Articles | Volume 18, issue 18
https://doi.org/10.5194/gmd-18-6219-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/gmd-18-6219-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Models of buoyancy-driven dykes using continuum plasticity or fracture mechanics: a comparison
Department of Earth Sciences, University of Oxford, Oxford, UK
Timothy Davis
Department of Earth Sciences, University of Oxford, Oxford, UK
School of Earth Sciences, University of Bristol, Bristol, UK
Adina E. Pusok
Department of Earth Sciences, University of Oxford, Oxford, UK
Richard F. Katz
Department of Earth Sciences, University of Oxford, Oxford, UK
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Hanwen Zhang, Richard F. Katz, and Laura A. Stevens
The Cryosphere, 19, 2087–2103, https://doi.org/10.5194/tc-19-2087-2025, https://doi.org/10.5194/tc-19-2087-2025, 2025
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In Antarctica, supraglacial lakes often form near grounding lines due to surface melting. We model viscoelastic tidal flexure in these regions to assess its contribution to lake drainage via hydrofracturing. Results show that tidal flexure and lake-water pressure jointly control drainage near unconfined grounding lines. Sensitivity analysis indicates the importance of the Maxwell time of ice in modulating the tidal response.
Marianne Haseloff, Ian J. Hewitt, and Richard F. Katz
EGUsphere, https://doi.org/10.5194/egusphere-2025-204, https://doi.org/10.5194/egusphere-2025-204, 2025
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We combine models for marine ice sheets (which terminate in the ocean) and water flux at the ice-bed interface. The coupled system evolves dynamically due to a positive feedback between ice flow, heat dissipation at the ice stream bed, and basal lubrication. Our results show that depending on the hydraulic properties of the bed, distinct dynamic regimes can be identified. These regimes include steady streaming, hydraulically controlled surges, and thermally controlled oscillations.
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.
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.
Cited articles
Abbo, A. J. and Sloan, S. W.: A Smooth Hyperbolic Approximation to the Mohr–Coulomb Yield Criterion, Comput. Struct. 54, 427–441, https://doi.org/10.1016/0045-7949(94)00339-5, 1995. a
Abdullin, R., Melnik, O., Rust, A., Blundy, J., Lgotina, E., and Golovin, S.: Ascent of Volatile-Rich Felsic Magma in Dykes: A Numerical Model Applied to Deep-Sourced Porphyry Intrusions, Geophys. J. Int., 236, 1863–1876, https://doi.org/10.1093/gji/ggae027, 2024. a
Acocella, V., Ripepe, M., Rivalta, E., Peltier, A., Galetto, F., and Joseph, E.: Towards Scientific Forecasting of Magmatic Eruptions, Nat. Rev. Earth Environ. 5, 5–22, https://doi.org/10.1038/s43017-023-00492-z, 2024. a
Anderson, T. L.: Fracture Mechanics: Fundamentals and Applications, Fourth Edition, in: 4th Edn., CRC Press, Boca Raton, ISBN 978-1-315-37029-3, https://doi.org/10.1201/9781315370293, 2017. a, b, c
Bader, J., Zhu, W., Montési, L., Qi, C., Cordonnier, B., Kohlstedt, D., and Warren, J.: Effects of Stress-Driven Melt Segregation on Melt Orientation, Melt Connectivity and Anisotropic Permeability, J. Geophys. Res.-Solid, 129, e2023JB028065, https://doi.org/10.1029/2023JB028065, 2024. a, b
Balay, S., Abhyankar, S., Adams, M. F., Benson, S., Brown, J., Brune, P., Buschelman, K., Constantinescu, E., Dalcin, L., Dener, A., Eijkhout, V., Gropp, W. D., Hapla, V., Isaac, T., Jolivet, P., Karpeev, D., Kaushik, D., Knepley, M. G., Kong, F., Kruger, S., May, D. A., McInnes, L. C., Mills, R. T., Mitchell, L., Munson, T., Roman, J. E., Rupp, K., Sanan, P., Sarich, J., Smith, B. F., Zampini, S., Zhang, H., Zhang, H., and Zhang, J.: PETSc/TAO Users Manual, Tech. Rep. ANL-21/39 – Revision 3.17, Argonne National Laboratory, https://web.cels.anl.gov/projects/petsc/vault/petsc-3.17/docs/docs/index.html (last access: 6 September 2025), 2022a. a
Balay, S., Abhyankar, S., Adams, M. F., Benson, S., Brown, J., Brune, P., Buschelman, K., Constantinescu, E. M., Dalcin, L., Dener, A., Eijkhout, V., Gropp, W. D., Hapla, V., Isaac, T., Jolivet, P., Karpeev, D., Kaushik, D., Knepley, M. G., Kong, F., Kruger, S., May, D. A., McInnes, L. C., Mills, R. T., Mitchell, L., Munson, T., Roman, J. E., Rupp, K., Sanan, P., Sarich, J., Smith, B. F., Zampini, S., Zhang, H., Zhang, H., and Zhang, J.: PETSc Web page, PETSc, https://petsc.org/ (last access: 6 September 2025), 2022b. a
Batchelor, G. K.: An Introduction to Fluid Dynamics, Cambridge Mathematical Library, Cambridge University Press, Cambridge, ISBN 978-0-521-66396-0, https://doi.org/10.1017/CBO9780511800955, 2000. a
Bercovici, D., Ricard, Y., and Schubert, G.: A Two-Phase Model for Compaction and Damage: 1. General Theory, J. Geophys. Res.-Solid , 106, 8887–8906, https://doi.org/10.1029/2000JB900430, 2001. a
Bolchover, P. and Lister, J. R.: The Effect of Solidification on Fluid–Driven Fracture, with Application to Bladed Dykes, P. Roy. Soc. Lond. A, 455, 2389–2409, https://doi.org/10.1098/rspa.1999.0409, 1999. a
Brune, S., Kolawole, F., Olive, J.-A., Stamps, D. S., Buck, W. R., Buiter, S. J. H., Furman, T., and Shillington, D. J.: Geodynamics of Continental Rift Initiation and Evolution, Nat. Rev. Earth Environ., 4, 235–253, https://doi.org/10.1038/s43017-023-00391-3, 2023. a
Buck, W. R.: The Role of Magma in the Development of the Afro-Arabian Rift System, Geol. Soc. Lond. Spec. Publ., 259, 43–54, https://doi.org/10.1144/gsl.sp.2006.259.01.05, 2006. a
Burov, E. B.: Rheology and Strength of the Lithosphere, Mar. Petrol. Geol., 28, 1402–1443, https://doi.org/10.1016/j.marpetgeo.2011.05.008, 2011. a
Cai, Z. and Bercovici, D.: Two-Phase Damage Models of Magma-Fracturing, Earth Planet. Sc. Lett., 368, 1–8, https://doi.org/10.1016/j.epsl.2013.02.023, 2013. a
Carol, I., Prat, P. C., and López, C. M.: Normal/Shear Cracking Model: Application to Discrete Crack Analysis, J. Eng. Mech., 123, 765–773, https://doi.org/10.1061/(asce)0733-9399(1997)123:8(765), 1997. a, b
Cerpa, N. G., Guillaume, B., and Martinod, J.: The Interplay between Overriding Plate Kinematics, Slab Dip and Tectonics, Geophys. J. Int., 215, 1789–1802, https://doi.org/10.1093/gji/ggy365, 2018. a
Connolly, J. A. D. and Podladchikov, Y.: Compaction-Driven Fluid Flow in Viscoelastic Rock, Geodinam. Acta, 11, 55–84, https://doi.org/10.1080/09853111.1998.11105311, 1998. a
Crameri, F.: Scientific Colour Maps, Zenodo [data set], https://doi.org/10.5281/zenodo.1243862, 2021. a
Crameri, F., Shephard, G. E., and Heron, P. J.: The Misuse of Colour in Science Communication, Nat. Commun., 11, 5444, https://doi.org/10.1038/s41467-020-19160-7, 2020. a
Daines, M. J. and Kohlstedt, D. L.: Influence of Deformation on Melt Topology in Peridotites, J. Geophys. Res., 102, 10257–10271, https://doi.org/10.1029/97jb00393, 1997. a, b
Davis, T., Rivalta, E., and Dahm, T.: Critical Fluid Injection Volumes for Uncontrolled Fracture Ascent, Geophys. Res. Lett., 47, e2020GL087774, https://doi.org/10.1029/2020gl087774, 2020. a
Davis, T., Rivalta, E., Smittarello, D., and Katz, R. F.: Ascent Rates of 3-D Fractures Driven by a Finite Batch of Buoyant Fluid, J. Fluid Mech., 954, A12, https://doi.org/10.1017/jfm.2022.986, 2023. a, b
Delcamp, A., Troll, V. R., van Wyk de Vries, B., Carracedo, J. C., Petronis, M. S., Pérez-Torrado, F. J., and Deegan, F. M.: Dykes and Structures of the NE Rift of Tenerife, Canary Islands: A Record of Stabilisation and Destabilisation of Ocean Island Rift Zones, Bull. Volcanol., 74, 963–980, https://doi.org/10.1007/s00445-012-0577-1, 2012. a
Drymoni, K., Tibaldi, A., Bonali, F. L., and Mariotto, F. A. P.: Dyke to Sill Deflection in the Shallow Heterogeneous Crust during Glacier Retreat: Part I, Bull. Volcanol., 85, 73, https://doi.org/10.1007/s00445-023-01684-7, 2023. a
Duretz, T., Borst, R., and Yamato, P.: Modelling lithospheric deformation using a compressible visco-elasto-viscoplastic rheology and the effective viscosity approach, Geochem. Geophy. Geosy., 22, e2021GC009675, https://doi.org/10.1029/2021gc009675, 2021. a
Duretz, T., Räss, L., de Borst, R., and Hageman, T.: A Comparison of Plasticity Regularization Approaches for Geodynamic Modeling, Geochem. Geophy. Geosy., 24, e2022GC010675, https://doi.org/10.1029/2022GC010675, 2023. a, b
Fernández, C., de la Nuez, J., Casillas, R., and García Navarro, E.: Stress Fields Associated with the Growth of a Large Shield Volcano (La Palma, Canary Islands), Tectonics, 21, 13-1–13-18, https://doi.org/10.1029/2000TC900038, 2002. a
Fiske, R. S., Jackson, E. D., and Sutton, J.: Orientation and Growth of Hawaiian Volcanic Rifts: The Effect of Regional Structure and Gravitational Stresses, P. Roy. Soc. Lond. A, 329, 299–326, https://doi.org/10.1098/rspa.1972.0115, 1997. a
Griffith, A. A.: VI. The Phenomena of Rupture and Flow in Solids, Philos. T. Roy. Soc. Lond. A, 221, 163–198, https://doi.org/10.1098/rsta.1921.0006, 1921. a, b
Gudmundsson, A.: Toughness and Failure of Volcanic Edifices, Tectonophysics, 471, 27–35, https://doi.org/10.1016/j.tecto.2009.03.001, 2009. a
Gudmundsson, A. and Loetveit, I. F.: Dyke Emplacement in a Layered and Faulted Rift Zone, J. Volcanol. Geoth. Res., 144, 311–327, https://doi.org/10.1016/j.jvolgeores.2004.11.027, 2005. a
Katz, R. F., Jones, D. W. R., Rudge, J. F., and Keller, T.: Physics of melt extraction from the mantle: Speed and style, Annu. Rev. Earth Planet. Sci., 50, 507–540, 2022. a
Kaus, B. J. P. and Podladchikov, Y. Y.: Initiation of Localized Shear Zones in Viscoelastoplastic Rocks, J. Geophys. Res.-Solid, 111, B04412, https://doi.org/10.1029/2005JB003652, 2006. a
Kelemen, P. B., Hirth, G., Shimizu, N., Spiegelman, M., and Dick, H.: A review of melt migration processes in the adiabatically upwelling mantle beneath oceanic spreading ridges, Philos. T. Roy. Soc. Lond. A, 355, 283–318, 1997. a
Keller, T., May, D. A., and Kaus, B. J. P.: Numerical modelling of magma dynamics coupled to tectonic deformation of lithosphere and crust, Geophys. J. Int., 195, 1406–1442, https://doi.org/10.1093/gji/ggt306, 2013. a, b, c, d
Kiss, D., Moulas, E., Kaus, B. J. P., and Spang, A.: Decompression and Fracturing Caused by Magmatically Induced Thermal Stresses, J. Geophys. Res.-Solid, 128, e2022JB025341, https://doi.org/10.1029/2022JB025341, 2023. a
Kjøll, H. J., Galland, O., Labrousse, L., and Andersen, T. B.: Emplacement Mechanisms of a Dyke Swarm across the Brittle-Ductile Transition and the Geodynamic Implications for Magma-Rich Margins, Earth Planet. Sc. Lett., 518, 223–235, https://doi.org/10.1016/j.epsl.2019.04.016, 2019. a
Krieg, R. D. and Krieg, D. B.: Accuracies of Numerical Solution Methods for the Elastic-Perfectly Plastic Model, J. Press. Vessel Technol., 99, 510–515, https://doi.org/10.1115/1.3454568, 1977. a
Lang, P. S., Paluszny, A., Nejati, M., and Zimmerman, R. W.: Relationship Between the Orientation of Maximum Permeability and Intermediate Principal Stress in Fractured Rocks, Water Resour. Res., 54, 8734–8755, https://doi.org/10.1029/2018WR023189, 2018. a
Lei, Q., Latham, J.-P., and Tsang, C.-F.: The Use of Discrete Fracture Networks for Modelling Coupled Geomechanical and Hydrological Behaviour of Fractured Rocks, Comput. Geotech., 85, 151–176, https://doi.org/10.1016/j.compgeo.2016.12.024, 2017. a
Li, J. H., Zhang, L. M., Wang, Y., and Fredlund, D. G.: Permeability Tensor and Representative Elementary Volume of Saturated Cracked Soil, Can. Geotech. J., 46, 928–942, https://doi.org/10.1139/t09-037, 2009. a
Li, Y., Davis, T., Pusok, A., and Katz, R.: poroVEVP model with benchmark (v1.0.0), Zenodo [code], https://doi.org/10.5281/zenodo.14238175, 2024. a
Maccaferri, F., Rivalta, E., Keir, D., and Acocella, V.: Off-Rift Volcanism in Rift Zones Determined by Crustal Unloading, Nat. Geosci., 7, 297–300, https://doi.org/10.1038/ngeo2110, 2014. a, b, c, d
McGuire, W. J. and Pullen, A. D.: Location and Orientation of Eruptive Fissures and Feederdykes at Mount Etna; Influence of Gravitational and Regional Tectonic Stress Regimes, J. Volcanol. Geoth. Res., 38, 325–344, https://doi.org/10.1016/0377-0273(89)90046-2, 1989. a
McKenzie, D.: The Generation and Compaction of Partially Molten Rock, J. Petrol., 25, 713–765, https://doi.org/10.1093/petrology/25.3.713, 1984. a
McKenzie, D., McKenzie, J. M., and Saunders, R. S.: Dike Emplacement on Venus and on Earth, J. Geophys. Res.-Planets, 97, 15977–15990, https://doi.org/10.1029/92JE01559, 1992. a
McLeod, P. and Tait, S.: The Growth of Dykes from Magma Chambers, J. Volcanol. Geoth. Res., 92, 231–245, https://doi.org/10.1016/S0377-0273(99)00053-0, 1999. a
Medici, G., Ling, F., and Shang, J.: Review of Discrete Fracture Network Characterization for Geothermal Energy Extraction, Front. Earth Sci., 11, 1328397, https://doi.org/10.3389/feart.2023.1328397, 2023. a
Moresi, L., Dufour, F., and Mühlhaus, H.-B.: A Lagrangian Integration Point Finite Element Method for Large Deformation Modeling of Viscoelastic Geomaterials, J. Comput. Phys., 184, 476–497, https://doi.org/10.1016/s0021-9991(02)00031-1, 2003. a
Murrell, S. A. F.: The Theory of the Propagation of Elliptical Griffith Cracks under Various Conditions of Plane Strain or Plane Stress: Part I, Brit. J. Appl. Phys., 15, 1195–1210, https://doi.org/10.1088/0508-3443/15/10/308, 1964. a
Odé, H.: Mechanical analysis of the dike pattern of the Spanish Peaks Area, Colorado, GSA Bull., 68, 567–576, https://doi.org/10.1130/0016-7606(1957)68[567:MAOTDP]2.0.CO;2, 1957. a
Papanastasiou, P.: The Effective Fracture Toughness in Hydraulic Fracturing, Int. J. Fract., 96, 127–147, https://doi.org/10.1023/A:1018676212444, 1999. a
Passarelli, L., Rivalta, E., and Shuler, A.: Dike Intrusions during Rifting Episodes Obey Scaling Relationships Similar to Earthquakes, Sci. Rep., 4, 3886, https://doi.org/10.1038/srep03886, 2014. a
Pusok, A., May, D. A., Li, Y., and Katz, R.: apusok/FD-PDE: v1.0.0, Zenodo [code], https://doi.org/10.5281/zenodo.6900871, 2022a. a, b
Pusok, A. E., Katz, R. F., May, D. A., and Li, Y.: Chemical Heterogeneity, Convection and Asymmetry beneath Mid-Ocean Ridges, Geophys. J. Int., 231, 2055–2078, https://doi.org/10.1093/gji/ggac309, 2022b. a
Pusok, A. E., Li, Y., Davis, T., May, D. A., and Katz, R. F.: Inefficient Melt Transport Across a Weakened Lithosphere Led to Anomalous Rift Architecture in the Turkana Depression, Geophys. Res. Lett., 52, e2025GL115228, https://doi.org/10.1029/2025GL115228, 2025. a
Rees Jones, D. W., Katz, R. F., Tian, M., and Rudge, J. F.: Thermal Impact of Magmatism in Subduction Zones, Earth Planet. Sc. Lett., 481, 73–79, https://doi.org/10.1016/j.epsl.2017.10.015, 2018. a
Rivalta, E., Taisne, B., Bunger, A., and Katz, R.: A Review of Mechanical Models of Dike Propagation: Schools of Thought, Results and Future Directions, Tectonophysics, 638, 1–42, https://doi.org/10.1016/j.tecto.2014.10.003, 2015. a, b, c
Roper, S. M. and Lister, J. R.: Buoyancy-Driven Crack Propagation: The Limit of Large Fracture Toughness, J. Fluid Mech., 580, 359–380, https://doi.org/10.1017/S0022112007005472, 2007. a, b, c
Rubin, A. M.: Propagation of Magma-Filled Cracks, Annu. Rev. Earth Planet. Sc., 23, 287–336, https://doi.org/10.1146/annurev.ea.23.050195.001443, 1995. a
Schmeling, H., Marquart, G., Weinberg, R., and Wallner, H.: Modelling Melting and Melt Segregation by Two-Phase Flow: New Insights into the Dynamics of Magmatic Systems in the Continental Crust, Geophys. J. Int., 217, 422–450, https://doi.org/10.1093/gji/ggz029, 2019. a
Seltzer, C., Peč, M., Zimmerman, M. E., and Kohlstedt, D. L.: Melt Network Reorientation and Crystallographic Preferred Orientation Development in Sheared Partially Molten Rocks, Geochem. Geophy. Geosy., 24, e2023GC010927, https://doi.org/10.1029/2023GC010927, 2023. a
Sibson, R. H.: Structural Permeability of Fluid-Driven Fault-Fracture Meshes, J. Struct. Geol., 18, 1031–1042, https://doi.org/10.1016/0191-8141(96)00032-6, 1996. a
Sigmundsson, F., Parks, M., Geirsson, H., Hooper, A., Drouin, V., Vogfjörd, K. S., Ófeigsson, B. G., Greiner, S. H. M., Yang, Y., Lanzi, C., De Pascale, G. P.,J́onsdóttir, K., Hreinsdóttir, S., Tolpekin, V., Friðriksdóttir, H. M., Einarsson, P., and Barsotti, S.: Fracturing and Tectonic Stress Drive Ultrarapid Magma Flow into Dikes, Science, 383, 1228–1235, https://doi.org/10.1126/science.adn2838, 2024. a
Sim, S. J., Spiegelman, M., Stegman, D. R., and Wilson, C.: The Influence of Spreading Rate and Permeability on Melt Focusing beneath Mid-Ocean Ridges, Phys. Earth Planet. Inter., 304, 106486, https://doi.org/10.1016/j.pepi.2020.106486, 2020. a
Snow, D. T.: Anisotropie Permeability of Fractured Media, Water Resour. Res., 5, 1273–1289, https://doi.org/10.1029/wr005i006p01273, 1969. a, b, c
Spence, D. A. and Turcotte, D. L.: Buoyancy-Driven Magma Fracture: A Mechanism for Ascent through the Lithosphere and the Emplacement of Diamonds, J. Geophys. Res., 95, 5133, https://doi.org/10.1029/JB095iB04p05133, 1990. a
Taisne, B., Tait, S., and Jaupart, C.: Conditions for the Arrest of a Vertical Propagating Dyke, Bull. Volcanol., 73, 191–204, https://doi.org/10.1007/s00445-010-0440-1, 2011. a
Takei, Y.: Stress-induced Anisotropy of Partially Molten Rock Analogue Deformed under Quasi-static Loading Test, J. Geophys. Res., 115, B03204, https://doi.org/10.1029/2009jb006568, 2010. a, b
Taylor-West, J. and Katz, R. F.: Melt-Preferred Orientation, Anisotropic Permeability and Melt-Band Formation in a Deforming, Partially Molten Aggregate, Geophys. J. Int., 203, 1253–1262, https://doi.org/10.1093/gji/ggv372, 2015. a
Terzaghi, K.: Theoretical Soil Mechanics, John Wiley & Sons, Inc., https://doi.org/10.1002/9780470172766, 1943. a
Thiele, S. T., Cruden, A. R., Micklethwaite, S., Bunger, A. P., and Köpping, J.: Dyke Apertures Record Stress Accumulation during Sustained Volcanism, Sci. Rep., 10, 17335, https://doi.org/10.1038/s41598-020-74361-w, 2020. a
Weertman, J.: Theory of Water-Filled Crevasses in Glaciers Applied to Vertical Magma Transport beneath Oceanic Ridges, J. Geophys. Res., 76, 1171–1183, https://doi.org/10.1029/JB076i005p01171, 1971. a
Short summary
Magmatic dykes transport magma to the Earth's surface, sometimes causing eruptions. We advanced a model of dyking, treating it as plastic deformation in a porous medium, unlike the classic model that treats dykes as fractures in elastic solids. Comparing the two, we found the plastic model aligns with the fracture model in dyke speed and energy consumption, despite quantitative differences. This new method could be a powerful tool for understanding volcanic processes during tectonic activity.
Magmatic dykes transport magma to the Earth's surface, sometimes causing eruptions. We advanced...
Special issue