can be well understood by combining seismological and geodynamic modelling with mineral physics, an approach that has been poorly adopted in the past. To this end we have developed ECOMAN, an open-source software package that is intended to overcome the computationally intensive nature of this multidisciplinary methodology and the lack of a dedicated and comprehensive computational framework.
Thomas Frasson, Stéphane Labrosse, Henri-Claude Nataf, Nicolas Coltice, and Nicolas Flament
Solid Earth, 15, 617–637, https://doi.org/10.5194/se-15-617-2024, https://doi.org/10.5194/se-15-617-2024, 2024
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Heat flux heterogeneities at the bottom of Earth's mantle play an important role in the dynamic of the underlying core. Here, we study how these heterogeneities are affected by the global rotation of the Earth, called true polar wander (TPW), which has to be considered to relate mantle dynamics with core dynamics. We find that TPW can greatly modify the large scales of heat flux heterogeneities, notably at short timescales. We provide representative maps of these heterogeneities.
Changyeol Lee, Nestor G. Cerpa, Dongwoo Han, and Ikuko Wada
Solid Earth, 15, 23–38, https://doi.org/10.5194/se-15-23-2024, https://doi.org/10.5194/se-15-23-2024, 2024
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Fluids and melts in the mantle are key to the Earth’s evolution. The main driving force for their transport is the compaction of the porous mantle. Numerically, the compaction equations can yield unphysical negative liquid fractions (porosity), and it is necessary to enforce positive porosity. However, the effect of such a treatment on liquid flow and mass conservation has not been quantified. We found that although mass conservation is affected, the liquid pathways are well resolved.
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.
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.
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
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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.
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.
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.
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Short summary
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.
Geodynamic models of mantle convection provide a powerful tool to study the structure and...