Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-18T14:09:41.129Z Has data issue: false hasContentIssue false

12 - Inverse Problems in Lava Dynamics

from Part III - ‘Solid’ Earth Applications: From the Surface to the Core

Published online by Cambridge University Press:  20 June 2023

By
Alik Ismail-Zadeh ,
Alexander Korotkii ,
Oleg Melnik ,
Ilya Starodubtsev ,
Yulia Starodubtseva ,
Igor Tsepelev  and
Natalya Zeinalova
Edited by
Alik Ismail-Zadeh ,
Fabio Castelli ,
Dylan Jones  and
Sabrina Sanchez
Alik Ismail-Zadeh
Affiliation:
Karlsruhe Institute of Technology, Germany
Fabio Castelli
Affiliation:
Università degli Studi, Florence
Dylan Jones
Affiliation:
University of Toronto
Sabrina Sanchez
Affiliation:
Max Planck Institute for Solar System Research, Germany
Get access

Summary

Abstract: Lava flow and lava dome growth are two main manifestations of effusive volcanic eruptions. Less-viscous lava tends to flow long distances depending on slope topography, heat exchange with the surroundings, eruption rate, and the erupted magma rheology. When magma is highly viscous, its eruption on the surface results in a lava dome formation, and an occasional collapse of the dome may lead to a pyroclastic flow. In this chapter, we consider two models of lava dynamics: a lava flow model to determine the internal thermal state of the flow from its surface thermal observations, and a lava dome growth model to determine magma viscosity from the observed lava dome morphological shape. Both models belong to a set of inverse problems. In the first model, the lava thermal conditions at the surface (at the interface between lava and the air) are known from observations, but its internal thermal state is unknown. A variational (adjoint) assimilation method is used to propagate the temperature and heat flow inferred from surface measurements into the interior of the lava flow. In the second model, the lava dome viscosity is estimated based on a comparison between the observed and simulated morphological shapes of lava dome shapes using computer vision techniques.

Keywords

computer visioncrystal contenteffusive eruptionsheat flowinverse problemlava flowlava domemorphologyvariational assimilationviscosity
Type
Chapter
Information
Applications of Data Assimilation and Inverse Problems in the Earth Sciences , pp. 196 - 208
Publisher: Cambridge University Press
Print publication year: 2023

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Branca, S., De Beni, E., and Proietti, C. (2013). The large and destructive 1669 AD eruption at Etna volcano: Reconstruction of the lava flow field evolution and effusion rate trend. Bulletin of Volcanology, 75, 694. https://doi.org/10.1007/s00445-013-0694-5.Google Scholar
Bryant, E. (2005). Natural Hazards. Cambridge: Cambridge University Press.Google Scholar
Buttner, R., Zimanowski, B., Blumm, J., and Hagemann, L. (1998). Thermal conductivity of a volcanic rock material (olivine-melilinite) in the temperature range between 288 and 1470 K. Journal of Volcanology and Geothermal Research, 80, 293–302.Google Scholar
Calder, E. S., Lavallée, Y., Kendrick, J. E., and Bernstein, M. (2015). Lava dome eruptions. In Sigurdsson, H., Houghton, B, Rymer, H, Stix, J, and McNutt, S, eds., Encyclopedia of Volcanoes, 2nd ed. San Diego, CA: Academic Press, pp. 343–62.Google Scholar
Calvari, S., Spampinato, L., Lodato, L. et al. (2005). Chronology and complex volcanic processes during the 2002–2003 flank eruption at Stromboli volcano (Italy) reconstructed from direct observations and surveys with a handheld thermal camera. Journal of Geophysical Research, 110, B02201. https://doi.org/10.1029/2004JB003129.Google Scholar
Castruccio, A., and Contreras, M. A. (2016). The influence of effusion rate and rheology on lava flow dynamics and morphology: A case study from the 1971 and 1988–1990 eruptions at Villarrica and Lonquimay volcanoes, Southern Andes of Chile. Journal of Volcanology and Geothermal Research, 327, 469–83.Google Scholar
Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability. Oxford: Oxford University Press.Google Scholar
Chevrel, M. O., Platz, T., Hauber, E., Baratoux, D., Lavallée, Y., and Dingwell, D. B. (2013). Lava flow rheology: A comparison of morphological and petrological methods. Earth and Planetary Science Letters, 384, 109–20.Google Scholar
Christensen, U. R. (1992). An Eulerian technique for thermomechanical modeling of lithospheric extension. Journal of Geophysical Research, 97, 2015–36.Google Scholar
Cordonnier, B., Lev, E., and Garel, F. (2015). Benchmarking lava-flow models. In Harris, A. J. L., De Groeve, T., Garel, F., and Carn, S. A., eds., Detecting, Modelling and Responding to Effusive Eruptions, Special Publications, 426. London: Geological Society, pp. 425–45.Google Scholar
Costa, A., and Macedonio, G. (2005). Computational modeling of lava flows: A review. In Manga, M. and Ventura, G., eds., Kinematics and Dynamics of Lava Flows, Special Paper 396, Boulder, CO: Geological Society of America, pp. 209–18.Google Scholar
Costa, A., Caricchi, L., and Bagdassarov, N. (2009). A model for the rheology of particle-bearing suspensions and partially molten rocks. Geochemistry, Geophysics, Geosystems, 10, Q03010. https://doi.org/10.1029/2008Gc002138.Google Scholar
Cutter, S., Ismail-Zadeh, A., Alcántara-Ayala, I. et al. (2015). Global risk: Pool knowledge to stem losses from disasters. Nature, 522, 277–9.Google Scholar
Daag, A. S., Dolan, M. T., Laguerta, E. et al. (1996). Growth of a postclimactic lava dome at Pinatubo Volcano, July‒October 1992. In Newhall, C. and Punongbayan, R., eds., Fire and Mud: Eruptions and Lahars of Mount Pinatubo, Philippines. Seattle: University of Washington Press, pp. 647–64.Google Scholar
Dragoni, M. A. (1989). A dynamical model of lava flows cooling by radiation. Bulletin of Volcanology, 51, 88–95.Google Scholar
Flynn, L. P., Harris, A. J. L., and Wright, R. (2001). Improved identification of volcanic features using Landsat 7 ETM+. Remote Sensing of Environment, 78, 180–93.Google Scholar
Giordano, D., and Dingwell, D. B. (2003). Viscosity of hydrous Etna basalt: Implications for Plinian-style basaltic eruptions. Bulletin of Volcanology, 65, 8–14.Google Scholar
Griffiths, R. W. (2000). The dynamics of lava flows. Annual Review of Fluid Mechanics, 32, 477–518.Google Scholar
Harris, A. J. L., Flynn, L. P., Keszthelyi, L. et al. (1998). Calculation of lava effusion rates from Landsat TM data. Bulletin of Volcanology, 60, 52–71.Google Scholar
Harris, A. J. L., Flynn, L. P., Matias, O., Rose, W. I., and Cornejo, J. (2004). The evolution of an active silicic lava flow field: An ETM+ perspective. Journal of Volcanology and Geothermal Research, 135, 147–68.Google Scholar
Harris, A. J. L., Rose, W. I., and Flynn, L. P. (2003). Temporal trends in lava dome extrusion at Santiaguito 1922–2000. Bulletin of Volcanology, 65, 77–89.Google Scholar
Heap, M. J., Troll, V., Kushnir, A. R. L. et al. (2019). Hydrothermal alteration of andesitic lava domes can lead to explosive volcanic behaviour. Nature Communications, 10, 5063. https://doi.org/10.1038/s41467-019-13102-8.Google Scholar
Hidaka, M., Goto, A., Umino, S., and Fujita, E. (2005). VTFS project: Development of the lava flow simulation code LavaSIM with a model for three-dimensional convection, spreading, and solidification. Geochemistry, Geophysics, Geosystems, 6, Q07008. https://doi.org/10.1029/2004GC000869.Google Scholar
Ismail-Zadeh, A., and Tackley, P. (2010). Computational Methods for Geodynamics. Cambridge: Cambridge University Press.Google Scholar
Ismail-Zadeh, A., and Takeuchi, K. (2007). Preventive disaster management of extreme natural events. Natural Hazards, 42, 459–67.Google Scholar
Ismail-Zadeh, A., Korotkii, A., Schubert, G., and Tsepelev, I. (2007). Quasi-reversibility method for data assimilation in models of mantle dynamics. Geophysical Journal International, 170, 1381–98.Google Scholar
Ismail-Zadeh, A., Korotkii, A., and Tsepelev, I. (2016). Data-Driven Numerical Modeling in Geodynamics: Methods and Applications. Heidelberg: Springer.Google Scholar
Jeffrey, D., and Acrivos, A. (1976). The rheological properties of suspensions of rigid particles. AIChE Journal, 22, 417–32.Google Scholar
Kabanikhin, S. I. (2011). Inverse and Ill-Posed Problems: Theory and Applications. Berlin: De Gruyter.Google Scholar
Kelfoun, K., and Vargas, S. V. (2015). VolcFlow capabilities and potential development for the simulation of lava flows. In Harris, A. J. L., De Groeve, T., Farel, F., and Carn, S. A., eds., Detecting, Modelling and Responding to Effusive Eruptions, Special Publications 426. London: Geological Society, pp. 337–43.Google Scholar
Kelfoun, K., Santoso, A. B., Latchimy, T. et al. (2021). Growth and collapse of the 2018–2019 lava dome of Merapi volcano. Bulletin of Volcanology, 83, 8. https://doi.org/10.1007/s00445-020-01428-x.Google Scholar
Kilburn, C. R. J. (2000). Lava flow and flow fields. In Sigurdsson, H., ed., Encyclopedia of Volcanoes. San Diego, CA: Academic Press, pp.291–305.Google Scholar
Korotkii, A. I., and Kovtunov, D. A. (2006). Reconstruction of boundary regimes in an inverse problem of thermal convection of a high viscous fluid. Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 12(2), 88–97.Google Scholar
Korotkii, A. I., and Starodubtseva, Y. V. (2014). Direct and inverse problems for models of stationary reactive-convective-diffusive flow. Proceedings of the Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 20(3), 98–113.Google Scholar
Korotkii, A., Kovtunov, D., Ismail-Zadeh, A., Tsepelev, I., and Melnik, O. (2016). Quantitative reconstruction of thermal and dynamic characteristics of lava from surface thermal measurements. Geophysical Journal International, 205, 1767–79.Google Scholar
Ladyzhenskaya, O. A. (1969). The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach.Google Scholar
Lavallée, Y., Varley, N. R., Alatorre-Ibarguengoitia, M. A. et al. (2012). Magmatic architecture of dome building eruptions at Volcán de Colima, Mexico. Bulletin of Volcanology, 74, 249–60.Google Scholar
Lejeune, A., and Richet, P. (1995). Rheology of crystal-bearing silicate melts: An experimental study at high viscosity. Journal of Geophysical Research, 100, 4215–29.Google Scholar
Lions, J. L. (1971). Optimal Control of Systems Governed by Partial Differential Equations. Berlin: Springer.Google Scholar
Lombardo, V., Musacchio, M., and Buongiorno, M. F. (2012). Error analysis of subpixel lava temperature measurements using infrared remotely sensed data. Geophysical Journal International, 191, 112–25.Google Scholar
Loughlin, S. C., Sparks, S., Brown, S. K., Jenkins, S. F., and Vye-Brown, C., eds. (2015). Global Volcanic Hazards and Risk. Cambridge: Cambridge University Press.Google Scholar
Mardles, E. (1940). Viscosity of suspensions and the Einstein equation. Nature, 145, 970. https://doi.org/10.1038/145970a0.Google Scholar
Marsh, B. D. (1981). On the crystallinity, probability of occurrence, and rheology of lava and magma. Contributions to Mineralogy and Petrology, 78, 85–98.Google Scholar
Melnik, O., and Sparks, R. S. J. (1999). Nonlinear dynamics of lava dome extrusion. Nature, 402, 37–41.Google Scholar
Naimark, B. M., and Ismail-Zadeh, A. T. (1995). Numerical models of subsidence mechanism in intracratonic basin: Application to North American basins. Geophysical Journal International, 123, 149–60.Google Scholar
Naimark, B. M., Ismail-Zadeh, A. T., and Jacoby, W. R. (1998). Numerical approach to problems of gravitational instability of geostructures with advected material boundaries. Geophysical Journal International, 134, 473–83.Google Scholar
Nakada, S., Shimizu, H., and Ohta, K. (1999). Overview of the 1990‒1995 eruption at Unzen Volcano. Journal of Volcanology and Geothermal Research, 89, 1–22.Google Scholar
Nakada, S., Zaennudin, A., Yoshimoto, M. et al. (2019). Growth process of the lava dome/flow complex at Sinabung volcano during 2013‒2016. Journal of Volcanology and Geothermal Research, 382, 120–36.Google Scholar
Navon, I. M., Zou, X., Derber, J. and Sela, J. (1992). Variational data assimilation with an adiabatic version of the NMC spectral model. Monthly Weather Review, 120, 1433–46.Google Scholar
Papale, P., ed. (2014). Volcanic Hazards, Risks and Disasters. Amsterdam: Elsevier.Google Scholar
Patankar, S. V., and Spalding, D. B. (1972). A calculation procedure for heat and mass transfer in three-dimensional parabolic flows. International Journal of Heat and Mass Transfer, 15, 1787–806.Google Scholar
Poland, M. P., and Anderson, K. R. (2020). Partly cloudy with a chance of lava flows: Forecasting volcanic eruptions in the twenty‐first century. Journal of Geophysical Research, 125, e2018JB016974. https://doi.org/10.1029/2018JB016974.Google Scholar
Polak, E., and Ribière, G. (1969). Note on the convergence of methods of conjugate directions. Revue Francaise d’Informatique et de Recherche Operationnelle, 3(16), 35–43.Google Scholar
Rumpf, M. E., Lev, E. and Wysocki, R. (2018). The influence of topographic roughness on lava flow emplacement. Bulletin of Volcanology, 80, 63. https://doi.org/10.1007/s00445-018-1238-9.Google Scholar
Salomon, D. (2007). Data Compression: The Complete Reference. London: Springer.Google Scholar
Sheldrake, T. E., Sparks, R. S. J., Cashman, K. V., Wadge, G., and Aspinall, W. P. (2016). Similarities and differences in the historical records of lava dome-building volcanoes: Implications for understanding magmatic processes and eruption forecasting. Earth-Science Reviews, 160, 240–63.Google Scholar
Short, N. M., and Stuart, L. M. (1983). The Heat Capacity Mapping Mission (HCMM) Anthology. Washington, DC: NASA Scientific and Technical Information Branch.Google Scholar
Starodubtseva, Y., Starodubtsev, I., Ismail-Zadeh, A. et al. (2021). A method for magma viscosity assessment by lava dome morphology. Journal of Volcanology and Seismology, 15, 159–68. https://doi.org/10.1134/S0742046321030064.Google Scholar
Swanson, D. A., Dzurisin, D., Holcomb, R. T. et al. (1987). Growth of the lava dome at Mount St Helens, Washington, (USA) 1981‒1983. In Fink, J. H., ed., The Emplacement of Silicic Domes and Lava Flows, Special Paper 212. Boulder, CO: Geological Society of America, pp. 1–16.Google Scholar
Takeuchi, S. (2011). Preeruptive magma viscosity: An important measure of magma eruptibility. Journal of Geophysical Research, 116, B10201. https://doi.org/10.1029/2011JB008243.Google Scholar
Temam, R. (1977). Navier–Stokes Equations: Theory and Numerical Analysis. Amsterdam: North-Holland.Google Scholar
Tikhonov, A. N. (1963). Solution of incorrectly formulated problems and the regularization method, Soviet Mathematics Doklady 4, 1035–8.Google Scholar
Tikhonov, A. N., and Arsenin, V. Y. (1977). Solution of Ill-Posed Problems. Washington, DC: Winston.Google Scholar
Tikhonov, A. N., and Samarskii, A. A. (1990). Equations of Mathematical Physics. New York: Dover Publications.Google Scholar
Tsepelev, I., Ismail-Zadeh, A., Melnik, O., and Korotkii, A. (2016). Numerical modelling of fluid flow with rafts: An application to lava flows. Journal of Geodynamics, 97, 31–41.Google Scholar
Tsepelev, I., Ismail-Zadeh, A., Starodubtseva, Y., Korotkii, A., and Melnik, O. (2019). Crust development inferred from numerical models of lava flow and its surface thermal measurements. Annals of Geophysics, 62(2), VO226. https://doi.org/10.4401/ag-7745.Google Scholar
Tsepelev, I., Ismail-Zadeh, A., and Melnik, O. (2020). Lava dome morphology inferred from numerical modelling. Geophysical Journal International, 223(3), 1597–609.Google Scholar
Tsepelev, I., Ismail-Zadeh, A., and Melnik, O. (2021). Lava dome evolution at Volcán de Colima, México during 2013: Insights from numerical modeling. Journal of Volcanology and Seismology, 15, 491–501. https://doi.org/10.1134/S0742046321060117.Google Scholar
Turcotte, D. L., and Schubert, G. (2002). Geodynamics, 2nd ed. Cambridge: Cambridge University Press.Google Scholar
Voight, B., and Elsworth, D. (2000). Instability and collapse of hazardous gas-pressurized lava domes. Geophysical Research Letters, 27(1), 1–4.Google Scholar
Wadge, G., Robertson, R. E. A., and Voight, B., eds. (2014). The Eruption of Soufrière Hills Volcano, Montserrat, from 2000 to 2010. GSL Memoirs, vol. 39. London: Geological Society. https://doi.org/10.1144/M39.Google Scholar
Wang, Z., Bovik, A. C., Sheikh, H. R., and Simoncelli, E. P. (2004). Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing, 13(4), 600–12.Google Scholar
Walker, G. P. L. (1973). Lengths of lava flows. Philosophical Transactions of the Royal Society, 274, 107–18.Google Scholar
Watts, R. B., Herd, R. A., Sparks, R. S. J., and Young, S. R. (2002). Growth patterns and emplacement of the andesitic lava dome at Soufrière Hills Volcano, Montserrat. In Druitt, T. H., and Kokelaar, B. P., eds., The Eruption of Soufrière Hills Volcano, Montserrat, from 1995 to 1999. GLS Memoirs, vol. 21. London: Geological Society, pp. 115–52.Google Scholar
Wright, R., Garbeil, H., and Davies, A. G. (2010). Cooling rate of some active lavas determined using an orbital imaging spectrometer. Journal of Geophysical Research, 115, B06205. https://doi.org/10.1029/2009JB006536.Google Scholar
Wright, T. L., and Okamura, R. T. (1977). Cooling and crystallization of tholeiitic basalt, 1965 Makaopuhi lava lake, Hawaii. US Geological Survey Professional Paper 1004.Google Scholar
Zakšek, K., Hort, M., and Lorenz, E. (2015). Satellite and ground based thermal observation of the 2014 effusive eruption at Stromboli volcano. Remote Sensing, 7, 17190–211.Google Scholar
Zeinalova, N., Ismail-Zadeh, A., Melnik, O. E., Tsepelev, I., and Zobin, V. M. (2021). Lava dome morphology and viscosity inferred from data-driven numerical modeling of dome growth at Volcán de Colima, Mexico during 2007–2009. Frontiers in Earth Science, 9, 735914. https://doi.org/10.3389/feart.2021.735914.Google Scholar
Zobin, V. M., Arámbula, R., Bretón, M. et al. (2015). Dynamics of the January 2013–June 2014 explosive-effusive episode in the eruption of Volcán de Colima, México: Insights from seismic and video monitoring. Bulletin of Volcanology, 77, 31. https://doi.org/10.1007/s00445-015-0917-z.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×