Articles | Volume 17, issue 24
https://doi.org/10.5194/gmd-17-9023-2024
© 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/gmd-17-9023-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Methods for assessment of models
| 
20 Dec 2024
Methods for assessment of models |
| 20 Dec 2024
| 20 Dec 2024
Reconciling surface deflections from simulations of global mantle convection
Conor P. B. O'Malley
Department of Earth Science and Engineering, Imperial College London, London, SW7 2BP, UK
now at: Cathie Group, 2–4 Hanover Square, Newcastle upon Tyne, NE1 3NP, UK
Gareth G. Roberts
CORRESPONDING AUTHOR
Department of Earth Science and Engineering, Imperial College London, London, SW7 2BP, UK
James Panton
School of Earth and Environmental Sciences, Cardiff University, Park Place, Cardiff, CF10 3AT, UK
Fred D. Richards
Department of Earth Science and Engineering, Imperial College London, London, SW7 2BP, UK
J. Huw Davies
School of Earth and Environmental Sciences, Cardiff University, Park Place, Cardiff, CF10 3AT, UK
Victoria M. Fernandes
Department of Earth Science and Engineering, Imperial College London, London, SW7 2BP, UK
now at: Section 4.6 Geomorphology, GFZ Potsdam, Telegrafenberg, 14473 Potsdam, Germany
Sia Ghelichkhan
Research School of Earth Sciences, Australian National University, 142 Mills Road, Acton, ACT 0200, Australia
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William Scott, Mark Hoggard, Thomas Duvernay, Sia Ghelichkhan, Angus Gibson, Dale Roberts, Stephan C. Kramer, and D. Rhodri Davies
EGUsphere, https://doi.org/10.5194/egusphere-2025-4168, https://doi.org/10.5194/egusphere-2025-4168, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
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Melting ice sheets drive solid Earth deformation and sea-level change on timescales of decades to thousands of years. Here, we present G-ADOPT, which models movement of the solid Earth in response to surface loads. It has flexibility in domain geometry, deformation mechanism parameterisation, and is scalable on high performance computers. Automatic derivation of adjoint sensitivity kernels also provides a means to assimilate historical and modern observations into future sea-level forecasts.
Gareth G. Roberts
Earth Surf. Dynam., 13, 563–570, https://doi.org/10.5194/esurf-13-563-2025, https://doi.org/10.5194/esurf-13-563-2025, 2025
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The use of new artificial intelligence (AI) techniques to learn how landscapes evolve is demonstrated. A few “snapshots” of an eroding landscape at different stages of its history provide enough information for AI to ascertain rules governing its evolution. Once the rules are known, predicting landscape evolution is extremely rapid and efficient, providing new tools to understand landscape change.
Matthew J. Morris and Gareth G. Roberts
EGUsphere, https://doi.org/10.5194/egusphere-2025-1953, https://doi.org/10.5194/egusphere-2025-1953, 2025
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We run many computer models that describe how landscapes evolve through time. We change how randomness (noise) is added to the models to explore how it affects the shapes and properties of the final landscape. We add different types of noise at the start, during, and at the end of models, aiming to mimic reality. The range of shapes and properties produced from different noises can be as large as ranges possibly caused by climate, but running many models can help with measuring this uncertainty.
Gwynfor T. Morgan, J. Huw Davies, Robert Myhill, and James Panton
Solid Earth, 16, 297–314, https://doi.org/10.5194/se-16-297-2025, https://doi.org/10.5194/se-16-297-2025, 2025
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Phase transitions can influence mantle convection, inhibiting or promoting vertical flow. We are motivated by two examples: the post-spinel reaction proceeding via akimotoite at cool temperatures and a curving post-garnet boundary. Some have suggested these could change mantle dynamics. We find this is unlikely for both reactions: the first due to the uniqueness of thermodynamic state and the second due to the low magnitude of the boundary’s slope in pressure–temperature space and density change.
Duo Zhang and J. Huw Davies
Solid Earth, 15, 1113–1132, https://doi.org/10.5194/se-15-1113-2024, https://doi.org/10.5194/se-15-1113-2024, 2024
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We numerically model the influence of an arc on back-arc extension. The arc is simulated by placing a hot region on the overriding plate. We investigate how plate ages and properties of the hot region affect back-arc extension and present regime diagrams illustrating the nature of back-arc extension for these models. We find that back-arc extension occurs not only in the hot region but also, surprisingly, away from it, and a hot region facilitates extension on the overriding plate.
Andrew Hollyday, Maureen E. Raymo, Jacqueline Austermann, Fred Richards, Mark Hoggard, and Alessio Rovere
Earth Surf. Dynam., 12, 883–905, https://doi.org/10.5194/esurf-12-883-2024, https://doi.org/10.5194/esurf-12-883-2024, 2024
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Sea level was significantly higher during the Pliocene epoch, around 3 million years ago. The present-day elevations of shorelines that formed in the past provide a data constraint on the extent of ice sheet melt and the global sea level response under warm Pliocene conditions. In this study, we identify 10 escarpments that formed from wave-cut erosion during Pliocene times and compare their elevations with model predictions of solid Earth deformation processes to estimate past sea level.
Sia Ghelichkhan, Angus Gibson, D. Rhodri Davies, Stephan C. Kramer, and David A. Ham
Geosci. Model Dev., 17, 5057–5086, https://doi.org/10.5194/gmd-17-5057-2024, https://doi.org/10.5194/gmd-17-5057-2024, 2024
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We introduce the Geoscientific ADjoint Optimisation PlaTform (G-ADOPT), designed for inverse modelling of Earth system processes, with an initial focus on mantle dynamics. G-ADOPT is built upon Firedrake, Dolfin-Adjoint and the Rapid Optimisation Library, which work together to optimise models using an adjoint method, aligning them with seismic and geologic datasets. We demonstrate G-ADOPT's ability to reconstruct mantle evolution and thus be a powerful tool in geosciences.
D. Rhodri Davies, Stephan C. Kramer, Sia Ghelichkhan, and Angus Gibson
Geosci. Model Dev., 15, 5127–5166, https://doi.org/10.5194/gmd-15-5127-2022, https://doi.org/10.5194/gmd-15-5127-2022, 2022
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Firedrake is a state-of-the-art system that automatically generates highly optimised code for simulating finite-element (FE) problems in geophysical fluid dynamics. It creates a separation of concerns between employing the FE method and implementing it. Here, we demonstrate the applicability and benefits of Firedrake for simulating geodynamical flows, with a focus on the slow creeping motion of Earth's mantle over geological timescales, which is ultimately the engine driving our dynamic Earth.
Cited articles
Al-Hajri, Y., White, N., and Fishwick, S.: Scales of transient convective support beneath Africa, Geology, 37, 883–886, https://doi.org/10.1130/G25703A.1, 2009. a
Bahadori, A., Holt, W. E., Feng, R., Austermann, J., Loughney, K. M., Salles, T., Moresi, L., Beucher, R., Lu, N., Flesch, L. M., Calvelage, C. M., Rasbury, E. T., Davis, D. M., Potochnik, A. R., Ward, W. B., Hatton, K., Haq, S. S. B., Smiley, T. M., Wooton, K. M., and Badgley, C.: Coupled influence of tectonics, climate, and surface processes on landscape evolution in southwestern North America, Nat. Commun., 13, 1–18, 2022. a
Ball, P. W., White, N. J., Maclennan, J., and Stephenson, S. N.: Global Influence of Mantle Temperature and Plate Thickness on Intraplate Volcanism, Nat. Commun., 12, 1–13, https://doi.org/10.1038/s41467-021-22323-9, 2021. a, b
Ball, P. W., Duvernay, T., and Davies, D. R.: A coupled geochemical–geodynamic approach for predicting mantle melting in space and time, Geochem. Geophy. Geosy., 23, 1–31, https://doi.org/10.1029/2022gc010421, 2022. a
Bangerth, W., Dannberg, J., Fraters, M., Gassmoeller, R., Glerum, A., Heister, T., Myhill, R., and Naliboff, J.: ASPECT v2.5.0, Zenodo [code], https://doi.org/10.5281/zenodo.8200213, 2023. a
Bauer, S., Huber, M., Ghelichkhan, S., Mohr, M., Rüde, U., and Wohlmuth, B.: Large-scale simulation of mantle convection based on a new matrix-free approach, J. Comput. Sci.-Neth, 31, 60–76, https://doi.org/10.1016/j.jocs.2018.12.006, 2019. a
Becker, T. W. and Boschi, L.: A comparison of tomographic and geodynamic mantle models, Geochem. Geophy. Geosy., 3, 1–48, https://doi.org/10.1029/2001GC000168, 2002. a
Biggin, A. J., Steinberger, B., Aubert, J., Suttie, N., Holme, R., Torsvik, T. H., Van Der Meer, D. G., and Van Hinsbergen, D. J.: Possible links between long-term geomagnetic variations and whole-mantle convection processes, Nat. Geosci., 5, 526–533, https://doi.org/10.1038/ngeo1521, 2012. a
Braun, J.: The many surface expressions of mantle dynamics, Nat. Geosci., 3, 825–833, https://doi.org/10.1038/ngeo1020, 2010. a
Bunge, H.-P. and Baumgardner, J. R.: Mantle convection modeling on parallel virtual machines, Comput. Phys., 9, 207–215, https://doi.org/10.1063/1.168525, 1995. a, b
Bunge, H.-P., Richards, M. A., and Baumgardner, J. R.: Mantle-circulation models with sequential data assimilation: Inferring present-day mantle structure from plate-motion histories, Philos. T. R. Soc. A, 360, 2545–2567, https://doi.org/10.1098/rsta.2002.1080, 2002. a
Bunge, H.-P., Hagelberg, C. R., and Travis, B. J.: Mantle circulation models with variational data assimilation: inferring past mantle flow and structure from plate motion histories and seismic tomography, Geophys. J. Int., 152, 280–301, https://doi.org/10.1046/j.1365-246X.2003.01948.x, 2003. a
Cao, Z. and Liu, L.: Origin of Three-Dimensional Crustal Stress Over the Conterminous United States, J. Geophys. Res.-Sol. Ea., 126, e2021JB022137, https://doi.org/10.1029/2021JB022137, 2021. a
Chang, C. and Liu, L.: Investigating the formation of the Cretaceous Western Interior Seaway using landscape evolution simulations, GSA Bulletin, 133, 347–361, https://doi.org/10.1130/B35653.1, 2021. a
Colli, L., Ghelichkhan, S., Bunge, H.-P., and Oeser, J.: Retrodictions of Mid Paleogene mantle flow and dynamic topography in the Atlantic region from compressible high resolution adjoint mantle convection models: Sensitivity to deep mantle viscosity and tomographic input model, Gondwana Res., 53, 252–272, https://doi.org/10.1016/j.gr.2017.04.027, 2018. a
Corrieu, V., Thoraval, C., and Ricard, Y.: Mantle dynamics and geoid Green functions, Geophys. J. Int., 120, 516–523, https://doi.org/10.1111/j.1365-246X.1995.tb01835.x, 1995. a, b
Craig, C. H. and McKenzie, D.: Surface deformation, gravity and the geoid from a three-dimensional convection model at low Rayleigh numbers, Earth Planet. Sc. Lett., 83, 123–136, https://doi.org/10.1016/0012-821X(87)90056-2, 1987. a
Crameri, F., Schmeling, H., Golabek, G. J., Duretz, T., Orendt, R., Buiter, S. J., May, D. A., Kaus, B. J., Gerya, T. V., and Tackley, P. J.: A comparison of numerical surface topography calculations in geodynamic modelling: An evaluation of the `sticky air' method, Geophys. J. Int., 189, 38–54, https://doi.org/10.1111/j.1365-246X.2012.05388.x, 2012. a
Czarnota, K., Hoggard, M. J., White, N., and Winterbourne, J.: Spatial and temporal patterns of Cenozoic dynamic topography around Australia, Geochem. Geophy. Geosy., 14, 634–658, https://doi.org/10.1029/2012GC004392, 2013. a
Dannberg, J., Eilon, Z., Faul, U., Gassmöller, R., Moulik, P., and Myhill, R.: The importance of grain size to mantle dynamics and seismological observations, Geochem. Geophy. Geosy., 18, 3034–3061, https://doi.org/10.1002/2017GC006944, 2017. a
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. a, b, c
Davies, D. R., Valentine, A. P., Kramer, S. C., Rawlinson, N., Hoggard, M. J., Eakin, C. M., and Wilson, C. R.: Earth's multi-scale topographic response to global mantle flow, Nat. Geosci., 12, 845–850, https://doi.org/10.1038/s41561-019-0441-4, 2019. a, b, c, d
Davies, D. R., Ghelichkhan, S., Hoggard, M. J., Valentine, A. P., and Richards, F. D.: Observations and Models of Dynamic Topography: Current Status and Future Directions, chap. 11, in: Dynamics of Plate Tectonics and Mantle Convection, edited by: Duarte, J., Elsevier, Amsterdam (Netherlands), Oxford (UK), Cambridge (MA, USA), https://doi.org/10.1016/B978-0-323-85733-8.00017-2, pp. 223–269, 2023. a, b
Fernandes, V. M. and Roberts, G. G.: Cretaceous to Recent net continental uplift from paleobiological data: Insights into sub-plate support, GSA Bulletin, 133, 1–20, https://doi.org/10.1130/b35739.1, 2021. a, b, c
Fernandes, V. M., Roberts, G. G., White, N., and Whittaker, A. C.: Continental-Scale Landscape Evolution: A History of North American Topography, J. Geophys. Res.-Earth, 124, 1–34, https://doi.org/10.1029/2018jf004979, 2019. a
Fernandes, V. M., Roberts, G. G., and Richards, F.: Testing Mantle Convection Simulations With Paleobiology and Other Stratigraphic Observations: Examples From Western North America, Geochem. Geophy. Geosy., 25, e2023GC011381, https://doi.org/10.1029/2023GC011381, 2024. a
Fichtner, A. and Villaseñor, A.: Crust and upper mantle of the western Mediterranean – Constraints from full-waveform inversion, Earth Planet. Sc. Lett., 428, 52–62, https://doi.org/10.1016/j.epsl.2015.07.038, 2015. a
Fichtner, A., Kennett, B. L. N., Igel, H., and Bunge, H.-P.: Full seismic waveform tomography for upper-mantle structure in the Australasian region using adjoint methods, Geophys. J. Int., 179, 1703–1725, https://doi.org/10.1111/j.1365-246X.2009.04368.x, 2009. a
Fichtner, A., Trampert, J., Cupillard, P., Saygin, E., Taymaz, T., Capdeville, Y., and Villaseñor, A.: Multiscale full waveform inversion, Geophys. J. Int., 194, 534–556, https://doi.org/10.1093/gji/ggt118, 2013. a
Flament, N.: Present-day dynamic topography and lower-mantle structure from palaeogeographically constrained mantle flow models, Geophys. J. Int., 216, 2158–2182, https://doi.org/10.1093/gji/ggy526, 2019. a, b
Flament, N., Gurnis, M., Williams, S., Seton, M., Skogseid, J., Heine, C., and Dietmar Müller, R.: Topographic asymmetry of the South Atlantic from global models of mantle flow and lithospheric stretching, Earth Planet. Sc. Lett., 387, 107–119, https://doi.org/10.1016/j.epsl.2013.11.017, 2014. a
Flament, N., Gurnis, M., Müller, R. D., Bower, D. J., and Husson, L.: Influence of subduction history on South American topography, Earth Planet. Sc. Lett., 430, 9–18, https://doi.org/10.1016/j.epsl.2015.08.006, 2015. a, b
Foley, S. F. and Fischer, T. P.: An essential role for continental rifts and lithosphere in the deep carbon cycle, Nat. Geosci., 10, 897–902, https://doi.org/10.1038/s41561-017-0002-7, 2017. a
Forte, A. M.: Constraints on Seismic Models from Other Disciplines – Implications for Mantle Dynamics and Composition, chap. 1.23, in: Seismology and the Structure of the Earth, edited by: Romanowicz, B. and Dziewonski, A., Elsevier B. V., Amsterdam, https://doi.org/10.1016/B978-044452748-6.00027-4, pp. 805–858, 2007. a, b, c
Forte, A. M. and Peltier, R.: Viscous Flow Models of Global Geophysical Observables 1. Forward Problems, J. Geophys. Res., 96, 20131–20159, https://doi.org/10.1029/91JB01709, 1991. a
Forte, A. M. and Peltier, W. R.: The Kinematics and Dynamics of Poloidal-Toroidal Coupling in Mantle Flow: The Importance of Surface Plates and Lateral Viscosity Variations, Adv. Geophys., 36, 1–119, https://doi.org/10.1016/S0065-2687(08)60537-3, 1994. a
Forte, A. M., Simmons, N. A., and Grand, S. P.: Constraints on Seismic Models from Other Disciplines – Constraints on 3-D Seismic Models from Global Geodynamic Observables: Implications for the Global Mantle Convective Flow, in: Treatise on Geophysics, Second Edition, vol. 1, Elsevier, https://doi.org/10.1016/B978-0-444-53802-4.00028-2, pp. 853–907, 2015. a
French, S. W. and Romanowicz, B.: Broad plumes rooted at the base of the Earth's mantle beneath major hotspots, Nature, 525, 95–99, https://doi.org/10.1038/nature14876, 2015. a
Galloway, W. E., Whiteaker, T. L., and Ganey-Curry, P.: History of Cenozoic North American drainage basin evolution, sediment yield, and accumulation in the Gulf of Mexico basin, Geosphere, 7, 938–973, https://doi.org/10.1130/GES00647.1, 2011. a
Gantmacher, F. R.: The Theory of Matrices, Chelsea Publishing Company, New York, ISBN 9780821813935, 1959. a
Ghelichkhan, S.: Propagator Matrix Code for Calculating Dynamic Topography (v0.0.1), Zenodo [code], https://doi.org/10.5281/zenodo.12696774, 2024. a
Ghelichkhan, S., Bunge, H.-P., and Oeser, J.: Global mantle flow retrodictions for the early Cenozoic using an adjoint method: Evolving dynamic topographies, deep mantle structures, flow trajectories and sublithospheric stresses, Geophys. J. Int., 226, 1432–1460, https://doi.org/10.1093/gji/ggab108, 2021. a, b, c, d, e, f, g, h
Ghosh, A. and Holt, W. E.: Plate Motions and Stresses from Global Dynamic Models, Science, 335, 838–843, https://doi.org/10.1126/science.1214209, 2012. a
Ghosh, A., Becker, T. W., and Zhong, S. J.: Effects of lateral viscosity variations on the geoid, Geophys. Res. Lett., 37, 2–7, https://doi.org/10.1029/2009GL040426, 2010. a
Glišović, P. and Forte, A. M.: A new back-and-forth iterative method for time-reversed convection modeling: Implications for the Cenozoic evolution of 3-D structure and dynamics of the mantle, J. Geophys. Res.-Sol. Ea., 121, 4067–4084, https://doi.org/10.1002/2016JB012841, 2016. a
Gunnell, Y. and Burke, K.: The African Erosion Surface: A Continental-Scale Synthesis of Geomorphology, Tectonics, and Environmental Change over the Past 180 Million Years, Memoir of the Geological Society of America, 201, 1–66, https://doi.org/10.1130/2008.1201, 2008. a
Gurnis, M., Mitrovica, J. X., Ritsema, J., and Van Heijst, H.-J.: Constraining mantle density structure using geological evidence of surface uplift rates: The case of the African Superplume, Geochem. Geophy. Geosy., 1, 1–35, https://doi.org/10.1029/1999GC000035, 2000. a
Hager, B. H.: Subducted Slabs and the Geoid: Constraints on Mantle Rheology and Flow, J. Geophys. Res., 89, 6003–6015, 1984. a
Hager, B. H. and Clayton, R. W.: Constraints on the Structure of Mantle Convection Using Seismic Observations, Flow Models, and the Geoid, chap. 9, in: Mantle Convection: Plate Tectonics and Global Dynamics, edited by Peltier, W. R., Gordon and Breach Science Publishers, New York, pp. 657–763, ISBN 9780677221205, 1989. a, b, c, d, e, f
Hager, B. H. and O'Connell, R. J.: A Simple Global Model of Plate Dynamics and Mantle Convection, J. Geophys. Res., 86, 4843–4867, https://doi.org/10.1029/JB086iB06p04843, 1981. a, b, c, d
Hager, B. H., Clayton, R. W., Richards, M. A., Comer, R. P., and Dziewonski, A. M.: Lower mantle heterogeneity, dynamic topography and the geoid, Nature, 313, 541–545, https://doi.org/10.1038/314752a0, 1985. a, b
Hazzard, J. A. N., Richards, F. D., Goes, S. D. B., and Roberts, G. G.: Probabilistic Assessment of Antarctic Thermomechanical Structure: Impacts on Ice Sheet Stability, EarthArXiv, https://doi.org/10.31223/X5C35R, 2022. a
Heister, T., Dannberg, J., Gassmöller, R., and Bangerth, W.: High accuracy mantle convection simulation through modern numerical methods – II: realistic models and problems, Geophys. J. Int., 210, 833–851, https://doi.org/10.1093/gji/ggx195, 2017. a
Hoggard, M. J., White, N., and Al-Attar, D.: Supplementary Information for “Global dynamic topography observations reveal limited influence of large-scale mantle flow”, Nat. Geosci., 9, 1–34, https://doi.org/10.1038/ngeo2709, 2016b. a
Hoggard, M. J., Austermann, J., Randel, C., and Stephenson, S.: Observational Estimates of Dynamic Topography Through Space and Time, chap. 15, in: Mantle Convection and Surface Expressions, edited by: Marquardt, H., Ballmer, M., Cottaar, S., and Konter, J., AGU, https://doi.org/10.1002/9781119528609.ch15, pp. 371–411, 2021. a, b, c, d, e
Jeans, J. H.: The Propagation of Earthquake Waves, P. Roy. Soc. Lond. A, 102, 554–574, 1923. a
Kramer, S. C., Davies, D. R., and Wilson, C. R.: Analytical solutions for mantle flow in cylindrical and spherical shells, Geosci. Model Dev., 14, 1899–1919, https://doi.org/10.5194/gmd-14-1899-2021, 2021. a
Lambeck, K., Smither, C., and Johnston, P.: Sea-level change, glacial rebound and mantle viscosity for northern Europe, Geophys. J. Int., 134, 102–144, https://doi.org/10.1046/j.1365-246X.1998.00541.x, 1998. a
Lau, H. C. P., Mitrovica, J. X., Davis, J. L., Tromp, J., Yang, H.-Y., and Al-Attar, D.: Tidal tomography constrains Earth's deep-mantle buoyancy, Nature, 551, 321–326, https://doi.org/10.1038/nature24452, 2017. a
Lees, M. E., Rudge, J. F., and McKenzie, D.: Gravity, topography, and melt generation rates from simple 3D models of mantle convection, Geochem. Geophy. Geosy., 21, 1–29, https://doi.org/10.1029/2019gc008809, 2020. a
Lekić, V. and Fischer, K. M.: Contrasting lithospheric signatures across the western United States revealed by Sp receiver functions, Earth Planet. Sc. Lett., 402, 90–98, https://doi.org/10.1016/j.epsl.2013.11.026, 2014. a
Liu, L. and Gurnis, M.: Simultaneous inversion of mantle properties and initial conditions using an adjoint of mantle convection, J. Geophys. Res.-Sol. Ea., 113, 1–17, https://doi.org/10.1029/2008jb005594, 2008. a
Liu, S. and King, S. D.: A benchmark study of incompressible Stokes flow in a 3-D spherical shell using ASPECT, Geophys. J. Int., 217, 650–667, https://doi.org/10.1093/gji/ggz036, 2019a. a, b
Liu, S. and King, S. D.: A benchmark study of incompressible Stokes flow in a 3-D spherical shell using ASPECT, Geophys. J. Int., 217, 650–667, https://doi.org/10.1093/gji/ggz036, 2019b. a
Lu, C., Forte, A. M., Simmons, N. A., Grand, S. P., Kajan, M. N., Lai, H., and Garnero, E. J.: The Sensitivity of Joint Inversions of Seismic and Geodynamic Data to Mantle Viscosity, Geochem. Geophy. Geosy., 21, 1–29, https://doi.org/10.1029/2019gc008648, 2020. a
McKenzie, D.: Surface deformation, gravity anomalies and convection, Geophys. J. Roy. Astr. S., 48, 211–238, https://doi.org/10.1111/j.1365-246X.1977.tb01297.x, 1977. a
McKenzie, D. P., Roberts, J. M., and Weiss, N. O.: Convection in the earth's mantle: Towards a numerical simulation, J. Fluid Mech., 62, 465–538, 1974. a
Merdith, A. S., Williams, S. E., Collins, A. S., Tetley, M. G., Mulder, J. A., Blades, M. L., Young, A., Armistead, S. E., Cannon, J., Zahirovic, S., and Müller, R. D.: Extending full-plate tectonic models into deep time: Linking the Neoproterozoic and the Phanerozoic, Earth-Sci. Rev., 214, 1–44, https://doi.org/10.1016/j.earscirev.2020.103477, 2021. a, b, c, d, e
Mitrovica, J. X. and Forte, A. M.: A new inference of mantle viscosity based upon joint inversion of convection and glacial isostatic adjustment data, Earth Planet. Sc. Lett., 225, 177–189, https://doi.org/10.1016/j.epsl.2004.06.005, 2004. a, b, c
Molnar, P., England, P. C., and Jones, C. H.: Mantle dynamics, isostasy, and the support of high terrain, J. Geophys. Res.-Sol. Ea., 120, 1932–1957, https://doi.org/10.1002/2014JB011724, 2015. a
Morris, M., Fernandes, V. M., and Roberts, G. G.: Extricating dynamic topography from subsidence patterns: Examples from Eastern North America's passive margin, Earth Planet. Sc. Lett., 530, 1–13, https://doi.org/10.1016/j.epsl.2019.115840, 2020. a
Moucha, R. and Forte, A. M.: Changes in African topography driven by mantle convection: supplementary information, Nat. Geosci., 4, 707–712, https://doi.org/10.1038/ngeo1235, 2011. a
Moucha, R., Forte, A. M., Mitrovica, J. X., and Daradich, A.: Lateral variations in mantle rheology: Implications for convection related surface observables and inferred viscosity models, Geophys. J. Int., 169, 113–135, https://doi.org/10.1111/j.1365-246X.2006.03225.x, 2007. a
Moucha, R., Forte, A. M., Mitrovica, J. X., Rowley, D. B., Quéré, S., Simmons, N. A., and Grand, S. P.: Dynamic topography and long-term sea-level variations: There is no such thing as a stable continental platform, Earth Planet. Sc. Lett., 271, 101–108, https://doi.org/10.1016/j.epsl.2008.03.056, 2008. a
O'Connell, R. J.: Pleistocene Glaciation and the Viscosity of the Lower Mantle, Geophys. J. Roy. Astr. S., 23, 299–327, https://doi.org/10.1111/j.1365-246X.1971.tb01823.x, 1971. a
O'Malley, C. P. B., White, N. J., Stephenson, S. N., and Roberts, G. G.: Large-Scale Tectonic Forcing of the African Landscape, J. Geophys. Res.-Earth, 126, 1–37, https://doi.org/10.1029/2021jf006345, 2021. a, b
Panasyuk, S. V., Hager, B. H., and Forte, A. M.: Understanding the effects of mantle compressibility on geoid kernels, Geophys. J. Int., 124, 121–133, https://doi.org/10.1111/j.1365-246X.1996.tb06357.x, 1996. a, b, c, d
Panton, J., Davies, J. H., and Myhill, R.: The Stability of Dense Oceanic Crust Near the Core-Mantle Boundary, J. Geophys. Res.-Sol. Ea., 128, 1–21, https://doi.org/10.1029/2022JB025610, 2023. a, b, c
Priestley, K. and McKenzie, D.: The relationship between shear wave velocity, temperature, attenuation and viscosity in the shallow part of the mantle, Earth Planet. Sc. Lett., 381, 78–91, https://doi.org/10.1016/j.epsl.2013.08.022, 2013. a, b
Ribe, N. M.: Analytical Approaches to Mantle Dynamics, Treatise on Geophysics, 7, 167–226, https://doi.org/10.1016/B978-044452748-6.00117-6, 2007. a, b
Ricard, Y.: Physics of Mantle Convection, Treatise on Geophysics, 7, 31–88, 2007. a
Richards, F. D., Hoggard, M. J., White, N., and Ghelichkhan, S.: Quantifying the relationship between short-wavelength dynamic topography and thermomechanical structure of the upper mantle using calibrated parameterization of anelasticity, J. Geophys. Res.-Sol. Ea., 125, 1–36, https://doi.org/10.1029/2019JB019062, 2020. a, b
Richards, F. D., Hoggard, M. J., Ghelichkhan, S., Koelemeijer, P., and Lau, H. C. P.: Geodynamic, geodetic, and seismic constraints favour deflated and dense-cored LLVPs, Earth Planet. Sc. Lett., 602, 1–13, https://doi.org/10.1016/j.epsl.2022.117964, 2023. a, b, c
Richards, M. A. and Hager, B. H.: Geoid Anomalies in a Dynamic Earth, J. Geophys. Res., 89, 5987–6002, https://doi.org/10.1029/JB089iB07p05987, 1984. a, b
Roberts, G., O'Malley, C., Panton, J., Richards, F., Davies, H., Milanez Fernandes, V., and Ghelichkhan, S.: 'Reconciling Surface Deflections From Simulations of Global Mantle Convection': Numerical model dataset, Zenodo [data set], https://doi.org/10.5281/zenodo.12704925, 2024. a
Salles, T., Flament, N., and Müller, D.: Influence of mantle flow on the drainage of eastern Australia since the Jurassic Period, Geochem. Geophy. Geosy., 18, 280–305, https://doi.org/10.1002/2016GC006617, 2017. a
Spasojevic, S. and Gurnis, M.: Sea level and vertical motion of continents from dynamic earth models since the Late Cretaceous, AAPG Bull., 96, 2037–2064, https://doi.org/10.1306/03261211121, 2012. a
Stanley, J. R., Braun, J., Baby, G., Guillocheau, F., Robin, C., Flowers, R. M., Brown, R., Wildman, M., and Beucher, R.: Constraining Plateau Uplift in Southern Africa by Combining Thermochronology, Sediment Flux, Topography, and Landscape Evolution Modeling, J. Geophys. Res.-Sol. Ea., 126, 1–34, https://doi.org/10.1029/2020JB021243, 2021. a, b
Steinberger, B.: Effects of latent heat release at phase boundaries on flow in the Earth's mantle, phase boundary topography and dynamic topography at the Earth's surface, Phys. Earth Planet. In., 164, 2–20, https://doi.org/10.1016/j.pepi.2007.04.021, 2007. a
Steinberger, B.: Topography caused by mantle density variations: Observation-based estimates and models derived from tomography and lithosphere thickness, Geophys. J. Int., 205, 604–621, https://doi.org/10.1093/gji/ggw040, 2016. a
Steinberger, B. and Antretter, M.: Conduit diameter and buoyant rising speed of mantle plumes: Implications for the motion of hot spots and shape of plume conduits, Geochem. Geophy. Geosy., 7, 1–25, https://doi.org/10.1029/2006GC001409, 2006. a
Steinberger, B. and Calderwood, A. R.: Models of large-scale viscous flow in the Earth's mantle with constraints from mineral physics and surface observations, Geophys. J. Int., 167, 1461–1481, https://doi.org/10.1111/j.1365-246X.2006.03131.x, 2006. a, b
Steinberger, B., Nelson, P. L., Grand, S. P., and Wang, W.: Yellowstone plume conduit tilt caused by large-scale mantle flow, Geochem. Geophy. Geosy., 20, 5896–5912, https://doi.org/10.1029/2019gc008490, 2019. a
Stephenson, S. N., White, N. J., Carter, A., Seward, D., Ball, P. W., and Klöcking, M.: Cenozoic Dynamic Topography of Madagascar, Geochem. Geophy. Geosy., 22, 1–38, https://doi.org/10.1029/2020gc009624, 2021. a
Tackley, P. J., Stevenson, D. J., Glatzmaier, G. A., and Schubert, G.: Effects of an endothermic phase transition at 670 km depth on spherical mantle convection, Nature, 361, 699–704, https://doi.org/10.1038/361699a0, 1993. a
Thoraval, C. and Richards, M. A.: The geoid constraint in global geodynamics: Viscosity structure, mantle heterogeneity models and boundary conditions, Geophys. J. Int., 131, 1–8, https://doi.org/10.1111/j.1365-246X.1997.tb00591.x, 1997. a, b
Thoraval, C., Machete, P., and Cazenave, A.: Influence of mantle compressibility and ocean warping on dynamical models of the geoid, Geophys. J. Int., 117, 566–573, https://doi.org/10.1111/j.1365-246X.1994.tb03954.x, 1994. a
Turcotte, D. L. and Schubert, G.: Geodynamics, 2nd edn., Cambridge University Press, Cambridge, ISBN 9780521186230, 2002. a
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. a
Wang, Y., Liu, L., and Zhou, Q.: Topography and Gravity Reveal Denser Cratonic Lithospheric Mantle Than Previously Thought, Geophys. Res. Lett., 49, e2021GL096844, https://doi.org/10.1029/2021GL096844, 2022. a, b, c, d
Wessel, P., Luis, J., Uieda, L., Scharroo, R., Wobbe, F., Smith, W. H. F., and Tian, D.: The Generic Mapping Tools Version 6, Geochem. Geophy. Geosy., 20, 1–9, https://doi.org/10.1029/2019gc008515, 2019. a
Wieczorek, M. A. and Meschede, M.: SHTools: Tools for Working with Spherical Harmonics, Geochem. Geophy. Geosy., 19, 1–19, https://doi.org/10.1029/2018GC007529, 2018. a
Zhong, S., Gurnis, M., and Hulbert, G.: Accurate determination of surface normal stress in viscous flow from a consistent boundary flux method, Phys. Earth Planet. In., 78, 1–8, https://doi.org/10.1016/0031-9201(93)90078-N, 1993. a
Zhou, Q. and Liu, L.: Topographic evolution of the western United States since the early Miocene, Earth Planet. Sc. Lett., 514, 1–12, https://doi.org/10.1016/j.epsl.2019.02.029, 2019. a
Zhou, Q., Liu, L., and Hu, J.: Western US volcanism due to intruding oceanic mantle driven by ancient Farallon slabs, Nat. Geosci., 11, 70–76, https://doi.org/10.1038/s41561-017-0035-y, 2018. a
Short summary
We wish to understand how the history of flowing rock within Earth's interior impacts deflection of its surface. Observations exist to address this problem, and mathematics and different computing tools can be used to predict histories of flow. We explore how modeling choices impact calculated vertical deflections. The sensitivity of vertical motions at Earth's surface to deep flow is assessed, demonstrating how surface observations can enlighten flow histories.
We wish to understand how the history of flowing rock within Earth's interior impacts deflection...
