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Volcanoes, Non-linear Processes in

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Encyclopedia of Complexity and Systems Science

Definition of the Subject

Magma transport is fundamentally episodic in character asa result of the inherent instability of magmatic systems at all time scales. This episodicity is reflected inseismic activity, which originates in dynamic interactions between gas, liquid and solid along magma transportpaths involving complex geometries. The geometrical complexity plays a central role in controlling flowdisturbances and also providing specific sites where pressure and momentum changes in the fluid are effectivelycoupled to the Earth.

Recent technological developments and improvements in the seismological instrumentation of volcanoes now allow the surface effects of subterraneanvolcanic processes to be imaged in unprecedented detail. Through detailed analyzes of the seismic wavefields radiated by volcanic activity, it has becomepossible for volcano seismologists to make direct measurements of the volcanic conduit response to flow processes, thus opening the way for detailedmodeling of...

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Abbreviations

Bubbly liquid:

Liquid‐gas mixture in which the gas phase is distributed as discrete bubbles dispersed in a continuous liquid phase.

Choked flow:

Flow condition where the transonic flow of a compressible fluid through a constriction becomes choked. As the fluid flows through a narrowing channel, it accelerates at a rate that depends on the ratio of channel inlet pressure to channel outlet pressure. At a critical pressure ratio, which is a function of the fractional change of cross‐sectional area, the speed of the fluid accelerating through the nozzle‐like constriction reaches a maximum value equal to its sound speed. This flow condition is termed choked flow.

Crack wave:

A dispersive wave generated by fluid-solid interaction in a fluid‐filled crack embedded in an elastic solid. The crack-wave speed is always smaller than the acoustic speed of the fluid.

Diffuse interface:

Thin mixing layer constituting the interface between two immiscible fluids. Interface dynamics is governed by molecular forces and is described by the mixing energy of the two fluid components.

Gas slug:

A gas bubble whose diameter is approximately the diameter of the pipe in which the slug is flowing. In a slug ascending a vertical pipe, the nose of the bubble has a characteristic spherical cap and the gas in the rising bubble is separated from the pipe wall by a falling film of liquid.

Long‐period (LP) event:

A seismic event originating under volcanoes with emergent onset of P waves, no distinct S waves, and a harmonic signature with periods in the range 0.2–2 s as compared to a tectonic earthquake of the same magnitude. LP events are attributed to the involvement of fluid such as magma and/or water in the source process (see also VLP event).

Magma:

Molten rock containing variable amounts of dissolved gases (principally water vapor, carbon dioxide, and sulfur dioxide), crystals (principally silicates and oxides), and, occasionally, preexisting solid rock fragments.

Moment tensor:

A symmetric second‐order tensor that completely characterizes an internal seismic point source. For an extended source, it represents a point‐source approximation and can be quantified from an analysis of seismic waves whose wavelengths are much longer than the source dimensions.

Nonlinear process:

Process involving physical variables governed by nonlinear equations that reflect the fundamental micro-scale dynamics of the system. Nonlinear phenomena can arise from a number of different sources, including convective acceleration in fluid dynamics, constitutive relations, boundary conditions representing gas‐liquid interfaces, nonlinear body forces, and geometric nonlinearities arising from large-scale deformation.

Phase‐field method:

Method treating the interface between two immiscible fluids as a diffuse thin layer; also known as the diffuse interface method. In this approach, the physical and chemical properties of the interfacial layer are defined by a phase-field variable ϕ, whose dynamics are expressed by the Cahn–Hilliard convection‐diffusion equation. Use of the phase-field variable avoids the necessity of tracking the interface and yields the correct interfacial tension from the free energy stored in the mixing layer.

Very‐long‐period (VLP) event:

A seismic event originating under volcanoes with typical periods in the range 2–100 s. VLP events are attributed to the involvement of fluid such as magma and/or water in the source process. Together with LP events, VLP events represent a continuum of fluid oscillations, including acoustic and inertial effects resulting from perturbations in the flow of fluid through conduits.

Volatile:

A chemical compound that is dissolved in magma at high pressure and exsolves from the melt and appears as a low‐density gas at low pressure. The most common volatiles in magma are water, carbon dioxide, and sulfur dioxide.

Waveform inversion:

Given an assumed model of the wave‐propagation medium, a procedure for determining the source mechanism and source location of a seismic event based on matching observed waveforms with synthetics calculated with the model.

Bibliography

  1. Acocella V, Neri M, Scarlato P (2006) Understanding shallow magma emplacement atvolcanoes: Orthogonal feeder dykes during the 2002–2003 Stromboli (Italy) eruption. Geophys Res Lett33:L17310. doi:10.1029/2006GL026862

    ADS  Google Scholar 

  2. Aki K, Fehler M, Das S (1977) Source mechanism of volcanic tremor:Fluid‐driven crack models and their application to the 1963 Kilauea eruption. J Volcanol Geotherm Res2:259–287

    ADS  Google Scholar 

  3. Aki K, Richards PG (1980) Quantitative Seismology. Freeman, New York,p 932

    Google Scholar 

  4. Almendros J, Chouet B, Dawson P (2001) Spatial extent of a hydrothermalsystem at Kilauea Volcano, Hawaii, determined form array analyses of shallow long‐period seismicity. J Geophys Res106:13581–13597

    ADS  Google Scholar 

  5. Almendros J, Chouet B, Dawson P, Huber C (2002) Mapping the sources of theseismic wave field at Kilauea Volcano, Hawaii, using data recorded on multiple seismic antennas. Bull Seismol Soc Am92:2333–2351

    Google Scholar 

  6. Almendros J, Chouet B, Dawson P, Bond T (2002) Identifying elements of theplumbing system beneath Kilauea Volcano, Hawaii, from the source locations of very‐long‐period signals. Geophys J Int148:303–312

    ADS  Google Scholar 

  7. Almendros J, Chouet B, Dawson P (2008) Shallow magma transport pathway underKilauea Volcano, Hawaii, imaged from waveform inversions of very‐long‐period seismic data. 2-Source modeling J Geophys Res,submitted

    Google Scholar 

  8. Anderson DM, McFadden GB, Wheeler AA (1998) Diffuse‐interface methods influid mechanics. Annu Rev Fluid Mech 30:139–165

    MathSciNet  ADS  Google Scholar 

  9. Arciniega‐Ceballos A, Chouet BA,Dawson P (1999) Very‐long‐period signals associated with Vulcanian explosions at Popocatepetl Volcano,Mexico. Geophys Res Lett 26:3013–3016

    Google Scholar 

  10. Arciniega‐Ceballos A, Chouet B,Dawson P (2003) Long‐period events and tremor at Popocatepetl Volcano (1994–2000) and their broadbandcharacteristics. Bull Volcanol 65:124–135

    Google Scholar 

  11. Arciniega‐Ceballos A, Chouet B, Dawson P, Asch G (2008) Broadbandseismic measurements of degassing activity associated with lava effusion at Popocatepetl Volcano, Mexico. J Volcanol Geotherm Res170:12–23

    Google Scholar 

  12. Ascher UM, Ruuth SJ, Wetton BTR (1995) Implicit‐explicit methods fortime‐dependent partial differential equations. SIAM J Numer Anal 3:797–823

    MathSciNet  Google Scholar 

  13. Aster R, Mah S, Kyle P, McIntosh W, Dunbar N, Johnson J, Ruiz M, McNamara S(2003) Very long period oscillations of Mount Erebus Volcano. J Geophys Res108(B11). doi:10.1029/2002JB002101

  14. Auger E, D'Auria L, Martini M, Chouet B, Dawson P (2006) Real-time monitoringand massive inversion of source parameters of very long period seismic signals: An application to Stromboli Volcano, Italy. Geophys Res Lett 33:L04301.doi:10.1029/2005GL024703

    ADS  Google Scholar 

  15. Badalassi VE, Ceniceros HD, Banerjee S (2003) Computation of multiphasesystems with phase field models. J Comput Phys 190:371–397

    MathSciNet  ADS  MATH  Google Scholar 

  16. Balazs AC, Verberg R, Pooley CM, Kuksenok O (2005) Modeling the flow ofcomplex fluids through heterogeneous channels. Soft Matter 1:44–54

    ADS  Google Scholar 

  17. Bray AJ (1994) Theory of phase‐ordering kinetics. Adv Phys43:357–459

    MathSciNet  ADS  Google Scholar 

  18. Burton M, Allard P, Muré F, La Spina A (2007) Magmatic gas compositionreveals the source depth of slug‐driven Strombolian explosive activity. Science 317(5835):227–230

    Google Scholar 

  19. Cahn JW, Hilliard JE (1958) Free energy of a nonuniformsystem. I. Interfacial free energy. J Chem Phys 28:258–267

    ADS  Google Scholar 

  20. Cahn JW, Hilliard JE (1959) Free energy of a nonuniform system. III,Nucleation in a two‐component incompressible fluid. J Chem Phys 31:688–689

    ADS  Google Scholar 

  21. Cervelli PF, Miklius A (2003) The shallow magmatic system of Kilauea Volcano.US Geol Surv Prof Paper 1676:149–163

    Google Scholar 

  22. Chouet B, Julian BR (1985) Dynamics of an expanding fluid‐filled crack.J Geophys Res 90:11187–11198

    ADS  Google Scholar 

  23. Chouet B (1986) Dynamics of a fluid‐driven crack in threedimensions by the finite difference method. J Geophys Res 91:13967–13992

    ADS  Google Scholar 

  24. Chouet B (1988) Resonance of a fluid‐driven crack: Radiationproperties and implications for the source of long‐period events and harmonic tremor. J Geophys Res93:4375–4400

    ADS  Google Scholar 

  25. Chouet B (1992) A seismic source model for the source oflong‐period events and harmonic tremor. In: Gasparini P, Scarpa R, Aki K (eds) IAVCEI Proceedings in Volcanology, vol 3. Springer, New York,pp 133–156

    Google Scholar 

  26. Chouet BA, Page RA, Stephens CD, Lahr JC, Power JA (1994) Precursory swarms oflong‐period events at Redoubt Volcano (1989–1990), Alaska: Their origin and use as a forecasting tool. J Volcanol Geotherm Res62:95–135

    ADS  Google Scholar 

  27. Chouet B (1996) Long‐period volcano seismicity: its source and use ineruption forecasting. Nature 380:309–316

    ADS  Google Scholar 

  28. Chouet B (1996) New methods and future trends in seismological volcanomonitoring. In: Scarpa R, Tilling RI (eds) Monitoring and Mitigation of Volcano Hazards. Springer, New York,pp 23–97

    Google Scholar 

  29. Chouet B, Saccorotti G, Martini M, Dawson P, De Luca G, Milana G, Scarpa R(1997) Source and path effects in the wave fields of tremor and explosions at Stromboli Volcano, Italy. J Geophys Res102:15129–15150

    ADS  Google Scholar 

  30. Chouet B, Saccorotti G, Dawson P, Martini M, Scarpa R, De Luca G, Milana G,Cattaneo M (1999) Broadband measurements of the sources of explosions at Stromboli Volcano, Italy. Geophys Res Lett26:1937–1940

    ADS  Google Scholar 

  31. Chouet B (2003) Volcano seismology. PAGEOPH 160(3–4):739–788

    Google Scholar 

  32. Chouet B, Dawson P, Ohminato T, Martini M, Saccorotti G, Giudicepietro F, De LucaG, Milana G, Scarpa R (2003) Source mechanisms of explosions at Stromboli Volcano, Italy, determined frommoment‐tensor inversions of very‐long‐period data. J Geophys Res108(B1):2019. doi:10.1029/2002JB001919

    Google Scholar 

  33. Chouet B, Dawson P, Arciniega‐Ceballos A (2005) Source mechanism ofVulcanian degassing at Popocatepetl Volcano, Mexico, determined from waveform inversions of very long period signals. J Geophys Res110:B07301. doi:10.1029/2004JB003524

  34. Chouet B, Dawson P, Nakano M (2006) Dynamics of bubble growth and pressurerecovery in a bubbly rhyolitic melt embedded in an elastic solid. J Geophys Res111:B07310. doi:10.1029/2005JB004174

    ADS  Google Scholar 

  35. Chouet B, Dawson P, Martini M (2008) Shallow‐conduit dynamics atStromboli Volcano, Italy, imaged from waveform inversion. In: Lane SJ, Gilbert JS (eds) Fluid Motions in Volcanic Conduits A Source of Seismic andAccoustic Signals. Geol Soc Lond Special Pub 307:57–84

    ADS  Google Scholar 

  36. Collier L, Neuberg JW, Lensky N, Lyakhovsky V, Navon O (2006) Attenuation ingas‐charged magma. J Volcanol Geotherm Res 153:21–36

    Google Scholar 

  37. Commander KW, Prosperetti A (1989) Linear pressure waves in bubbly liquids:Comparison between theory and experiments. J Acoust Soc Am 85:732–746

    ADS  Google Scholar 

  38. Dawson PB, Dietel C, Chouet BA, Honma K, Ohminato T, Okubo P (1998)A digitally telemetered broadband seismic network at Kilauea Volcano, Hawaii. US Geol Surv Open-File Rep 98–108:1–121

    Google Scholar 

  39. Dawson P, Whilldin D, Chouet B (2004) Application of near real-time radialsemblance to locate the shallow magmatic conduit at Kilauea Volcano, Hawaii. Geophys Res Lett31:L21606. doi:10.1029/2004GL021163

    ADS  Google Scholar 

  40. Dzurisin D, Vallance JW, Gerlach TM, Moran SC, Malone SD (2005) MountSt. Helens reawakens. Eos Trans AGU 86:25,29 doi:10.1029/2005EO030001

    ADS  Google Scholar 

  41. Evans R (1979) The nature of the liquid‐vapour interface and othertopics in the statistical mechanics of non‐uniform, classical fluids. Adv Phys 28:148–200

    ADS  Google Scholar 

  42. Ferrazini V, Aki K (1987) Slow waves trapped in a fluid‐filledinfinite crack: Implications for volcanic tremor. J Geophys Res 92:9215–9233

    ADS  Google Scholar 

  43. Fujita E, Ida Y, Oikawa J (1995) Eigen oscillation of a fluid sphere andsource mechanism of harmonic volcanic tremor. J Volcanol Geotherm Res 69:365–378

    ADS  Google Scholar 

  44. Fujita E, Ukawa M, Yamamoto E (2004) Subsurface cyclic magma sill expansionsin the 2000 Miyakejima Volcano eruption: Possibility of two-phase flow oscillation. J Geophys Res109:B04205. doi:10.1029/2003JB002556

    ADS  Google Scholar 

  45. Gil Cruz F, Chouet BA (1997) Long‐period events, the most characteristicseismicity accompanying the emplacement and extrusion of a lava dome in Galeras Volcano, Colombia, in 1991. J Volcanol Geotherm Res77:121–158

    ADS  Google Scholar 

  46. Hamada N, Jingu H, Ikumoto K (1976) On the volcanic earthquake with slowlydecaying coda wave (in Japanese with English abstract). Bull Volcanol Soc Jpn 21:167–183

    Google Scholar 

  47. Hasegawa A, Zhao D, Hori S, Yamamoto A, Horiuchi S (1991) Deep structure ofthe northeastern Japan arc and its relationship to seismic and volcanic activity. Nature 352:683–689

    ADS  Google Scholar 

  48. Heliker C, Mattox T (2003) The first two decades of the Pu'uO'o‐Kupaianaha eruption: Chronology and selected bibliography. US Geol Surv Prof Paper 1676:1–27

    Google Scholar 

  49. Hess K, Dingwell DB (1996) Viscosities of hydrous leucogranitic melts: A non‐Arrhenian model. Am Mineral 81:1297–1300

    Google Scholar 

  50. Hidayat D, Voight B, Langston C, Ratdomopurbo A, Ebeling C (2000) Broadbandseismic experiment at Merapi Volcano, Java, Indonesia: Very‐long‐period pulses embedded in multiphase earthquakes. J Volcanol GeothermRes 100:215–231

    ADS  Google Scholar 

  51. Hidayat D, Chouet B, Voight B, Dawson P, Ratdomopurbo A (2002) Sourcemechanism of very‐long‐period signals accompanying dome growth activity at Merapi Volcano, Indonesia. Geophys Res Lett29(23):2118. doi:10.1029/2002GL015013

    ADS  Google Scholar 

  52. Hidayat D, Chouet B, Voight B, Dawson P, Ratdomopurbo A (2003) Correction toSource mechanism of very‐long‐period signals accompanying dome growth activity at Merapi Volcano, Indonesia. Geophys Res Lett30(10):2118. doi:10.1029/2003GL017211

    Google Scholar 

  53. Hill DP, Dawson P, Johnston MJS, Pitt AM, Biasi G, Smith K (2002)Very‐long‐period volcanic earthquakes beneath Mammoth Mountain, California. Geophys Res Lett29(10):1370. doi:10.1029/2002GL014833

    ADS  Google Scholar 

  54. Hill DP, Prejean S (2005) Magmatic unrest beneath Mammoth Mountain,California. J Volcanol Geotherm Res 146:257–283

    ADS  Google Scholar 

  55. Hirabayashi J (1999) Formation of volcanic fluid reservoir and volcanicactivity. J Balneol Soc Jpn 49:99–105

    Google Scholar 

  56. Ichihara M, Kameda M (2004) Propagation of acoustic waves ina visco‐elastic two-phase system: Influences of the liquid viscosity and the internal diffusion. J Volcanol Geotherm Res137:73–91

    ADS  Google Scholar 

  57. Iverson RM, Dzurisin D, Gardner CA, Gerlach TM, LaHusen RG, Lisowski M, MajorJJ, Malone SD, Messerich JA, Moran SC, Pallister JS, Qamar AI, Schilling SP, Vallance JW (2006) Dynamics of seismogenic volcanic extrusion at MountSt. Helens in 2004–05. Nature 444:439–443. doi:10.1038/nature05322

    ADS  Google Scholar 

  58. Jacqmin D (1999) Calculation of two-phase Navier–Stokes Flows usingphase-field modeling. J Comput Phys 155:96–127

    MathSciNet  ADS  MATH  Google Scholar 

  59. James MR, Lane SJ, Chouet B, Gilbert JS (2004) Pressure changes associatedwith the ascent and bursting of gas slugs in liquid‐filled vertical and inclined conduits. J Volcanol Geotherm Res129:61–82

    ADS  Google Scholar 

  60. James MR, Lane SJ, Chouet BA (2006) Gas slug ascent through changes in conduitdiameter: Laboratory insights into a volcano‐seismic source process in low‐viscosity magmas. J Geophys Res111:B05201. doi:10.1029/2005JB003718

    ADS  Google Scholar 

  61. Jones RAL (2002) Soft Condensed Matter. Oxford University Press, Oxford,p 195

    Google Scholar 

  62. Julian BR (1994) Volcanic tremor, Nonlinear excitation by fluidflow. J Geophys Res 99:11859–11877

    ADS  Google Scholar 

  63. Kanamori H, Given JW (1982) Analysis of long‐period waves excited by theMay 18, 1980, eruption of Mount St. Helens – A terrestrial monopole? J Geophys Res 87:5422–5432

    ADS  Google Scholar 

  64. Kanamori H, Given JW, Lay T (1984) Analysis of seismic body waves excited bythe Mount St. Helens eruption of May 18:1980. J Geophys Res 89:1856–1866

    ADS  Google Scholar 

  65. Kaneshima S, Kawakatsu H, Matsubayashi H, Sudo Y, Tsutsui T, Ohminato T, ItoH, Uhira K, Yamasato H, Oikawa J, Takeo M, Iidaka T (1996) Mechanism of phreatic eruptions at Aso Volcano inferred from near-field broadband seismicobservations. Science 273:642–645

    ADS  Google Scholar 

  66. Kawakatsu H (1989) Centroid single force inversion of seismic waves generatedby landslides. J Geophys Res 94:12363–12374

    ADS  Google Scholar 

  67. Kawakatsu H, Ohminato T, Ito H, Kuwahara Y (1992) Broadband seismicobservation at Sakurajima Volcano, Japan. Geophys Res Lett 19:1959–1962

    ADS  Google Scholar 

  68. Kawakatsu H, Ohminato T, Ito H (1994) 10-s‑period volcanic tremorsobserved over a wide area in southwestern Japan. Geophys Res Lett 21:1963–1966

    ADS  Google Scholar 

  69. Kawakatsu H, Kaneshima S, Matsubayashi H, Ohminato T, Sudo Y, Tsutsui T, UhiraK, Yamasato H, Ito H, Legrand D (2000) Aso94: Aso seismic observation with broadband instruments. J Volcanol Geotherm Res101:129–154

    ADS  Google Scholar 

  70. Kedar S, Sturtevant B, Kanamori H (1996) The origin of harmonic tremor at OldFaithful Geyser. Nature 379:708–711

    ADS  Google Scholar 

  71. Kendon VM, Cates ME, Pagonabarraga I, Desplat J-C, Bladon P (2001) Inertialeffects in three‐dimensional spinodal decomposition of a symmetric binary fluid mixture: A lattice Boltzmann study. J Fluid Mech440:147–203

    ADS  MATH  Google Scholar 

  72. Kieffer SW (1977) Sound speed in liquid‐gas mixtures: Water-air andwater‐steam. J Geophys Res 82:2895–2904

    ADS  Google Scholar 

  73. Kim J, Kang K, Lowengrub J (2004) Conservative multigrid methods forCahn–Hilliard fluids. J Comput Phys 193:511–543

    MathSciNet  ADS  MATH  Google Scholar 

  74. Klein FW, Koyanagi RY, Nakata JS, Tanigawa WR (1987) The seismicity ofKilauea's magma system. In: Decker RW, Wright TL, Stauffer RW (eds) Volcanism in Hawaii. US Geol. Surv. Prof. Pap., 1350. US government printing office,Washington, pp 1019–1185

    Google Scholar 

  75. Koyanagi RY, Chouet B, Aki K (1987) Origin of volcanic tremor in Hawaii. PartI: Compilation of seismic data from the Hawaiian Volcano Observatory, 1972 to 1985. In: Decker RW, Wright TL, Stauffer RW (eds) Volcanism in Hawaii, USGeol. Surv. Prof. Pap., 1350. US government printing office, Washington, pp 1221–1257

    Google Scholar 

  76. Kumagai H, Chouet BA (1999) The complex frequencies of long‐periodseismic events as probes of fluid composition beneath volcanoes. Geophys Int 138:F7–F12

    ADS  Google Scholar 

  77. Kumagai H, Chouet BA (2000) Acoustic properties of a crack containingmagmatic or hydrothermal fluids. J Geophys Res 105:25493–25512

    ADS  Google Scholar 

  78. Kumagai H, Ohminato T, Nakano M, Ooi M, Kubo A, Inoue H, Oikawa J (2001)Very‐long‐period seismic signals and caldera formation at Miyake Island, Japan. Science 293:687–690

    ADS  Google Scholar 

  79. Kumagai H, Chouet BA, Nakano M (2002) Temporal evolution ofa hydrothermal system in Kusatsu‐Shirane Volcano, Japan, inferred from the complex frequencies of long‐period events. J Geophys Res107(B10):2236. doi:10.1029/2001JB000653

    Google Scholar 

  80. Kumagai H, Chouet BA, Nakano M (2002) Waveform inversion of oscillatorysignatures in long‐period events beneath volcanoes. J Geophys Res 107(B11)2301.doi:10.1029/2001JB001704

  81. Kumagai H, Miyakawa K, Negishi H, Inoue H, Obara K, Suetsugu D (2003) Magmaticdyke resonances inferred from very‐long‐period seismic signals. Science 299:2058–2061

    ADS  Google Scholar 

  82. Kumagai H, Chouet BA, Dawson PB (2005) Source process ofa long‐period event at Kilauea Volcano, Hawaii. Geophys J Int 161:243–254

    ADS  Google Scholar 

  83. Kumagai H (2006) Temporal evolution of a magmatic dike system inferredfrom the complex frequencies of very long period seismic signals. J Geophys Res111:B06201. doi:10.1029/2005JB003881

    ADS  Google Scholar 

  84. Kumagai H, Yepes H, Vaca M, Caceres V, Nagai T, Yokoe K, Imai T, Miyakawa K,Yamashina T, Arrais S, Vasconez F, Pinajota E, Cisneros C, Ramos C, Paredes M, Gomezjurado L, Garcia‐Aristizabal A, Molina I, Ramon P, Segovia M,Palacios P, Troncoso L, Alvarado A, Aguilar J, Pozo J, Enriquez W, Mothes P, Hall M, Inoue I, Nakano M, Inoue H (2007) Enhancing volcano‐monitoringcapabilities in Ecuador. Eos Trans Am Geophys Union 88:245–246

    Google Scholar 

  85. Lane SJ, Chouet BA, Phillips JC, Dawson P, Ryan GA, Hurst E (2001)Experimental observations of pressure oscillations and flow regimes in an analogue volcanic system. J Geophys Res106:6461–6476

    ADS  Google Scholar 

  86. Legrand D, Kaneshima S, Kawakatsu H (2000) Moment tensor analysis ofnear-field broadband waveforms observed at Aso Volcano, Japan. J Volcanol Geotherm Res 101:155–169

    ADS  Google Scholar 

  87. Lensky NG, Lyakhovsky V, Navon O (2002) Expansiondynamics of volatile‐saturated liquids and bulk viscosity of bubbly magmas. J Fluid Mech 460:39–56

    ADS  MATH  Google Scholar 

  88. Lensky NG, Navon O, Lyakhovsky V (2004) Bubble growth during decompression ofmagma: experimental and theoretical investigation. J Volcanol Geotherm Res 129:7–22

    ADS  Google Scholar 

  89. Lowengrub J, Truskinovsky L (1998) Quasi‐incompressibleCahn‐Hilliard fluids and topological transitions. Proc Royal Soc Lond A 454:2617–2654

    MathSciNet  MATH  Google Scholar 

  90. Lyakhovsky V, Hurwitz S, Navon O (1996) Bubble growth in rhyolitic melts:experimental and numerical investigation. Bull Volcanol 58:19–32

    ADS  Google Scholar 

  91. Major JJ, Scott WE, Driedger C, Dzurisin D (2005) Mount St. Helens eruptsagain – Activity from September 2004 through March 2005. US Geological Survey Fact Sheet FS2005‐3036. US goverment printing office,Washington, p 4

    Google Scholar 

  92. Meier GEA, Grabitz G, Jungowsky WM, Witczak KJ, Anderson JS (1978)Oscillations of the supersonic flow downstream of an abrupt inrease in duct crosssection. Mitteilungen aus dem Max-Plank Institut fürStrömungsforschung und der Aerodynamischen Versuchsanstalt65:1–172

    Google Scholar 

  93. Migler KB (2001) String formation in sheared polymer blends: coalescence,breakup, and finite size effects. Phys Rev Lett 86(6):1023–1026

    ADS  Google Scholar 

  94. Moran SC, Malone SD, Qamar AI, Thelen W, Wright AK, Caplan‐Auerbach J(2007) 2004–2005 seismicity associated with the renewed dome‐building eruption of Mount St. Helens. In: Sherrod DR, Scott WE, Stauffer PH(eds) A Volcano rekindled: the first year of renewed eruptions at Mount St. Helens, 2004–2006. US Geological SurveyProf. Pap. 2007-XXXX

    Google Scholar 

  95. Morrissey MM, Chouet BA (1997) A numerical investigation of choked flowdynamics and its application to the triggering mechanism of long‐period events at Redoubt Volcano, Alaska. J Geophys Res102:7965–7983

    ADS  Google Scholar 

  96. Nakano M, Kumagai H, Kumazawa M, Yamaoka K, Chouet BA (1998) The excitationand characteristic frequency of the long‐period volcanic event: An approach based on an inhomogeneous autoregressive model of a linear dynamicsystem. J Geophys Res 103:10031–10046

    ADS  Google Scholar 

  97. Nakano M, Kumagai H, Chouet BA (2003) Source mechanism of long‐periodevents at Kusatsu‐Shirane Volcano, Japan, inferred from waveform inversion of the effective excitation functions. J Volcanol Geotherm Res122:149–164

    ADS  Google Scholar 

  98. Navon O, Lyakhovsky V (1998) Vesiculation processes in silicic magmas. GeolSoc Lond Special Pub 145:27–50

    ADS  Google Scholar 

  99. Neuberg J, Luckett R, Ripepe M, Braun T (1994) Highlights from a seismicbroadband array on Stromboli Volcano. Geophys Res Lett 21:749–752

    ADS  Google Scholar 

  100. Neuberg JW, Tuffen H, Collier L, Green D, Powell T, Dingwell D (2006) Thetrigger mechanism of low‐frequency earthquakes on Montserrat. J Volcanol Geotherm Res 153:37–50

    ADS  Google Scholar 

  101. Nishimura T, Nakamichi H, Tanaka S, Sato M, Kobayashi T, Ueki S, HamaguchiH, Ohtake M, Sato H (2000) Source process of very long period seismic events associated with the 1998 activity of Iwate Volcano, northeasternJapan. J Geophys Res 105:19135–19147

    ADS  Google Scholar 

  102. Nishimura T, Chouet B (2003) A numerical simulation of magma motion,crustal deformation, and seismic radiation associated with volcanic eruptions. Geophys. J Int 153:699–718

    Google Scholar 

  103. Nishimura T, Ueki S, Yamawaki T, Tanaka S,Hasino H, Sato M, Nakamichi H, Hamaguchi H (2003) Broadband seismic signals associated with the 2000 volcanic unrest of Mount Bandai, northeasternJapan. J Volcanol Geotherm Res 119:51–59

    ADS  Google Scholar 

  104. Nishimura T (2004) Pressure recovery in magma due to bubble growth. GeophysRes Lett 31:L12613. doi:10.1029/2004GL019810

    ADS  Google Scholar 

  105. Ochs FA, Lange RA (1999) The density of hydrous magmatic liquids. Science283:1314–1317

    ADS  Google Scholar 

  106. Ohba T, Hirabayashi J, Nogami K (2000) D/H and \( { ^{18}\text{O}/^{16}\text{O} } \) ratios of water in thecrater lake of Kusatsu‐Shirane Volcano, Japan. J Volcanol Geotherm Res 97:329–346

    ADS  Google Scholar 

  107. Ohminato T, Chouet BA (1997) A free‐surface boundary conditionfor including 3D topography in the finite‐difference method. Bull Seismol Soc Am 87:494–515

    Google Scholar 

  108. Ohminato T, Ereditato D (1997) Broadband seismic observations atSatsuma‐Iwojima Volcano, Japan. Geophys Res Lett 24:2845–2848

    ADS  Google Scholar 

  109. Ohminato T, Chouet BA, Dawson PB, Kedar S (1998) Waveform inversion ofvery‐long‐period impulsive signals associated with magmatic injection beneath Kilauea volcano, Hawaii. J Geophys Res103:23839–23862

    ADS  Google Scholar 

  110. Ohminato T (2006) Characteristics and source modeling of broadband seismicsignals associated with the hydrothermal system at Satsuma–IwoJima volcano, Japan. J Volcanol Geotherm Res158:467–490

    ADS  Google Scholar 

  111. Ohminato T, Takeo M, Kumagai H, Yamashina T, Oikawa J, Koyama E, Tsuji H,Urabe T (2006) Vulcanian eruptions with dominant single force components observed during the Asama 2004 volcanic activity in Japan. Earth Planets Space58:583–593

    ADS  Google Scholar 

  112. Orlandini E, Swift MR, Yeomans JM (1995) A Lattice Boltzmann Model ofbinary fluid mixtures. Europhys Lett 32:463

    ADS  Google Scholar 

  113. Pooley CM, Kuksenok O, Balasz AC (2005) Convection‐driven patternformation in phase‐separating binary fluids. Phys Rev E 71:030501(R)

    ADS  Google Scholar 

  114. Power JA, Stihler SD, White RA, Moran SC (2004) Observations of deeplong‐period (DLP) seismic events beneath Aleutian Arc Volcanoes, 1989–2002. J Volcanol Geotherm Res138:243–266

    ADS  Google Scholar 

  115. Proussevitch AA, Sahagian DL, Anderson AT (1993) Dynamics of diffusivebubble growth in magmas: Isothermal case. J Geophys Res 98:22283–22307

    ADS  Google Scholar 

  116. Proussevitch AA, Sahagian DL (1996) Dynamics of coupled diffusive anddecompressive bubble growth in magmatic systems. J Geophys Res 101:17447–17455

    ADS  Google Scholar 

  117. Proussevitch AA, Sahagian DL (1998) Dynamics and energetics of bubble growthin magmas: Analytical formulation and numerical modeling. J Geophys Res 103:18223–18251

    ADS  Google Scholar 

  118. Ripepe M, Poggi P, Braun T, Gordeev E (1996) Infrasonic waves and volcanictremor at Stromboli. Geophys Res Lett 23:181–184

    ADS  Google Scholar 

  119. Rowe CA, Aster RC, Kyle PR, Schlue JW, Dibble RR (1998) Broadband recordingof Strombolian explosions and associated very‐long‐period seismic signals on Mount Erebus Volcano, Ross Island, Antarctica. Geophys Res Lett25:2297–2300

    ADS  Google Scholar 

  120. Saccorotti G, Chouet B, Dawson P (2001) Wavefield properties ofa shallow long‐period event and tremor at Kilauea Volcano, Hawaii. J Volcanol Geotherm Res 109:163–189

    ADS  Google Scholar 

  121. Scriven LE (1959) On the dynamics of phase growth. Chem Eng Sci10:1–13

    Google Scholar 

  122. Shaw HR, Chouet B (1989) Singularity spectrum of intermittent seismic tremorat Kilauea Volcano, Hawaii. Geophys Res Lett 16:195–198

    ADS  Google Scholar 

  123. Shaw HR, Chouet B (1991) Fractal hierarchies of magma transport in Hawaiiand critical self‐organization of tremor. J Geophys Res 96:10191–10207

    ADS  Google Scholar 

  124. Shimomura Y, Nishimura T, Sato H (2006) Bubble growth processes in magmasurrounded by an elastic medium. J Volcanol Geotherm Res 155:307–322

    ADS  Google Scholar 

  125. Sparks R (1978) The dynamics of bubble formation and growth in magmas:A review and analysis. J Volcanol Geotherm Res 3:1–38

    Google Scholar 

  126. Stephens CD, Chouet BA (2001) Evolution of the December 14, 1989 precursorylong‐period event swarm at Redoubt Volcano, Alaska. J Volcanol Geotherm Res 109:133–148

    ADS  Google Scholar 

  127. Swift MR, Osborn WR, Yeomans JM (1995) Lattice Boltzmann simulation ofnonideal fluids. Phys Rev Lett 75(5):0–833

    Google Scholar 

  128. Swift MR, Orlandini E, Osborn WR, Yeomans JM (1996) Lattice Boltzmannsimulations of liquid‐gas and binary fluid systems. Phys Rev E 54(5):5041–5052

    ADS  Google Scholar 

  129. Takei Y, Kumazawa M (1994) Why have the single force and torque beenexcluded from seismic source models? Geophys J Int 118:20–30

    ADS  Google Scholar 

  130. Tannehill JC, Anderson DA, Pletcher RH (1997) Computational Fluid Mechanicsand Heat Transfer, 2nd edn. Taylor and Francis, Philadelphia, p 792

    Google Scholar 

  131. Toramaru A (1989) Vesiculation process and bubble size distributions inascending magmas with constant velocities. J Geophys Res 94:17523–17542

    ADS  Google Scholar 

  132. Toramaru A (1995) Numerical study of nucleation and growth of bubbles inviscous magmas. J Geophys Res 100:1913–1931

    ADS  Google Scholar 

  133. Tuffen H, Dingwell DB, Pinkerton H (2003) Repeated fracture and healing ofsilicic magma generates flow banding and earthquakes? Geology 31:1089–1092

    ADS  Google Scholar 

  134. Uhira K, Yamasato H, Takeo M (1994) Source mechanism of seismic wavesexcited by pyroclastic flows observed at Unzen Volcano, Japan. J Geophys Res 99:17757–17773

    ADS  Google Scholar 

  135. van der Waals JD (1979) The thermodynamic theory of capillarity under thehypothesis of a continuous variation of density. Verhandel Konink. Acad. Weten. Amsterdam, (Sect. 1), 1, pp 1–56. Translation byRowlingson JS. J Statist Phys 20:197–244

    Google Scholar 

  136. Vergniolle S, Brandeis G, Mareschal JC (1996) Strombolian explosions,2. Eruption dynamics determined from acoustic measurements. J Geophys Res 101:20449–20466

    ADS  Google Scholar 

  137. Waite GP, Chouet BA, Dawson PB (2008) Eruption dynamics at Mount St. Helensimaged from broadband seismic waveforms: Interaction of the shallow magmatic and hydrothermal systems. J Geophys Res 113,B02305. doi:10.1029/2007JB005259

  138. Wallis GB (1969) One‐dimensional Two-phase Flow. MacGraw‐Hill,New York, pp 408

    Google Scholar 

  139. White RA (1996) Precursory deep long‐period earthquakes at MountPinatubo: Spatio‐temporal link to a basalt trigger. In: Newhall CG, Punongbayan RS (eds) Fire and Mud: Eruptions and Lahars of Mount Pinatubo,Philippines. University of Washington Press, Seattle, pp 307–326

    Google Scholar 

  140. Wilson L, Head JW (1981) Ascent and eruption of basaltic magma on the earthand moon. J Geophys Res 86:2971–3001

    ADS  Google Scholar 

  141. Xu A, Gonnella G, Lamura A (2003) Phase‐separating binary fluids underoscillatory shear. Phys Rev E 67:056105

    ADS  Google Scholar 

  142. Xu A, Gonnella G, Lamura A (2004) Phase separation of incompressible binaryfluids with lattice Boltzmann methods. Physica A 331:10–22

    ADS  Google Scholar 

  143. Yamamoto M, Kawakatsu H, Kaneshima S, Mori T, Tsutsui T, Sudo Y, Morita Y(1999) Detection of a crack-like conduit beneath the active crater at Aso Volcano, Japan. Geophys Res Lett26:3677–3680

    ADS  Google Scholar 

  144. Yamamoto M, Kawakatsu H, Yomogida K, Koyama J (2002) Long‐period (12sec) volcanic tremor observed at Usu 2000 eruption: seismological detection of a deep magma plumbing system. Geophys Res Lett29(9):1329. doi:10.1029/2001GL013996

    ADS  Google Scholar 

  145. Yoon SW, Crum LA, Prosperetti A, Lu NQ (1991) An investigation of thecollective oscillations of a bubble cloud. J Acoust Soc Am 89:700–706

    ADS  Google Scholar 

  146. Yue P, Feng JJ, Liu C, Shen J (2004) A diffuse‐interface methodfor simulating two-phase flows of complex fluids. J Fluid Mech 515:293–317

    MathSciNet  ADS  MATH  Google Scholar 

  147. Zhang Y, Xu Z, Liu Y (2003) Viscosity of hydrous rhyolitic melts inferredfrom kinetic experiments: A new viscosity model. Am Mineral 88:1741–1752

    Google Scholar 

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Acknowledgment

I am grateful to Phil Dawson for his assistance in drafting figures. I am indebted to RobertTilling and David Hill for careful reviews and helpful suggestions.

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  1. US Geological Survey, Menlo Park, USA

    Bernard Chouet

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Chouet, B. (2009). Volcanoes, Non-linear Processes in. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_582

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