Non classé Numerical volcanology

Numerical volcanology

The volcanology team has numerical simulation tools, some of which were developed in the laboratory: the VolcFlow code for modelling volcanic flows, deformation models and magma transfers using boundary elements and fictitious domains (DefVolc). This activity is partly based on the computing resources of the UCA’s mesocentre and the platform for remote sensing.

  • Contact : Karim Kelfoun

    Simulations of volcanic flows: debris avalanches, pyroclastic flows, lahars


    Examples of simulations: debris avalanche from Socompa (Chile, left) and dilute pyroclastic flow (surge) from Merapi (Indonesia, right), performed with VolcFlow.

    Main publications:

    Gueugneau V., Kelfoun K., Druitt T. (2019). Investigation of surge-derived pyroclastic flow formation by numerical modelling of the 25 June 1997 dome collapse at Soufrière Hills Volcano, Montserrat. Bulletin of Volcanology vol.81, p.25, DOI:10.1007/s00445-019-1284-y .

    Benjamin J., Rosser N.J., Dunning S.A., Hardy R.J., Kelfoun K., Szczuciński W. (2018). Transferability of a calibrated numerical model of rock avalanche run‐out: Application to 20 rock avalanches on the Nuussuaq Peninsula, West Greenland. Earth Surface Processes and Landforms DOI:10.1002/esp.4469 .

    Gueugneau V., Kelfoun K., Roche O., Chupin L. (2017). Effects of pore pressure in pyroclastic flows: Numerical simulation and experimental validation. Geophysical Research Letters vol.44, DOI:10.1002/2017GL072591 .

    Kelfoun K. (2017). A two-layer depth-averaged model for both the dilute and the concentrated parts of pyroclastic currents. Journal of Geophysical Research – Solid Earth vol.122, DOI:10.1002/2017JB014013 .

    Kelfoun K., Gueugneau V., Komorowsk J.C., Aisyah N., Cholik N., Merciecca C. (2017). Simulation of block-and-ash flows and ash-cloud surges of the 2010 eruption of Merapi volcano with a two-layer model. Journal of Geophysical Research – Solid Earth vol.122, DOI:10.1002/2017JB013981 .

    Paris R., Coello Bravo J.J., Martin Gonzalez M.E., Kelfoun K., Nauret F. (2017). Explosive eruption, flank collapse and megatsunami at Tenerife ca. 170 ka. Nature Communications vol.8, p.15246, DOI:10.1038/ncomms15246 .

    zdemir Y., Akkaya I., Oyan U., Kelfoun K. (2016). A debris avalanche at Süphan stratovolcano (Turkey) and implications for hazard evaluation. Bulletin of Volcanology vol.78, p.9, DOI:10.1007/s00445-016-1007-6 .

    Kelfoun K.  and S. Vallejo Vargas (2016)  VolcFlow capabilities and potential development for the simulation of lava flows. Testing a GIS for damage and evacuation assessment during an effusive crisis. In: Harris, A., De Groeve, T., Garel, F., & Carn, S.A. (eds) Detecting, Modelling and Responding to Effusive Eruptions. Geological Society, London, Special Publications, 426.

    Kelfoun K., 2011. Suitability of simple rheological laws for the numerical simulation of dense pyroclastic flows and long-runout volcanic avalanches. Journal of Geophysical Research – Solid Earth B007622.

    Kelfoun K., P. Samaniego, P. Palacios, D. Barba, 2009. Testing the suitability of frictional behaviour for pyroclastic flow simulation by comparison with a well-constrained eruption at Tungurahua volcano (Ecuador). Bulletin of Volcanology, 71(9), 1057-1075.

    Kelfoun K. and T.H. Druitt, 2005. Numerical modelling of the emplacement of the 7500 BP Socompa rock avalanche, Chile. Journal of Geophysical Research B12202.


  • Lava flow modelling


    Contact : Oryaëlle Chevrel; Andrew Harris

    The advance of a lava flow can be modelled by following the evolution of the thermo-rheological properties of the molten rock. These rheological properties, defined by the viscosity and the yield strength, evolve with cooling and crystallisation during the emplacement of a flow. The FLOWGO model, developed by Harris and Rowland (2001), calculates the heat loss of a volume of lava flowing through a channel and derives these rheological properties and the lava flow rate for a given flow. PyFLOWGO is an updated version of FLOWGO written in Python 3, which is open-source and compatible with any operating system. This numerical code offers a variety of model choices for calculating lava viscosity as a function of crystal shape and bubble fraction.

    PyFLOWGO en association avec DOWNFLOW (Favalli et al. 2005) permet de modélisé la longueur d’une coulée de lave pour un débit donnée et en prenant en compte les caractéristiques pétrologiques de la lave. Cette méthode est utilisée pour estimer rapidement la distance qu’une coulée peux atteindre lors de crise effusive.



    Main publications:

    Chevrel O., Labroquère J., Harris A., Rowland S.K. (2018). PyFLOWGO: An open-source platform for simulation of channelized lava thermo-rheological properties. Computers and Geosciences vol.111, p.167-180, DOI:10.1016/j.cageo.2017.11.009 .

    Harris A.Chevrel O., Coppola D., Ramsey M.S., Hrysiewicz A.Thivet S., Villeneuve N., Favalli M., Peltier A., Kowalski P., Di Muro A., Froger J.L.Gurioli L. (2019). Validation of an integrated satellite-data-driven response to an effusive crisis: the April–May 2018 eruption of Piton de la Fournaise. Annals of Geophysics vol.61, DOI:10.4401/ag-7972.

    Ramsey MS, Chevrel O., Harris A., Coppola D. (2019) The Influence of Emissivity on the Thermo- Rheological Modeling of the Channelized Lava Flows at Tolbachik Volcano. Ann. Geophys. v.62,2, VO222.

    Harris A., Carn S., Dehn J., Del Negro C., Gudmundsson M.T., Cordonnier B., Barnie T., Chahi E., Calvari S., Catry T., De Groeve T., Coppola D., Davies A., Favalli M., Ferrucci F., Fujita E., Ganci G., Garel F., Huet P., Kauahikaua J., Kelfoun K., Lombardo V., Macedonio G., Pacheco J., Patrick M., Pergola N., Ramsey M., Rongo R., Sahy F., Smith K., Tarquini S., Thordarson T., Villeneuve N., Webley P., Wright R., Zaksek K. (2016). Conclusion: recommendations and findings of the RED SEED working group. p.567-648, Detecting, Modelling and Responding to Effusive Eruptions. Harris, A. J. L., De Groeve, T., Garel, F.&Carn, S. A. (eds), Geological Society, London, Special Publications, 426, The Geological Society of London (ed.), DOI:10.1144/SP426.11 .

    Rhety, M., Harris A., N. Villeneuve, Gurioli , E. Medard, Chevrel O., and P. Bachelery (2017), A comparison of cooling-limited and volume-limited flow systems: Examples from channels in the Piton de la Fournaise April 2007 lava-flow field, Geochem. Geophys. Geosyst., 18, doi:10.1002/ 2017GC006839.

    Harris A., Rowland, S.K., 2001. FLOWGO: a kinematic thermo-rheological model for lava flowing in a channel. Bull. Volcanol. 63, 20–44.


    Contact : Karim Kelfoun

    A modified version of VOLCFLOW can also simulate lava flows.

    Simulation of a lava flow, Reventador volcano, Ecuador.
    Consideration of cooling and associated rheological variations.


    Simulation of lava/river interaction. Tseax volcano, Canada (BC).
    The river imposes the flow directions of the lava by curving the flow. The simulation reproduces the thickness and extent of the flow from the late 17th century as well as the durations described in Aboriginal oral traditions.

    Principales publications:

    Kelfoun K., Vallejo Vargas S. (2016). VolcFlow capabilities and potential development for the simulation of lava flows. Testing a GIS for damage and evacuation assessment during an effusive crisis. vol.426, In : Harris, A., De Groeve, T., Garel, F., & Carn, S.A. (eds) Detecting, Modelling and Responding to Effusive Eruptions, Geological Society, London, Special Publications.

  • Contact : Raphael Paris

    Numerical modelling of eruptive and volcano-gravity tsunamis


    Simulation of a volcano side collapse and tsunami in Tenerife (Canary Islands). Computed with VolcFlow.


    Simulation of pyroclastic flows and tsunami from the Kolumbo submarine volcano (Aegean Sea). Computed with COMCOT-FIREWAVES.

    Simulation of explosion and tsunami in Karymsky Lake, Kamchatka. Computed with COMCOT-FIREWAVES.


    Simulation of a tsunami generated by the collapse of the Anak Krakatau (Indonesia). Computed with VolcFlow.


    Main publications:

    Paris, R., Ulvrova, M., Selva, J., Brizuela, B., Costa, A., Grezio, A., Lorito, S., Tonini, R., 2019. Probabilistic hazard analysis for tsunamis generated by subaqueous volcanic explosions in the Campi Flegrei caldera, Italy. Journal of Volcanology and Geothermal Research 379, 106-116.

    Paris, R., Ulvrova, M., 2019. Tsunamis generated by subaqueous volcanic explosions in Taal Caldera Lake, Philippines. Bulletin of Volcanology 81, 14.

    Ulvrova, M., Paris, R., Nomikou, P., Kelfoun, K., Leibrandt, S., Tappin, D.R., McCoy, F.W., 2016. Source of the tsunami generated by the 1650 AD eruption of Kolumbo submarine volcano (Aegean Sea, Greece). Journal of Volcanology and Geothermal Research 321, 125-139.

    Ulvrová, M., Paris, R., Kelfoun, K., Nomikou, P., 2014. Numerical simulations of tsunami generated by underwater volcanic explosions at Karymskoye Lake (Kamchatka, Russia) and Kolumbo volcano (Aegean Sea, Greece). Natural Hazards and Earth System Sciences 14, 401-412.

    Ontowirjo, B., Paris, R., Mano, A., 2013. Modeling of coastal erosion and sediment deposition during the 2004 Indian Ocean tsunami in Lhok Nga, Sumatra, Indonesia. Natural Hazards 65, 1967-1979.

    Giachetti, T., Paris, R., Kelfoun, K., Ontowirjo, B., 2012. Tsunami hazard related to a flank collapse of Anak Krakatau Volcano, Sunda Strait, Indonesia. Geological Society, London, Special Publications 361, 79-90.

    Paris, R., Giachetti, T., Chevalier, J., Guillou, H., Frank, N., 2011. Tsunami deposits in Santiago Island (Cape Verde archipelago) as possible evidence of a massive flank failure of Fogo volcano. Sedimentary Geology 239, 129-145.

    Giachetti, T., Paris, R., Kelfoun, K., Pérez Torrado, F.J., 2011. Numerical modelling of the tsunami triggered by the Güìmar debris avalanche, Tenerife (Canary Islands): comparison with field-based data. Marine Geology 284, 189-202.

    Kelfoun, K., Giachetti, T., Labazuy, P., 2010. Landslide-generated tsunamis at Reunion Island. Journal of Geophysical Research, F04012.

    Torsvik, T., Paris, R., Didenkulova, I., Pelinovsky, E., Belousov, A., Belousova, M., 2010. Numerical simulation of explosive tsunami wave generation and propagation in Karymskoye Lake, Russia. Natural Hazards and Earth System Sciences 10 (11), 2359-2369.

  • Inverse modelling of volcano deformation

    Contact : Valérie Cayol

    In order to monitor magma transfers and determine their influence on the stability of volcanic edifices, we analyse volcano deformations, measured by radar interferometry (OI2), by combining mixed boundary element, MBEM, (Cayol and Cornet, 1998) or fictitious domain (Bodart et al., 2015) simulations with inversions (Fukushima et al., 2015). Boundary element models are three-dimensional and assume an elastic and homogeneous rock medium. These models take into account the topography, and all kinds of sources, whether reservoir or fractures (faults or magma intrusions). For the consideration of fractures located in heterogeneous media, we are currently developing a finite element method based on a fictitious domain approach, in collaboration with F. Dabaghi (post-doc CNES 2019-) and O. Bodart from the Camille Jourdan Institute, J. Koko from LIMOS.

    Modelling example: inverse models obtained by DefVolc from ASAR interferograms for the May 2016 Piton de la Founaise eruption (adapted from Smittarelllo et al., JGR, 2019).

    Two videos present DefVolc. The first one presents the web interface and the second one presents the pre- and post-processor.

    To obtain an account in order to run your on-demand calculations on the mesocentre clusters, please contact me at

    Main publications using DefVolc or mixed boundary elements, MBEM (publications not involving LMV researchers are also indicated):

    1. Shreve T., R. Grandin, D. Smittarello, V. Cayol, V. Pinel, Y. Morishita, What triggers caldera ring-fault subsidence at Ambrym volcano? Insights from the 2015 dike intrusion and eruption, in revisions for Journal of Geophysical Research, Sept. 2020.
    2. Smittarello, D., V. Cayol, V. Pinel, J.L. Froger, A. Peltier, Q. Dumont, Combining InSAR and GNSS to track magma transport at basaltic volcanoes, Invited publication at Remote sensing, 2019.
    3. Smittarello, D., Cayol, V., Pinel, V., Peltier, A., Froger, J‐L., & Ferrazzini, V. Magma propagation at Piton de la Fournaise from joint inversion of InSAR and GNSS. Journal of Geophysical Research, 124, 1361– 1387,, 2019.
    4. Conway, S., Wauthier, C., Fukushima, Y., & Poland, M. A retrospective look at the February 1993 east rift zone intrusion at Kīlauea volcano, Hawaii. Journal of Volcanology and Geothermal Research, 358, 241-251, 2018.
    5. Tridon, M., V. Cayol, J−L. Froger, A. Augier, and P. Bachèlery, Inversion of coeval shear and normal stress of Piton de la Fournaise flank displacement, Journal of Geophysical Research:Solid Earth, doi: 10.1002/2016JB013330, 2016.
    6. Froger J. L., V. Cayol, V. Famin, The March-April 2007 eruption of Piton de la Fournaise as recorded by interferometric data, In: P. Bachèlery, Lénat, J.-F., Di Muro, A., Michon, L. (Editors), Active Volcanoes of the Southwest Indian Ocean: Piton de la Fournaise and Karthala. Active Volcanoes of the World. Springer-Verlag Berlin and Heidelberg, 428p., ISBN 978-3-642-31394-3, 2016.
    7. Wauthier, C., Smets, B., & Keir, D. Diking‐induced moderate‐magnitude earthquakes on a youthful rift border fault: The 2002 Nyiragongo‐Kalehe sequence, DR Congo. Geochemistry, Geophysics, Geosystems, 16(12), 4280-4291, 2015.
    8. Beauducel F., and D. Carbone, 2015. A strategy to explore the topography-driven distortions in the tilt field induced by a spherical pressure source. The case of Mt. Etna, Geophys. J. Int., 201(3), 1471-1481, doi: 10.1093/gji/ggv076
    9. Froger J.-L., V. Famin V., V. Cayol, A. Augier, L. Michon, J-F Lénat, Time-dependent displacements during and after the April 2007 eruption of Piton de la Fournaise, revealed by interferometric data, J. Volcanol. Geotherm. Res., 296, p.55-68, doi:10.1016/j.jvolgeores.2015.02.014, 2015.
    10. Wauthier, C., V. Cayol, B. Smets, N. d’Oreye, F. Kervyn, Magma pathways and their interactions inferred from InSAR and stress modeling at Nyamulagira Volcano, D.R. Congo, Remote Sensing, 7, 15179-15202, doi:10.3390/rs71115179, 2015.
    11. Remy, D., Froger, J. L., Perfettini, H., Bonvalot, S., Gabalda, G., Albino, F., Cayol, V., Legrand, D., De Saint Blanquat, M., Persistent uplift of the Lazufre volcanic complex (Central Andes): New insights from PCAIM inversion of InSAR time series and GPS data. Geochemistry, Geophysics, Geosystems, 15, DOI: 10.1002/2014GC005370, 2014.
    12. Bodart O., V. Cayol, S. Court, J. Koko (2014), Fictituous domain method for fracture models in elasticity, Proceedings of the 18th European Conference on Mathematics for Industry.
    13. V. Cayol, T. Catry, L. Michon, M. Chaput, V. Famin, O. Bodart, J. L. Froger, C. Romagnoli (2014), Sheared sheet intrusions as mechanism for lateral flank displacement on basaltic volcanoes: Application to Réunion Island volcanoes, J. Geophys. Res., 119, doi:10.1002/2014JB011139.
    14. Takada, Y. and Y. Fukushima, Volcanic subsidence triggered by the 2011 Tohoku earthquake in Japan, Nature Geoscience, 6, 2013
    15. Wauthier C., V. Cayol, M. Poland, F. Kervyn, N. d’Oreye, A. Hooper, S. Samsonov, K. Tiampo, B. Smets, Nyamulagira’s Magma Plumbing System Inferred from 15 Years of InSAR, Geol. Soc. London Special Publications: Remote Sensing of Volcanoes and Volcanic Processes: Integrating Observation and Modelling, 380, doi:10.1144/SP380.9, 2013.
    16. Wauthier, C., V. Cayol, F. Kervyn and N. d’Oreye, Magma sources involved in the 2002 Nyiragongo eruption, as inferred from an InSAR analysis, J. Geophys. Res., 117, doi:10.1029/2011JB008257, 2012.
    17. Fukushima, Y., V. Cayol, P. Durand, and D. Massonnet, Evolution of magma conduits during the 1998–2000 eruptions of Piton de la Fournaise volcano, Réunion Island, J. Geophys. Res., 115, B10204, doi:10.1029/2009JB007023, 2010.
    18. Fukushima, Y., Mori, J., Hashimoto, M., & Kano, Y. Subsidence associated with the LUSI mud eruption, East Java, investigated by SAR interferometry. Marine and Petroleum Geology, 26(9), 1740-1750, 2009
    19. Michon L., V. Cayol, L. Letourneur, A. Peltier, N. Villeneuve, T. Staudacher, Edifice growth, deformation and rift zone development in basaltic setting: insights from Piton de la Fournaise shield volcano (Réunion Island, Indian Ocean). J. Volcanol. Geotherm. Res., 184, 14–30, doi:10.1016/j.jvolgeores.2008.11.002, 2009.
    20. Peltier, A., Staudacher, T., Bachèlery, P., & Cayol, V.. Formation of the April 2007 caldera collapse at Piton de La Fournaise volcano: Insights from GPS data. Journal of Volcanology and Geothermal Research, 184(1-2), 152-163, 2009.
    21. Peltier A., V. Famin, P. Bachèlery, V. Cayol, Y. Fukushima, T. Staudacher, Cyclic magma storages and transfers at Piton de La Fournaise volcano (La Reunion hotspot) inferred from deformation and geochemical data, Earth. Planet. Sci. Lett., 270, 2-4, 180-188, doi:10.1016/j.epsl.2008.02.042, 2008.
    22. Peltier, A., Staudacher, T., & Bachèlery, P. (2007). Constraints on magma transfers and structures involved in the 2003 activity at Piton de La Fournaise from displacement data. Journal of Geophysical Research: Solid Earth, 112(B3), 2007.
    23. Peltier, A., Staudacher, T., Catherine, P., Ricard, L. P., Kowalski, P., & Bachèlery, P. Subtle precursors of volcanic eruptions at Piton de la Fournaise detected by extensometers. Geophysical research letters, 33(6) , 2006.
    24. Green, D. N., J. Neuberg, and V. Cayol, Shear stress along the conduit wall as a plausible source of tilt at Soufrière Hills volcano, Montserrat, Geophys. Res. Lett., 33, L10306, doi:10.1029/2006GL025890, 2006.
    25. Fukushima, Y., Cayol, V., & Durand, P. . Finding realistic dike models from interferometric synthetic aperture radar data: The February 2000 eruption at Piton de la Fournaise. Journal of Geophysical Research – Solid Earth 110(B3), 2005
    26. Beauducel, F., G. De Natale, F. Obrizzo, and F. Pingue. 3-D modelling of Campi Flegrei ground deformations: Role of caldera boundary discontinuities. Pure Appl. Geophys., 161:7, 1329-1344, 2004
    27. Froger, J. L., Fukushima, Y., Briole, P., Staudacher, T., Souriot, T., & Villeneuve, N. The deformation field of the August 2003 eruption at Piton de la Fournaise, Reunion Island, mapped by ASAR interferometry. Geophysical research letters 31 (14), 2004.
    28. Dieterich J., V. Cayol, and P. Okubo, Stress Changes Before and During the Pu`u `O`o-Kupaianaha Eruption, U.S. Geological Survey Prof. Paper, 1676, 187-201, 2003. 26 citations
    29. Dieterich, J., V. Cayol et P. Okubo, The use of earthquake rate changes as a stress-meter at Kilauea volcano, Nature, 408, 457-460, 2000.
    30. Cayol, V., J. Dieterich., A. Okamura et A. Miklius, High Magma Storage Rates Before the 1983 Eruption of Kilauea, Hawaii, Science, 288, 2343-2346, 2000.
    31. Beauducel, F., F.H. Cornet, E. Suhanto, T. Duquesnoy, and M. Kasser. Constraints on magma flux from displacements data at Merapi volcano, Java. J. Geophys. Res., 105:B4, 8193-8204, 2000.
    32. Beauducel, F., P. Briole, and J.L. Froger. Volcano wide fringes in ERS SAR interferograms of Etna: Deformation or tropospheric effect? J. Geophys. Res., 105:B7, 16,391-16,402, 2000.
    33. Beauducel, F., and F.H. Cornet, 1999. Collection and three-dimensional modeling of GPS and tilt data at Merapi volcano, Java.J. Geophys. Res., 104:B1, 725-736, 1999.
    34. Cayol, V. and F.H. Cornet, Effect of Topography on the interpretation of the deformation field of prominent volcanoes – Application to Etna, Geophys. Res. Let., 25, 1979-1982, 1998.
    35. Cayol, V., & Cornet, F. H.. Three‐dimensional modeling of the 1983–1984 eruption at Piton de la Fournaise Volcano, Réunion Island. Journal of Geophysical Research , 103(B8), 18025-18037, 1998.
    36. Cayol, V., et F. H. Cornet, 3D Mixed Boundary Elements for Elastic Deformation Field Analysis, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 34, 275-287, 1997.
  • Contact : Julien Monteux

    Numerical modelling with COMSOL software

    Radar interferometry (InSAR) is revealing an increasing number of volcanic structures and complexes with large surface displacements, sustained over many years, which suggest deep magma storage. However, the interpretation of these displacements remains complex, and it is still not clear which displacements may precede an eruption and which are merely a small accumulation of magma. One of the puzzles to be solved is how magma accumulates in a region of the crust and how this accumulation of hot magma affects the rheology of the crust and deforms it over time. This question is at the heart of the ClerVolc project “Probing the mechanics governing the growth, evolution and eruption of large silicic magma bodies”, which started in spring 2016 with Nicolas Le Corvec’s postdoc. Using COMSOL Multiphysics and the Structural Mechanics module, the team is developing a numerical protocol to control COMSOL via Matlab using the Matlab Livelink module to simulate the growth of a magma body by intermittent sill accretion. The Heat Transfer module will then be incorporated to model the rheological evolution of the rocks around the sills and to determine the deformations generated at the surface over time as well as the breaking point of the system, i.e. if and when an eruption can take place.


    Sketch of a maar-diatreme eruption and formation of the magmatic plumbing system (from Le Corverc et al., 2018). a The proto-diatreme (aka excavation stage) and b developing diatreme (aka infilling stage). The colored arrows represent the orientation of the minimum compressional stress (σ3), the blue and red colors represent the differential tectonic stress, extensional and compressional, respectively.

    Another difficulty in interpreting InSAR measurements is the rapid accumulation of lava on the flanks of volcanic structures. This is the case at Piton de la Fournaise in Réunion. InSAR measurements show a significant displacement of the eastern flank since 2007 and thus the potential for a catastrophic flank collapse, as has already happened several times in its history. However, the repeated emplacement of lava on this flank for more than 20 years and its compaction following cooling contribute significantly to the displacements measured by InSAR, and it is difficult at the moment to distinguish between the different phenomena and to characterise precisely a possible global slip of the eastern flank. Alexis Hrysiewicz has precisely quatified the lava flows emitted since the early 1980s.

    Principales publications:

    Zorn EU, Le Corvec N, Varley NR, Salzer JT, Walter TR, Navarro-Ochoa C, Vargas-Bracamontes DM, Thiele ST and Arámbula Mendoza R (2019) Load Stress Controls on Directional Lava Dome Growth at Volcán de Colima, Mexico. Front. Earth Sci. 7:84. doi: 10.3389/feart.2019.00084

    Le Corvec N., McGovern P.J. (2018). The effect of ocean loading on the growth of basaltic ocean island volcanoes and their magmatic plumbing system. Frontiers in Earth Science DOI:10.3389/feart.2018.00119.

    Le Corvec N., Muirhead J.D., White J.D.L. (2018). Shallow magma diversions during explosive diatreme-forming eruptions. Nature Communications vol.9, p.1459, DOI:10.1038/s41467-018-03865-x.



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