Articles | Volume 19, issue 21
https://doi.org/10.5194/gmd-19-10447-2026
© Author(s) 2026. 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-19-10447-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Hybrid implicit–explicit XFEM simulation of injection-induced seismicity: resolving multi-scale rupture nucleation and dynamics
Mohammad Sabah
CORRESPONDING AUTHOR
Institute for Applied Geosciences, Technische Universität Berlin, 10587 Berlin, Germany
Center for Modeling of Coupled Subsurface Dynamics, Department of Mathematics, University of Bergen, 5020 Bergen, Norway
Mauro Cacace
GFZ Helmholtz Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
Inga Berre
Center for Modeling of Coupled Subsurface Dynamics, Department of Mathematics, University of Bergen, 5020 Bergen, Norway
Iman R. Kivi
Global Change Research Group (GCRG), Mediterranean Institute for Advanced Studies (IMEDEA-UIB-CSIC), 07190 Esporles, Spain
Hannes Hofmann
Institute for Applied Geosciences, Technische Universität Berlin, 10587 Berlin, Germany
GFZ Helmholtz Centre for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
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We develop a simplified model which describes the geological geometry of the Vendenheim site, the solid and fluid properties were adapted from studies in the area. We implement compute the hydrothermal flow with a temperature dependent density and viscosity in a porous medium, in order to verify if a hydrothermal convective system is compatible with known observations at the Vendenheim site, and to get a better idea of the initial conditions of a model for an induced seismicity model.
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Concepts of High-Temperature Aquifer Thermal Energy Storage (HT-ATES) are investigated for system application in the German Molasse Basin. We quantify via physics-based numerical modelling the system performance with respect to HT-ATES concept development and provide a predictive analysis of HT-ATES application in the Upper Jurassic reservoir. Results demonstrate a non-uniform layer-specific distribution of the thermal front propagation, while promising heat recovery efficiencies are predicted.
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We compute a realistic three-dimensional model of the temperatures down to 75 km deep within the Earth, below the Caribbean Sea and northwestern South America. Using this, we estimate at which rock temperatures past earthquakes nucleated in the region and find that they agree with those derived from laboratory experiments of rock friction. We also analyse how the thermal state of the system affects the spatial distribution of seismicity in this region.
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In times of worldwide energy transitions, an understanding of the subsurface is increasingly important to provide renewable energy sources such as geothermal energy. To validate our understanding of the subsurface we require data. However, the data are usually not distributed equally and introduce a potential misinterpretation of the subsurface. Therefore, in this study we investigate the influence of measurements on temperature distribution in the European Alps.
Cited articles
Alkhimenkov, Y., Khakimova, L., and Podladchikov, Y.: Stability of discrete schemes of Biot's poroelastic equations, Geophys. J. Int., 225, 354–377, 2021.
Bandis, S. C., Lumsden, A. C., and Barton, N. R.: Fundamentals of rock joint deformation, Int. J. Rock Mech. Min., 20, 249–268, https://doi.org/10.1016/0148-9062(83)90595-8, 1983.
Biot, M. A.: Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range, J. Acoust. Soc. Am., 28, 179–191, 1956.
Bommer, J. J.: Earthquake hazard and risk analysis for natural and induced seismicity: towards objective assessments in the face of uncertainty, B. Earthq. Eng., 20, 2825–3069, 2022.
Boyet, A., De Simone, S., Ge, S., and Vilarrasa, V.: Poroelastic stress relaxation, slip stress transfer and friction weakening controlled post-injection seismicity at the Basel Enhanced Geothermal System, Commun. Earth Environ., 4, 104, https://doi.org/10.1038/s43247-023-00764-y, 2023.
Cao, W., Durucan, S., Shi, J.-Q., Cai, W., Korre, A., and Ratouis, T.: Induced seismicity associated with geothermal fluids re-injection: Poroelastic stressing, thermoelastic stressing, or transient cooling-induced permeability enhancement?, Geothermics, 102, 102404, https://doi.org/10.1016/j.geothermics.2022.102404, 2022.
Cappa, F., Guglielmi, Y., Nussbaum, C., and Birkholzer, J.: On the Relationship Between Fault Permeability Increases, Induced Stress Perturbation, and the Growth of Aseismic Slip During Fluid Injection, Geophys. Res. Lett., 45, 11012–11020, https://doi.org/10.1029/2018GL080233, 2018.
Cerfontaine, B., Dieudonné, A.-C., Radu, J.-P., Collin, F., and Charlier, R.: 3D zero-thickness coupled interface finite element: Formulation and application, Comput. Geotech., 69, 124–140, 2015.
Cheng, Y., Liu, W., Xu, T., Zhang, Y., Zhang, X., Xing, Y., Feng, B., and Xia, Y.: Seismicity induced by geological CO2 storage: A review, Earth-Sci. Rev., 239, 104369, https://doi.org/10.1016/j.earscirev.2023.104369, 2023.
Cueto-Felgueroso, L., Vila, C., Santillán, D., and Mosquera, J. C.: Numerical Modeling of Injection-Induced Earthquakes Using Laboratory-Derived Friction Laws, Water Resour. Res., 54, 9833–9859, https://doi.org/10.1029/2017WR022363, 2018.
Damirchi, B. V., Bitencourt, L. A. G., Manzoli, O. L., and Dias-da-Costa, D.: Coupled hydro-mechanical modelling of saturated fractured porous media with unified embedded finite element discretisations, Comput. Methods Appl. Mech. Eng., 393, 114804, https://doi.org/10.1016/j.cma.2022.114804, 2022.
Day, S. M., Dalguer, L. A., Lapusta, N., and Liu, Y.: Comparison of finite difference and boundary integral solutions to three-dimensional spontaneous rupture, J. Geophys. Res.-Sol. Ea., 110, B12307, https://doi.org/10.1029/2005JB003813, 2005.
Dieterich, J. H.: Modeling of rock friction: 1. Experimental results and constitutive equations, J. Geophys. Res.-Sol. Ea., 84, 2161–2168, 1979.
Dolbow, J., Moës, N., and Belytschko, T.: Discontinuous enrichment in finite elements with a partition of unity method, Finite Elem. Anal. Des., 36, 235–260, 2000.
Erickson, B., Jiang, J., and Dunham, E.: SEAS Benchmark Problems BP3-QD and BP3-FD, Southern California Earthquake Center (SCEC), https://strike.scec.org/cvws/seas/ (last access: 30 October 2026), 2020.
Fries, T.-P. and Belytschko, T.: The extended/generalized finite element method: an overview of the method and its applications, Int. J. Numer. Meth. Eng., 84, 253–304, 2010.
Gerardi, G., Dublanchet, P., Jeannin, L., Kazantsev, A., Duboeuf, L., Ramadhan, I., Azis, H., Ganefianto, N., and Nugroho, I. A.: Geomechanical modelling of injection-induced seismicity: the case study of the Muara Laboh geothermal plant, Geophys. J. Int., 237, 818–837, https://doi.org/10.1093/gji/ggae084, 2024.
Grigoli, F., Cesca, S., Priolo, E., Rinaldi, A. P., Clinton, J. F., Stabile, T. A., Dost, B., Fernandez, M. G., Wiemer, S., and Dahm, T.: Current challenges in monitoring, discrimination, and management of induced seismicity related to underground industrial activities: A European perspective, Rev. Geophys., 55, 310–340, 2017.
Grigoratos, I., Savvaidis, A., and Rathje, E.: Distinguishing the causal factors of induced seismicity in the Delaware Basin: Hydraulic fracturing or wastewater disposal?, Seismol. Res. Lett., 93, 2640–2658, 2022.
Han, Z. and Younis, R. M.: Adaptive time-stepping to capture induced seismicity for unconventional reservoir exploration, Unconventional Resources Technology Conference, 13–15 June 2023, 361–371, https://doi.org/10.15530/urtec-2023-3862235, 2023.
Harris, R. A., Barall, M., Archuleta, R., Dunham, E., Aagaard, B., Ampuero, J.-P., Bhat, H., Cruz-Atienza, V., Dalguer, L., Dawson, P., Day, S., Duan, B., Ely, G., Kaneko, Y., Kase, Y., Lapusta, N., Liu, Y., Ma, S., Oglesby, D., Olsen, K., Pitarka, A., Song, S., and Templeton, E.: The SCEC/USGS dynamic earthquake rupture code verification exercise, Seismol. Res. Lett., 80, 119–126, https://doi.org/10.1785/gssrl.80.1.119, 2009.
Heimisson, E. R., Liu, S., Lapusta, N., and Rudnicki, J.: A Spectral Boundary-Integral Method for Faults and Fractures in a Poroelastic Solid: Simulations of a Rate-and-State Fault With Dilatancy, Compaction, and Fluid Injection, J. Geophys. Res.-Sol. Ea., 127, e2022JB024185, https://doi.org/10.1029/2022JB024185, 2022.
Hosseini, N., Paluszny, A., and Zimmerman, R. W.: Dynamics of Fluid-Driven Slip on a 3D Heterogeneous Fault With Rate-and-State Friction, J. Geophys. Res.-Sol. Ea., 130, e2025JB031221, https://doi.org/10.1029/2025JB031221, 2025.
Im, K. and Avouac, J.-P.: Maximum Magnitude of Induced Earthquakes in Rate and State Friction Framework, Seismol. Res. Lett., 96, 1654–1664, 2025.
Ito, S., Furui, K., and Tsusaka, K.: Analysis of Fluid-Injection-Induced Seismicity Using Dynamic Sliding Model with Rate-And State-Dependent Friction Law, in: SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, D021S013R008, https://doi.org/10.2118/214891-MS, 2023.
Ito, S., Furui, K., and Tsusaka, K.: Analysis of Fluid-Injection-Induced Seismicity Using a Dynamic Sliding Model Incorporating the Rate-and State-Dependent Friction Law, SPE J., 29, 3567–3583, 2024.
Jaeger, J. C., Cook, N. G., and Zimmerman, R.: Fundamentals of rock mechanics, John Wiley & Sons, ISBN 978-0-632-05759-7, 2009.
Jin, L. and Zoback, M. D.: Fully dynamic spontaneous rupture due to quasi-static pore pressure and poroelastic effects: An implicit nonlinear computational model of fluid-induced seismic events, J. Geophys. Res.-Sol. Ea., 123, 9430–9468, 2018.
Katsman, R. and Ben-Avraham, Z.: Modeling Reservoir-Induced Seismicity: A Dynamic Poro-Visco-Elasto-Plastic Earthquake Simulator With Spontaneous Dilatant Coseismic Rupture, Earth Space Sci., 12, e2024EA004029, https://doi.org/10.1029/2024EA004029, 2025.
Khoei, A. R.: Extended finite element method: theory and applications, John Wiley & Sons, Inc, Chichester, West Sussex, https://doi.org/10.1002/9781118869673, 2015.
Kivi, I. R., Boyet, A., Wu, H., Walter, L., Hanson-Hedgecock, S., Parisio, F., and Vilarrasa, V.: Global physics-based database of injection-induced seismicity, Earth Syst. Sci. Data, 15, 3163–3182, https://doi.org/10.5194/essd-15-3163-2023, 2023.
Kivi, I. R., Vilarrasa, V., Kim, K.-I., Yoo, H., and Min, K.-B.: On the role of poroelastic stressing and pore pressure diffusion in discrete fracture and fault system in triggering post-injection seismicity in enhanced geothermal systems, Int. J. Rock Mech. Min., 175, 105673, https://doi.org/10.1016/j.ijrmms.2024.105673, 2024.
Kontoe, S., Zdravkovic, L., Potts, D., and Menkiti, C.: On the relative merits of simple and advanced constitutive models in dynamic analysis of tunnels, Géotechnique, 61, 815–829, 2011.
Koutromanos, I.: Fundamentals of finite element analysis: Linear finite element analysis, John Wiley & Sons, ISBN 978-1-119-26008-0, 2018.
Lapusta, N. and Liu, Y.: Three-dimensional boundary integral modeling of spontaneous earthquake sequences and aseismic slip, J. Geophys. Res.-Sol. Ea., 114, B09303, https://doi.org/10.1029/2008JB005934, 2009.
Lapusta, N., Rice, J. R., Ben-Zion, Y., and Zheng, G.: Elastodynamic analysis for slow tectonic loading with spontaneous rupture episodes on faults with rate-and state-dependent friction, J. Geophys. Res.-Sol. Ea., 105, 23765–23789, 2000.
Liu, F. and Borja, R. I.: An extended finite element framework for slow-rate frictional faulting with bulk plasticity and variable friction, Int. J. Numer. Anal. Met., 33, 1535–1560, 2009.
Liu, F. and Borja, R. I.: Stabilized low-order finite elements for frictional contact with the extended finite element method, Comput. Methods Appl. Mech. Eng., 199, 2456–2471, https://doi.org/10.1016/j.cma.2010.03.030, 2010.
Liu, M. and Gorman, D. G.: Formulation of Rayleigh damping and its extensions, Comput. Struct., 57, 277–285, 1995.
Lysmer, J. and Kuhlemeyer, R. L.: Finite dynamic model for infinite media, J. Eng. Mech. Div.-ASCE, 95, 859–877, 1969.
Maddio, P. D., Sinatra, R., and Cammarata, A.: A novel 2D penalty formulation for frictionless contact, Multibody Syst. Dyn., 1–25, https://doi.org/10.1007/s11044-025-10119-4, 2025.
Moës, N., Dolbow, J., and Belytschko, T.: A finite element method for crack growth without remeshing, Int. J. Numer. Meth. Eng., 46, 131–150, 1999.
Newmark, N. M.: A method of computation for structural dynamics, J. Eng. Mech. Div., 85, 67–94, 1959.
Pampillon, P., Santillan, D., Mosquera, J. C., and Cueto-Felgueroso, L.: Dynamic and quasi-dynamic modeling of injection-induced earthquakes in poroelastic media, J. Geophys. Res.-Sol. Ea., 123, 5730–5759, 2018.
Riga, V. Y. and Turuntaev, S. B.: Induced Seismicity Modeling Based on Two-Parameter Rate-and-State Law, Izv. Phys. Solid Earth, 57, 627–643, https://doi.org/10.1134/S1069351321050153, 2021.
Romanet, P., Ampuero, J.-P., Cappa, F., Scuderi, M. M., and Chaillat, S.: Combined boundary element and finite volume methods for modelling fluid-induced seismicity in fault networks within low-permeability rocks, Geophys. J. Int., 243, ggaf377, https://doi.org/10.1093/gji/ggaf377, 2025.
Ruina, A.: Slip instability and state variable friction laws, J. Geophys. Res.-Sol. Ea., 88, 10359–10370, 1983.
Sabah, M.: Fully coupled poro-elastodynamic XFEM-based injection-induced seismicity simulator using hybrid time integration strategy, Zenodo [code, data set], https://doi.org/10.5281/zenodo.19220256, 2026.
Sabah, M., Hofmann, H., Yaghoubi, A., Arjmand, Y., and Dusseault, M. B.: Hydro-shearing and traffic light protocols in mitigating seismic risks: A fully-coupled poroelastic boundary integral modeling approach, J. Rock Mech. Geotech. Eng., 17, 5660–5682, https://doi.org/10.1016/j.jrmge.2024.11.060, 2025.
Sabah, M., Hofmann, H., Cacace, M., Jalali, M. R., and Kivi, I. R.: Modeling Injection-Induced Seismicity Using a Fully Coupled Poroviscoelasto-Dynamic Extended Finite Element Approach with Stabilized Contact and Rate-and-State Friction, Comput. Geotech., 191, 107803, https://doi.org/10.1016/j.compgeo.2025.107803, 2026.
Segura, J. M. and Carol, I.: Coupled HM analysis using zero-thickness interface elements with double nodes. Part I: Theoretical model, Int. J. Numer. Anal. Met., 32, 2083–2101, 2008.
Sun, W., Gu, Y. J., Liu, Y., Li, T., Wang, R., Wang, J., Harrington, R., Roth, M., Schultz, R., and Xu, G.: Rupture cascade initiated by wastewater disposal: Nucleation and domino effect of Canada's largest induced earthquake, Geophys. Res. Lett., 53, e2025GL118405, https://doi.org/10.1029/2025GL118405, 2026.
Templeton, D. C., Schoenball, M., Layland-Bachmann, C. E., Foxall, W., Guglielmi, Y., Kroll, K. A., Burghardt, J. A., Dilmore, R., and White, J. A.: A project lifetime approach to the management of induced seismicity risk at geologic carbon storage sites, Seismol. Res. Lett., 94, 113–122, https://doi.org/10.1785/0220210284, 2023.
Trutnevyte, E. and Ejderyan, O.: Managing geoenergy-induced seismicity with society, J. Risk Res., 21, 1287–1294, 2018.
Wang, H.: Theory of linear poroelasticity with applications to geomechanics and hydrogeology, Princeton University Press, ISBN 978-0-691-03746-2, 2000.
Zhou, W., Lanza, F., Grigoratos, I., Schultz, R., Cousse, J., Trutnevyte, E., Muntendam-Bos, A., and Wiemer, S.: Managing induced seismicity risks from enhanced geothermal systems: A good practice guideline, Rev. Geophys., 62, e2024RG000849, https://doi.org/10.1029/2024RG000849, 2024.
Zienkiewicz, O. C. and Shiomi, T.: Dynamic behaviour of saturated porous media; the generalized Biot formulation and its numerical solution, Int. J. Numer. Anal. Met., 8, 71–96, 1984.
Zimmerman, R. W. and Paluszny, A.: Fluid flow in fractured rocks, Wiley, Hoboken, NJ, Chichester, West Sussex, 272 pp., ISBN 978-1-119-24801-9, 2024.
Short summary
Injecting fluids underground for energy projects can trigger earthquakes. Predicting these events is difficult because underground pressure changes slowly, while faults can move in a fraction of a second. We developed a computer method that switches between two ways of calculating these processes. In our test, it reduced computing time by 62 % while giving similar estimates of earthquake size and total fault movement. Differences in the fastest movements show that further testing is needed.
Injecting fluids underground for energy projects can trigger earthquakes. Predicting these...
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