ANALYTICAL MODEL OF SMALL FLUCTUATIONS OF COMPRESSIBLE MAGMA WITH MAXWELL RHEOLOGY IN THE FEEDING SYSTEM OF A VOLCANO. PART 2. OSCILLATIONS OF VERTICAL VELOCITY

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Abstract

The analytical solution for vertical magma movements in a volcanic conduit within the occurrence of low-frequency volcanic seismic events is presented. Magma is described by Maxwell's compressible body model. When the density of the magmatic melt is disturbed, for example, when dense magma enters from deep layers or the melt degasses at a certain depth, density oscillations may occur in the channel as a reaction to this event. For the magma conduit of the simplest cylindrical shape, the magma density and two components of the velocity of movement are subject to oscillations. In this case, the vertical component of the velocity experiences forced oscillations, both under the influence of density oscillations and under the influence of the initiating disturbance. All these oscillations are harmonic damped oscillations, the damping coefficient of which is determined by the relaxation time of the magmatic melt, and the natural frequency depends on the physical characteristics of the magmatic melt and the geometric dimensions of the conduit. Melt density oscillations lead to periodic variations in the lithostatic pressure drop, which in turn causes vertical movements of the melt, the most amplitude along the axis of the magma conduit. The model is used to describe crater surface displacements observed on the surface of the Santiaguito volcano crater.

About the authors

A. A. Radionoff

Southern Mathematical Institute – the Affiliate of Vladikavkaz Scientific Center of Russian Academy of Sciences

Email: aar200772@mail.ru
ORCID iD: 0000-0002-6934-6873
SPIN-code: 5402-0548
Scopus Author ID: 8139101100
department of mathematical modeling, candidate of technical sciences 2006-2022

References

  1. Анфилогов В. Н., Быков В. Н., Осипов А. А. Силикатные расплавы. — Москва : Наука, 2005. — 357 с.
  2. Бармин А. А., Мельник О. Э., Скульский О. И. Модель стационарного неизотермического течения магмы в канале вулкана с учетом скольжения на границе // Вычислительная механика сплошных сред. — 2012. — Т. 5, № 2. — С. 354—358. — doi: 10.7242/1999-6691/2012.5.3.42.
  3. Лебедев Е. Б., Хитаров Н. И. Физические свойства магматических расплавов. — Москва : Наука, 1979. — 200 с.
  4. Персиков Э. С. Вязкость магматических расплавов. — Москва : Наука, 1984. — 159 с.
  5. Полянин А. Д. Справочник по линейным уравнениям математической физики. — Москва : Физико-математическая литература, 2001. — 576 с.
  6. Радионов А. А. О малых колебаниях магмы в питающей системе вулкана // Известия вузов. Северо-Кавказский регион. Естественные науки. — 2020. — 1 (205). — С. 78—84. — doi: 10.18522/1026-2237-2020-1-78-84.
  7. Радионов А. А. Аналитическая модель малых колебаний сжимаемой магмы с реологией Максвелла в питающей системе вулкана. Часть 1. Осцилляции плотности // Russian Journal of Earth Sciences. — 2023. — Т. 23. — ES2005. — doi: 10.2205/2023ES000845.
  8. Уткин И. С., Мельник О. Э. Динамика взрывной дегазации вулкана // Труды математического института им. В. А. Стеклова. — 2018. — Т. 300, № 01. — С. 190—196. — doi: 10.1134/s0371968518010156.
  9. Шакирова А. А., Фирстов П. П., Паровик Р. И. Феноменологическая модель генерации землетрясений сейсмического режима «Drumbeats», сопровождавших извержение вулкана Кизимен в 2011-2012 гг. // Вестник КРАУНЦ. Физико-математические науки. — 2020. — Т. 33, № 4. — С. 86—101. — doi: 10.26117/2079-6641-2020-33-4-86-101.
  10. Chouet B. A. Long-period volcano seismicity: its source and use in eruption forecasting // Nature. — 1996. — Vol. 380, no. 6572. — P. 309–316. — doi: 10.1038/380309a0.
  11. Crosson R. S., Bame D. A. A spherical source model for low frequency volcanic earthquakes // Journal of Geophysical Research: Solid Earth. — 1985. — Vol. 90, B12. — P. 10237–10247. — doi: 10.1029/JB090iB12p10237.
  12. Fujita E., Ida Y., Oikawa J. Eigen oscillation of a fluid sphere and source mechanism of harmonic volcanic tremor // Journal of Volcanology and Geothermal Research. — 1995. — Vol. 69, no. 3/4. — P. 365–378. — doi: 10.1016/0377-0273(95)00027-5.
  13. Girona T., Caudron C., Huber C. Origin of Shallow Volcanic Tremor: The Dynamics of Gas Pockets Trapped Beneath Thin Permeable Media // Journal of Geophysical Research: Solid Earth. — 2019. — Vol. 124, no. 5. — P. 4831–4861. — doi: 10.1029/2019JB017482.
  14. Gonnermann H. M., Manga M. The Fluid Mechanics Inside a Volcano // Annual Review of Fluid Mechanics. — 2007. — Vol. 39, no. 1. — P. 321–356. — doi: 10.1146/annurev.fluid.39.050905.110207.
  15. Gottschämmer E., Rohnacher A., Carter W., et al. Volcanic emission and seismic tremor at Santiaguito, Guatemala: New insights from long-term seismic, infrasound and thermal measurements in 2018-2020 // Journal of Volcanology and Geothermal Research. — 2021. — Vol. 411. — P. 107154. — doi: 10.1016/j.jvolgeores.2020.107154.
  16. Iverson R. M., Dzurisin D., Gardner C. A., et al. Dynamics of seismogenic volcanic extrusion at Mount St Helens in 2004-05 // Nature. — 2006. — Vol. 444, no. 7118. — P. 439–443. — doi: 10.1038/nature05322.
  17. Johnson J. B., Lees J. M., Gerst A., et al. Long-period earthquakes and co-eruptive dome inflation seen with particle image velocimetry // Nature. — 2008. — Vol. 456, no. 7220. — P. 377–381. — doi: 10.1038/nature07429.
  18. Johnson J. B., Lyons J. J., Andrews B. J., et al. Explosive dome eruptions modulated by periodic gas-driven inflation // Geophysical Research Letters. — 2014. — Vol. 41, no. 19. — P. 6689–6697. — doi: 10.1002/2014GL061310.
  19. Kumagai H., Chouet B. A. The complex frequencies of long-period seismic events as probes of fluid composition beneath volcanoes // Geophysical Journal International. — 1999. — Vol. 138, no. 2. — F7–F12. — doi: 10.1046/j.1365-246X.1999.00911.x.
  20. Kumagai H., Chouet B. A. The dependence of acoustic properties of a crack on the resonance mode and geometry // Geophysical Research Letters. — 2001. — Vol. 28, no. 17. — P. 3325–3328. — doi: 10.1029/2001GL013025.
  21. Kurzon I., Lyakhovsky V., Lensky N. G., et al. Forcing of seismic waves travelling through a bubbly magma // AGU Fall Meeting Abstracts. Vol. 2005. — New York : AGU, 2005.
  22. Kurzon I., Lyakhovsky V., Navon O., et al. Pressure waves in a supersaturated bubbly magma: Pressure waves and bubbly magma // Geophysical Journal International. — 2011. — Vol. 187, no. 1. — P. 421–438. — doi: 10.1111/j.1365-246X.2011.05152.x.
  23. Lamb O. D., Lamur A., Díaz-Moreno A., et al. Disruption of Long-Term Effusive-Explosive Activity at Santiaguito, Guatemala // Frontiers in Earth Science. — 2019. — Vol. 6. — doi: 10.3389/feart.2018.00253.
  24. Neuberg J. W., Tuffen H., Collier L., et al. The trigger mechanism of low-frequency earthquakes on Montserrat // Journal of Volcanology and Geothermal Research. — 2006. — Vol. 153, no. 1/2. — P. 37–50. — doi: 10.1016/j.jvolgeores.2005.08.008.
  25. Nishimura T., Hamaguchi H., Ueki S. Source mechanisms of volcanic tremor and low-frequency earthquakes associated with the 1988-89 eruptive activity of Mt Tokachi, Hokkaido, Japan // Geophysical Journal International. — 1995. — Vol. 121, no. 2. — P. 444–458. — doi: 10.1111/j.1365-246X.1995.tb05725.x.
  26. Ohmi S., Obara K. Deep low-frequency earthquakes beneath the focal region of the Mw 6.7 2000 Western Tottori earthquake // Geophysical Research Letters. — 2002. — Vol. 29, no. 16. — doi: 10.1029/2001GL014469.
  27. Ozerov A., Ispolatov I., Lees J. Modeling Strombolian eruptions of Karymsky volcano, Kamchatka, Russia // Journal of Volcanology and Geothermal Research. — 2003. — Vol. 122, no. 3/4. — P. 265–280. — doi: 10.1016/S0377- 0273(02)00506-1.

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