Bulletin of Volcanology

, Volume 74, Issue 8, pp 1777–1805 | Cite as

Probabilistic eruption forecasting at short and long time scales

  • Warner MarzocchiEmail author
  • Mark S. Bebbington
Review Article


Any effective volcanic risk mitigation strategy requires a scientific assessment of the future evolution of a volcanic system and its eruptive behavior. Some consider the onus should be on volcanologists to provide simple but emphatic deterministic forecasts. This traditional way of thinking, however, does not deal with the implications of inherent uncertainties, both aleatoric and epistemic, that are inevitably present in observations, monitoring data, and interpretation of any natural system. In contrast to deterministic predictions, probabilistic eruption forecasting attempts to quantify these inherent uncertainties utilizing all available information to the extent that it can be relied upon and is informative. As with many other natural hazards, probabilistic eruption forecasting is becoming established as the primary scientific basis for planning rational risk mitigation actions: at short-term (hours to weeks or months), it allows decision-makers to prioritize actions in a crisis; and at long-term (years to decades), it is the basic component for land use and emergency planning. Probabilistic eruption forecasting consists of estimating the probability of an eruption event and where it sits in a complex multidimensional time–space–magnitude framework. In this review, we discuss the key developments and features of models that have been used to address the problem.


Probabilistic eruption forecasting Precursors Stochastic modeling Time-space-magnitude forecasts 



The authors thank Geoff Wadge and Britt Hill for their painstaking and helpful reviews of the manuscript content and style, and editor Stephen Self for careful checking of, and additional suggestions on, the result. Commitments elsewhere forced Willy Aspinall to withdraw from the authoring team, after making a number of contributions to the paper organization.


  1. Akaike H (1977) On entropy maximization principle. In: Krishnaiah PR (ed) Applications of statistics. North-Holland, Amsterdam, pp 27–41Google Scholar
  2. Amoruso A, Crescentini L (2009) Shape and volume change of pressurized ellipsoidal cavities from deformation and seismic data. J Geophys Res 114:B02210CrossRefGoogle Scholar
  3. Amoruso A, Crescentini L (2011) Modelling deformation due to a pressurized ellipsoidal cavity, with reference to the Campi Flegrei caldera, Italy. Geophys Res Lett 38:L01303CrossRefGoogle Scholar
  4. Amoruso A, Crescentini L, Berrino G (2008) Simultaneous inversion of deformation and gravity changes in a horizontally layered half-space: evidences for magma intrusion during the 1982–1984 unrest at Campi Flegrei caldera (Italy). Earth Plan Sci Lett 272:181–188CrossRefGoogle Scholar
  5. Aspinall W (2006) Structured elicitation of expert judgement for probabilistic hazard and risk assessment in volcanic eruptions. In: Mader HM, Coles SG, Connor CB, Connor LJ (eds) Statistics in volcanology. IAVCEI Publications. ISBN 978-1-86239-208-3, pp 15–30Google Scholar
  6. Aspinall WP, Woo G, Voight B, Baxter PJ (2003) Evidence-based volcanology: application to eruption crises. J Volcanol Geotherm Res 128:273–285CrossRefGoogle Scholar
  7. Aspinall W, Carniel R, Jaquet O, Woo G, Hincks T (2006) Using hidden multi-state Markov models with multi-parameter volcanic data to provide empirical evidence for alert level decision-support. J Volcanol Geotherm Res 153:112–124CrossRefGoogle Scholar
  8. Bak P, Tang C, Wiesenfeld K (1987) Self-organized criticality: an explanation of the 1/f noise. Phys Rev Lett 59:381–384CrossRefGoogle Scholar
  9. Battaglia M, Hill DP (2009) Analytical modeling of gravity changes and crustal deformation at volcanoes: the Long Valley caldera, California, case study. Tectonophysics 471:45–57CrossRefGoogle Scholar
  10. Battaglia M, Roberts C, Segall P (2003) The mechanics of unrest at Long Valley caldera, California: 2. Constraining the nature of the source using geodetic and micro-gravity data. J Volcanol Geotherm Res 127:219–245CrossRefGoogle Scholar
  11. Battaglia J, Ferrazzini V, Staudacher T, Aki K, Cheminee J (2005) Pre-eruptive migration of earthquakes at the Piton de la Fournaise volcano (Reunion Island). Geophys J Int 161:549–558CrossRefGoogle Scholar
  12. Bebbington MS (2007) Identifying volcanic regimes using hidden Markov models. Geophys J Int 171:921–942CrossRefGoogle Scholar
  13. Bebbington M (2008) Incorporating the eruptive history in a stochastic model for volcanic eruptions. J Volcanol Geotherm Res 175:325–333CrossRefGoogle Scholar
  14. Bebbington M (2009) Volcanic eruptions: stochastic models of occurrence patterns. In: Meyers B (ed) Encyclopedia of complexity and system science, vol 9. Springer, New York, pp 9831–9861Google Scholar
  15. Bebbington M (2010) Trends and clustering in the onsets of volcanic eruptions. J Geophys Res 115:B01203CrossRefGoogle Scholar
  16. Bebbington M, Cronin SJ (2011) Spatio-temporal hazard estimation in the Auckland Volcanic Field, New Zealand, with a new event-order model. Bull Volcanol 73:55–72CrossRefGoogle Scholar
  17. Bebbington M, Harte D (2001) On the statistics of the linked stress release process. J Appl Probab 38A:176–187CrossRefGoogle Scholar
  18. Bebbington MS, Lai CD (1996a) On nonhomogeneous models for volcanic eruptions. Math Geol 28:585–600CrossRefGoogle Scholar
  19. Bebbington MS, Lai CD (1996b) Statistical analysis of New Zealand volcanic occurrence data. J Volcanol Geotherm Res 74:101–110CrossRefGoogle Scholar
  20. Bebbington MS, Lai CD (1998) A generalised negative binomial and applications. Commun Stat, Theory Methods 27:2515–2533CrossRefGoogle Scholar
  21. Bebbington MS, Marzocchi, W (2011) Stochastic models for earthquake triggering of volcanic eruptions. J Geophys Res 116:B05204CrossRefGoogle Scholar
  22. Bebbington M, Cronin S, Chapman I, Turner M (2008) Quantifying volcanic ash fall hazard to electricity infrastructure. J Volcanol Geotherm Res 177:1055–1062CrossRefGoogle Scholar
  23. Bedford T, Cooke R (2001) Probabilistic risk analysis: foundations and methods. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  24. Bell A, Naylor M, Heap M, Main I (2011) Forecasting volcanic eruptions and other material failure phenomena: an evaluation of the failure forecast method. Geophys Res Lett 38:L15304CrossRefGoogle Scholar
  25. Benoit JP, McNutt SR, Barboza V (2003) Duration-amplitude distribution of volcanic tremor. J Geophys Res 108:2146CrossRefGoogle Scholar
  26. Bommer J, Scherbaum F (2008) The use and misuse of logic trees in probabilistic seismic hazard analysis. Earthq Spectra 24:9970–1009CrossRefGoogle Scholar
  27. Bonaccorso A, Aloisi M, Mattia M (2002) Dike emplacement forerunning the Etna July 2001 eruption modeled through continuous tilt and GPS data. Geophys Res Lett 29:1624CrossRefGoogle Scholar
  28. Bonafede M (1991) Hot fluid migration: an efficient source of ground deformation—application to the 1982–84 crisis at Phlegraean Fields, Italy. J Volcanol Geotherm Res 48:187–198CrossRefGoogle Scholar
  29. Brenguier F, Shapiro N, Campillo M, Ferrazzini V, Duputel Z, Coutant O, Nercessian A (2008) Towards forecasting volcanic eruptions using seismic noise. Nat Geosci 1:126–130CrossRefGoogle Scholar
  30. Bryan CJ, Sherburn S (2003) Eruption-induced modifications to volcanic seismicity at Ruapehu, New Zealand, and its implications for eruption forecasting. Bull Volcanol 65:30–42Google Scholar
  31. Budnitz RJ, Apostolakis G, Boore DM, Cluff LS, Coppersmith KJ, Cornell CA, Morris PA (1997) Senior Seismic Hazard Analysis Committee; recommendations for probabilistic seismic hazard analysis: guidance on uncertainty and use of experts, vol 1–2. U.S. Nuclear Regulatory Commission, U.S. Dept. of Energy, Electric Power Research Institute; NUREG/CR-6372, UCRL-ID-122160Google Scholar
  32. Burt ML, Wadge G, Curnow RN (2001) An objective method for mapping hazardous flow deposits from the stratigraphic record of stratovolcanoes: a case example from Montange Pelée. Bull Volcanol 63:98–111CrossRefGoogle Scholar
  33. Burt ML, Wadge G, Scott WA (1994) Simple stochastic modelling of the eruption history of a basaltic volcano: Nyamuragira, Zaire. Bull Volcanol 56:87–97Google Scholar
  34. Caniaux G (2005) Statistical analysis of the volcanic eruption frequency in the Azores Islands: a contribution to risk assessment. Bull Soc Géol Fr 176:107–120Google Scholar
  35. Carta S, Figari R, Sartoris G, Sassi R, Scandone R (1981) A statistical model for Vesuvius and its volcanological implications. Bull Volcanol 44:129–151CrossRefGoogle Scholar
  36. Castro JM, Dingwell DB (2009) Rapid ascent of rhyolitic magma at Chaitén volcano, Chile. Nature 461:780–784CrossRefGoogle Scholar
  37. Chastin SFM, Main IG (2003) Statistical analysis of daily seismic event rate as a precursor to volcanic eruptions. Geophys Res Lett 30:1671CrossRefGoogle Scholar
  38. Chouet B (1996) Long-period volcano seismicity: its source and use in eruption forecasting. Nature 380:309–316CrossRefGoogle Scholar
  39. Claeskens G, Hjort NL (2008) Model selection and model averaging. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  40. Condit CD, Connor CB (1996) Recurrence rates of volcanism in basaltic volcanic fields: an example from the Springerville volcanic field, Arizona. Geol Soc Am Bull 108:1225–1241CrossRefGoogle Scholar
  41. Connor CB, Connor LJ (2009) Estimating spatial density with kernel methods. In: Connor CB, Chapman NA, Connor LJ (eds) Volcanic and tectonic hazard assessment for nuclear facilities. Cambridge University Press, Cambridge, UK, pp 346–368CrossRefGoogle Scholar
  42. Connor CB, Hill BE (1995) Three nonhomogeneous Poisson models for the probability of basaltic volcanism: application to the Yucca Mountain region, Nevada. J Geophys Res 100:10107–10125CrossRefGoogle Scholar
  43. Connor CB, Stamatakos JA, Ferrill DA, Hill BE, Ofoegbu G, Conway FM, Sagar B, Trapp JS (2000) Geologic factors controlling patterns of small-volume basaltic volcanism: application to a volcanic hazards assessment at Yucca Mountain, Nevada. J Geophys Res 105:417–432CrossRefGoogle Scholar
  44. Connor CB, Sparks RSJ, Mason RM, Bonadonna C, Young SR (2003) Exploring links between physical and probabilistic models of volcanic eruptions: the Soufriere Hills volcano, Montserrat. Geophys Res Lett 30:1701CrossRefGoogle Scholar
  45. Conway FM, Connor CB, Hill BE, Condit CD, Mullaney K, Hall CM (1998) Recurrence rates of basaltic volcanism in SP cluster, San Francisco volcanic field, Arizona. Geology 26:655–658CrossRefGoogle Scholar
  46. Cooke RM (1991) Experts in uncertainty: opinion and subjective probability in science. Oxford Univ Press, OxfordGoogle Scholar
  47. Cornelius RR, Voight B (1996) Real-time seismic amplitude measurement (RSAM) and seismic spectral amplitude measurement (SSAM) analyses with the materials failure forecast method (FFM), June 1991 explosive eruption at Mount Pinatubo. In: Newhall CG, Punongbayan RS (eds) Fire and mud, eruptions and lahars of Mount Pinatubo Philippines, pp 249–267Google Scholar
  48. Cox DR, Lewis PAW (1966) The statistical analysis of series of events. Methuen, LondonGoogle Scholar
  49. Cronin S, Bebbington M, Lai CD (2001) A probabilistic assessment of eruption recurrence on Taveuni volcano, Fiji. Bull Volcanol 63:274–288CrossRefGoogle Scholar
  50. Crowe BM, Johnson ME, Beckman RJ (1982) Calculation of the probability of volcanic disruption of a high-level radioactive waste repository within southern Nevada, USA. Radioact Waste Manage 3:167–190Google Scholar
  51. Crowe BM, Wallmann P, Bowker LM (1998) Probabilistic modeling of volcanism data: Final volcanic hazard studies for the Yucca Mountain site. In: Perry FV et al (eds) Volcanism studies: final report for the Yucca Mountain project. Los Alamos National Laboratory Report LA-13478, Los Alamos National Laboratory, Los Alamos, NM, p 415Google Scholar
  52. Davis PM (1986) Surface deformation due to inflation of an arbitrarily oriented triaxial ellipsoidal cavity in an elastic half-space, with reference to Kilauea Volcano, Hawaii. J Geophys Res 91:7429–7438CrossRefGoogle Scholar
  53. Decker RW (1986) Forecasting volcanic eruptions. Ann Rev Earth Planet Sci 14:267–291CrossRefGoogle Scholar
  54. De la Cruz-Reyna S (1991) Poisson-distributed patterns of explosive eruptive activity. Bull Volcanol 54:57–67CrossRefGoogle Scholar
  55. De la Cruz-Reyna S (1993) Random patterns of occurrence of explosive eruptions at Colima volcano, Mexico. J Volcanol Geotherm Res 55:51–68CrossRefGoogle Scholar
  56. De la Cruz-Reyna S, Carrasco-Nunez G (2002) Probabilistic hazard analysis of Citlaltepetl (Pico de Orizaba) volcano, eastern Mexican volcanic belt. J Volcanol Geotherm Res 113:307–318CrossRefGoogle Scholar
  57. Deligne NI, Coles SG, Sparks RSJ (2010) Recurrence rates of large explosive volcanic eruptions. J Geophys Res 115:B06203. doi: 10.1029/2009JB006554 CrossRefGoogle Scholar
  58. Duong T (2007) ks: kernel density estimations and kernel discriminant analysis for multivariate data in R. J Statist Softw 21(7):1–16Google Scholar
  59. Dzierma Y, Wehrmann H (2010) Eruption time series statistically examined: Probabilities of future eruptions at Villarrica and Llaima Volcanoes, Southern Volcanic Zone, Chile. J Volcanol Geotherm Res 193:82–92CrossRefGoogle Scholar
  60. Dzurisin D (2003) A comprehensive approach to monitoring volcano deformation as a window on the eruption cycle. Rev Geophys 41:1001CrossRefGoogle Scholar
  61. Eliasson J, Larsen G, Gudmundsson MT, Sigmundsson F (2006) Probabilistic model for eruptions and associated flood events in the Katla caldera, Iceland. Comput Geosci 10:179–200CrossRefGoogle Scholar
  62. Field EH, Dawson TE, Felzer KR, Frankel AD, Gupta V, Jordan TH, Parsons T, Petersen MD, Stein RS, Weldon RJ, Wills CJ (2007) The uniform California earthquake rupture forecast, Version 2 (UCERF 2). USGS Open File Report 2007–1437Google Scholar
  63. Fournier T J, Pritchard ME, Riddick SN (2010) Duration, magnitude, and frequency of subaerial volcano deformation events: new results from Latin America using InSAR and a global synthesis. Geochem Geophys Geosyst 11:Q01003CrossRefGoogle Scholar
  64. Furlan, C (2010) Extreme value methods for modelling historical series of large volcanic magnitudes. Statist Model 10:113–132CrossRefGoogle Scholar
  65. Garcia-Aristizabal A, Marzocchi W, Fujita E (2012) A Brownian model for recurrent volcanic eruptions: an application to Miyakejima volcano (Japan). Bull Volcanol 74:545–558CrossRefGoogle Scholar
  66. Gelman A, Carlin JB, Stern HS, Rubin DB (1995) Bayesian data analysis. CRC, Boca Raton, FLGoogle Scholar
  67. Gerst A, Savage M (2004) Seismic anisotropy beneath Ruapehu Volcano: a possible eruption forecasting tool. Science 306:1543–1547CrossRefGoogle Scholar
  68. Gillies D (2000) Philosophical theories of probability. New York, RoutledgeGoogle Scholar
  69. Grasso JR, Zaliapin I (2004) Predictability of volcano eruption: Lessons from a basaltic effusive volcano. Geophys Res Lett 31:L05602CrossRefGoogle Scholar
  70. Guidoboni E, Ciuccarelli C (2011) The Campi Flegrei caldera: historical revision and new data on seismic crises, bradyseisms, the Monte Nuovo eruption and ensuing earthquakes (twelfth century 1582 AD). Bull Volcanol 73:655–677CrossRefGoogle Scholar
  71. Guttorp P, Thompson ML (1991) Estimating second-order parameters of volcanicity from historical data. J Am Statist Assoc 86:578–583CrossRefGoogle Scholar
  72. Hainzl S, Ogata Y (2005) Detecting fluid signals in seismicity data through statistical earthquake modeling. J Geophys Res 110:B05S07CrossRefGoogle Scholar
  73. Hammer C, Neuberg J (2009) On the dynamical behavior of low-frequency earthquake swarms prior to a dome collapse of Soufrière Hill volcano, Montserrat. Geophys Res Lett 36:L06305CrossRefGoogle Scholar
  74. Hill BE, Connor CB, Jarzemba MS, La Femina PC, Navarro M, Strauch W (1998) 1995 eruptions of Cerro Negro volcano, Nicaragua, and risk assessment for future eruptions. Geol Soc Am Bull 110:1231–1241CrossRefGoogle Scholar
  75. Ho CH (1990) Bayesian analysis of volcanic eruptions. J Volcanol Geotherm Res 43:91–98CrossRefGoogle Scholar
  76. Ho CH (1991) Nonhomogeneous Poisson model for volcanic eruptions. Math Geol 23:167–173CrossRefGoogle Scholar
  77. Ho CH (1992) Statistical control chart for regime identification in volcanic time-series. Math Geol 24:775–787CrossRefGoogle Scholar
  78. Hurvich CM, Tsai CL (1989) Regression and time series model selection in small samples. Biometrika 76:297–307CrossRefGoogle Scholar
  79. Iguchi M, Yakiwara H, Tameguri T, Hendrasto M, Hirabayashi JI (2008) Mechanism of explosive eruption revealed by geophysical observations at the Sakurajima, Suwanosejima and Semeru volcanoes. J Volcanol Geotherm Res 178:1–9CrossRefGoogle Scholar
  80. Jaquet O, Carniel R (2001) Stochastic modelling at Stromboli: a volcano with remarkable memory. J Volcanol Geotherm Res 105:249–262CrossRefGoogle Scholar
  81. Jaquet O, Low S, Martinelli B, Dietrich V, Gilby D (2000) Estimation of volcanic hazards based on Cox stochastic processes. Phys Chem Earth (A) 25:571–579CrossRefGoogle Scholar
  82. Jaquet O, Carniel R, Sparks S, Thompson G, Namar R, Dicecca M (2006) DEVIN: a forecasting approach using stochastic methods applied to the Soufriere Hills Volcano. J Volcanol Geotherm Res 153:97–111CrossRefGoogle Scholar
  83. Jellinek AM, Bercovici D (2011) Seismic tremors and magma wagging during explosive volcanism. Nature 470:522–526. doi: 10.1038/nature09828 CrossRefGoogle Scholar
  84. Jeffreys H (1961) Theory of probability, 3rd edn. Oxford University Press, OxfordGoogle Scholar
  85. Jiang R, Murthy DNP (1998) Mixture of Weibull distributions—parametric characterization of failure rate function. Appl Stoc Models Data Anal 14:47–65CrossRefGoogle Scholar
  86. Jordan TH (2006) Earthquake predictability, brick by brick. Seismol Res Lett 77:3–6CrossRefGoogle Scholar
  87. Jordan TH, Chen Y-T, Gasparini P, Madariaga R, Main I, Marzocchi W, Papadopoulos G, Sobolev G, Yamaoka K, Zschau J (2011) Operational earthquake forecasting: state of knowledge and guidelines for implementation. Ann Geophys 54:315–391. doi: 10.4401/ag-5350 Google Scholar
  88. Kiyosugi K, Connor CB, Zhao D, Connor LJ, Tanaka K (2010) Relationships between volcano distribution, crustal structure, and P-wave tomography: an example from the Abu Monogenetic Volcano Group, SW Japan. Bull Volcanol 72:331–340CrossRefGoogle Scholar
  89. Klein FW (1982) Patterns of historical eruptions at Hawaiian volcanoes. J Volcanol Geotherm Res 12:1–35CrossRefGoogle Scholar
  90. Kilburn C (2003) Multiscale fracturing as a key to forecasting volcanic eruptions. J Volcanol Geotherm Res 125:271–289CrossRefGoogle Scholar
  91. Kilburn CRJ, Voight B (1998) Slow rock fracture as eruption precursor at Soufriere Hills volcano, Montserrat. Geophys Res Lett 25:3665–3668CrossRefGoogle Scholar
  92. Lavallée Y, Meredith P, Dingwell D, Hess K, Wassermann J, Cordonnier B, Gerik A, Kruhl J (2008) Seismogenic lavas and explosive eruption forecasting. Nature 453:507–510CrossRefGoogle Scholar
  93. Linde AT, Ágústsson K, Sacks IS, Stefánsson R (1993) Mechanism of the 1991 eruption of Hekla from continuous borehole strain monitoring. Nature 365:737–740CrossRefGoogle Scholar
  94. Lindsay J, Marzocchi W, Jolly G, Constantinescu R, Selva J, Sandri L (2010) Towards real-time eruption forecasting in the Auckland Volcanic Field: application of BET_EF during the New Zealand national disaster exercise ‘Ruaumoko’. Bull Volcanol 72:185–204CrossRefGoogle Scholar
  95. Lombardi AM, Marzocchi W, Selva J (2006) Exploring the evolution of a volcanic seismic swarm: the case of the 2000 Izu Islands swarm. Geophys Res Lett 33:L07310CrossRefGoogle Scholar
  96. Luhr JF, Carmichael ISE (1990) Petrological modeling of cyclical eruptive activity at Volcan Colima, Mexico. J Volcanol Geotherm Res 42:235–260CrossRefGoogle Scholar
  97. Lutz TM (1986) An analysis of the orientation of large-scale crustal structures: a statistical approach based on areal distributions of pointlike features. J Geophys Res 91:421–434CrossRefGoogle Scholar
  98. Lutz TM, Gutmann JT (1995) An improved method for determining and characterizing alignments of point-like features and its implications for the Pinacate volcanic field, Sonora, Mexico. J Geophys Res 100:17659–17670CrossRefGoogle Scholar
  99. Magill CR, McAneney KJ, Smith IEM (2005) Probabilistic assessment of vent locations for the next Auckland volcanic field event. Math Geol 37:227–242CrossRefGoogle Scholar
  100. Manga M, Brodsky, E (2006) Seismic triggering of eruptions in the far field: volcanoes and geysers. Ann Rev Earth Planet Sci 34:263–291CrossRefGoogle Scholar
  101. Marti J, Aspinall WP, Sobradelo R, Felpeto A, Geyer A, Ortiz R, Baxter P, Cole P, Pacheco J, Blanco MJ, Lopez C (2008) A long-term volcanic hazard event tree for Teide-Pico Viejo stratovolcanoes (Tenerife, Canary Islands). J Volcanol Geoth Res 178:543–552CrossRefGoogle Scholar
  102. Martin AJ, Umeda K, Connor CB, Weller JN, Zhao D, Takahashi M (2004) Modeling long-term volcanic hazards through Bayesian inference: an example from the Tohoku volcanic arc, Japan. J Geophys Res 109:B10208CrossRefGoogle Scholar
  103. Martin DP, Rose WI (1981) Behavioral patterns of Fuego volcano, Guatemala. J Volcanol Geotherm Res 10:67–81CrossRefGoogle Scholar
  104. Marzocchi W, Woo G (2007) Probabilistic eruption forecasting and the call for an evacuation. Geophys Res Lett 34:L22310CrossRefGoogle Scholar
  105. Marzocchi W, Woo G (2009) Principles of volcanic risk metrics: theory and the case study of Mt. Vesuvius and Campi Flegrei (Italy). J Geophys Res 114:B03213CrossRefGoogle Scholar
  106. Marzocchi W, Zaccarelli L (2006) A quantitative model for the time-size distribution of eruptions. J Geophys Res 111:B04204CrossRefGoogle Scholar
  107. Marzocchi W, Zechar JD (2011) Earthquake forecasting and earthquake prediction: different approaches for obtaining the best model. Seismol Res Lett 82:442–448CrossRefGoogle Scholar
  108. Marzocchi W, Mulargia F, Gonzato G (1997) Detecting low-dimensional chaos in geophysical time series. J Geophys Res 102:3195–3209CrossRefGoogle Scholar
  109. Marzocchi W, Sandri L, Gasparini P, Newhall C, Boschi E (2004) Quantifying probabilities of volcanic events: the example of volcanic hazard at Mt Vesuvius. J Geophys Res 109:B11201CrossRefGoogle Scholar
  110. Marzocchi W, Sandri L, Selva J (2008) BET_EF: a probabilistic tool for long- and short-term eruption forecasting. Bull Volcanol 70:623–632CrossRefGoogle Scholar
  111. Marzocchi W, Sandri L, Selva J (2010) BET_VH: a probabilistic tool for long-term volcanic hazard assessment. Bull Volcanol 72:705–716CrossRefGoogle Scholar
  112. Mastrolorenzo G, Petrone P, Pappalardo L, Sheridan MF (2006) The Avellino 3780 yr BP catastrophe as worst-case scenario for a future eruption at Vesuvius. Proc Natl Acad Sci USA 103:4366–4370CrossRefGoogle Scholar
  113. Medina Martinez F (1983) Analysis of the eruptive history of the Volcan de Colima, Mexico (1560–1980). Geofis Int 22:157–178Google Scholar
  114. Mendoza-Rosas AT, De la Cruz-Reyna S (2008) A statistical method liking geological and historical eruption time series for volcanic hazard estimations: application to active polygenetic volcanoes. J Volcanol Geotherm Res 176:277–290CrossRefGoogle Scholar
  115. Mendoza-Rosas AT, De la Cruz-Reyna S (2009) A mixture of exponentials distribution for simple and precise assessment of the volcanic hazard. Nat Hazards Earth Syst Sci 9:425–431CrossRefGoogle Scholar
  116. Mendoza-Rosas AT, De la Cruz-Reyna S (2010) Hazard estimates for El Chicon volcano, Chiapas, Mexico: a statistical approach for complex eruptive histories. Nat Hazards Earth Syst Sci 10:1159–1170CrossRefGoogle Scholar
  117. Miller V, Savage M (2001) Changes in seismic anisotropy after volcanic eruptions: evidence from Mount Ruapehu. Science 293:2231–2233CrossRefGoogle Scholar
  118. Mogi K (1958) Relations between the eruptions of various volcanoes and the deformations of the ground surface around them. Bull Earthq Res Inst Univ Tokyo 36:99–134Google Scholar
  119. Moran SC, Newhall CG, Roman DC (2011) Failed magmatic eruptions: late-stage cessation of magma ascent. Bull Volcanol 73(2):115–122 doi: 10.1007/s00445-010-0444-x CrossRefGoogle Scholar
  120. Mulargia F, Tinti S, Boschi E (1985) A statistical analysis of flank eruptions on Etna volcano. J Volcanol Geotherm Res 23:263–272CrossRefGoogle Scholar
  121. Mulargia F, Gasperini P, Tinti S (1987) Identifying regimes in eruptive activity: an application to Etna volcano. J Volcanol Geotherm Res 34:89–106CrossRefGoogle Scholar
  122. Mulargia F, Gasperini P, Marzocchi W (1991) Pattern recognition applied to volcanic activity: identification of the precursory patterns to Etna recent flank eruptions and periods of rest. J Volcanol Geotherm Res 45:187–196CrossRefGoogle Scholar
  123. Mulargia F, Marzocchi W, Gasperini P (1992) Statistical identification of physical patterns which accompany eruptive activity on Mount Etna, Sicily. J Volcanol Geotherm Res 53:289–296CrossRefGoogle Scholar
  124. Munoz M (1983) Eruption patterns of the Chilean volcanoes Villarrica, Llaima, and Tupungatito. Pure Appl Geophys 121:835–852CrossRefGoogle Scholar
  125. Neri A, Aspinall W, Cioni R, Bertagnini A, Baxter P, Zuccaro G, Andronico D, Barsotti S, Cole P, Esposti Ongaro T (2008) Developing an event tree for probabilistic hazard and risk assessment at Vesuvius. J Volcanol Geotherm Res 178:397–415CrossRefGoogle Scholar
  126. Neuberg J (2000) Characteristics and causes of shallow seismicity in andesite volcanoes. Philos Trans Roy Soc A 358:1533–1546CrossRefGoogle Scholar
  127. Neuberg JW (2011) Earthquakes, volcanogenic. In: Gupta HK (ed) Encyclopedia of solid earth geophysics, vol 1. Springer, pp 261–269Google Scholar
  128. Newhall C, Hoblitt R (2002) Constructing event trees for volcanic crises. Bull Volcanol 64:3–20CrossRefGoogle Scholar
  129. Newhall CG, Self S (1982) The volcanic explosivity index (VEI): an estimate of the explosive magnitude for historical eruptions. J Geophys Res 87:1231–1238CrossRefGoogle Scholar
  130. Novelo-Casanova DA, Valdes-Gonzales C (2008) Seismic pattern recognition techniques to predict large eruptions at the Popocatépetl, Mexico, volcano. J Volcanol Geotherm Res 176:583–590CrossRefGoogle Scholar
  131. Ogata Y (1988) Statistical models for earthquake occurrences and residual analysis for point processes. J Am Statist Assoc 83:9–27CrossRefGoogle Scholar
  132. Ogata Y (1998) Space-time point-process models for earthquake occurrences. Ann Inst Stat Math 50:379–402CrossRefGoogle Scholar
  133. Orsi G, Di Vito MA, Selva J, Marzocchi W (2009) Long-term forecast of eruption style and size at Campi Flegrei caldera (Italy). Earth Plan Sci Lett 287:265–276CrossRefGoogle Scholar
  134. Passarelli L, Brodsky EE (2012) The correlation between run-up and repose times of volcanic eruptions. Geophys J Int 188(3):1025–1045 doi: 10.1111/j.1365-246X.2011.05298.x CrossRefGoogle Scholar
  135. Passarelli L, Sandri L, Bonazzi A, Marzocchi W (2010a) Bayesian hierarchical time predictable model for eruption occurrence: an application to Kilauea Volcano. Geophys J Int 181:1525–1538Google Scholar
  136. Passarelli L, Sanso B, Sandri L, Marzocchi W (2010b) Testing forecasts of a new Bayesian time-predictable model of eruption occurrence. J Volcanol Geotherm Res 198:57–75CrossRefGoogle Scholar
  137. Pozgay SH, White RA, Wiens DA, Shore PJ, Sauter AW, Kaipat JL (2005) Seismicity and tilt associated with the 2003 Anatahan eruption sequence. J Volcanol Geotherm Res 146:60–76CrossRefGoogle Scholar
  138. Proschan F (1963) Theoretical explanation of decreasing failure rate. Technometrics 5:375–383CrossRefGoogle Scholar
  139. Pyle DM (1998) Forecasting sizes and repose times of future extreme volcanic events. Geology 26:367–370CrossRefGoogle Scholar
  140. Pyle DM (2000) Sizes of volcanic eruptions. In: Sigurdsson H et al (eds) Encyclopedia of volcanoes. Academic Press, San Diego, pp 263–269Google Scholar
  141. Ramos EG, Laguerta EP, Hamburger MW (1996) Seismicity and magmatic resurgence at Mount Pinatubo in 1992. In: Newhall CG, Punongbayan RS (eds) Fire and mud, eruptions and lahars of Mount Pinatubo, Philippines, pp 387–406Google Scholar
  142. Reyment RA (1969) Statistical analysis of some volcanologic data regarded as series of point events. Pure Appl Geophys 74:57–77CrossRefGoogle Scholar
  143. Rodado A, Bebbington M, Noble A, Cronin S, Jolly G (2011) On selection of analogue volcanoes. Math Geosci 43:505–519CrossRefGoogle Scholar
  144. Roman D, Neuberg J, Luckett R (2006) Assessing the likelihood of volcanic eruption through analysis of volcanotectonic earthquake faultplane solutions. Earth Plan Sci Lett 248:229–237CrossRefGoogle Scholar
  145. Rosi M (1996) Quantitative reconstruction of recent volcanic activity: a contribution to fore- casting of future eruptions. In: Scarpa R, Tilling RI (eds) Monitoring and mitigation of volcano hazards. Springer, Berlin, pp 631–674Google Scholar
  146. Salvi F, Scandone R, Palma C (2006) Statistical analysis of the historical activity of Mount Etna, aimed at the evaluation of volcanic hazard. J Volcanol Geotherm Res 154:159–168CrossRefGoogle Scholar
  147. Sandri L, Marzocchi W, Gasperini P (2005) Some insights on the occurrence of recent volcanic eruptions of Mount Etna volcano (Sicily, Italy). Geophys J Int 163:1203–1218CrossRefGoogle Scholar
  148. Sandri L, Guidoboni E, Marzocchi W, Selva J (2009) Bayesian Event Tree (BET) for eruption forecasting at Vesuvius, Italy: a retrospective forward application to 1631 eruption. Bull Volcanol 71:729–745CrossRefGoogle Scholar
  149. Sandri L, Jolly G, Lindsay J, Howe T, Marzocchi W (2012) Combining long- and short-term probabilistic volcanic hazard assessment with cost-benefit analysis to support decision making in a volcanic crisis from the Auckland Volcanic Field, New Zealand. Bull Volcanol 74(3):705–723 doi: 10.1007/s00445-011-0556-y CrossRefGoogle Scholar
  150. Scandone R, Arganese G, Galdi F (1993) The evaluation of volcanic risk in the Vesuvian area. J Volcanol Geotherm Res 58:263–271CrossRefGoogle Scholar
  151. Selva J, Marzocchi W, Civetta L, Del Pezzo E, Papale P (2010a) Emergency preparedness: community-based short-term eruption forecasting at Campi Flegrei. EGU General Assembly 2010, held 2–7 May 2010 in Vienna, Austria, p 10318Google Scholar
  152. Selva J, Costa A, Marzocchi W, Sandri L (2010b) BET_VH: exploring the influence of natural uncertainties on long-term hazard from tephra fallout at Campi Flegrei (Italy). Bull Volcanol 72:717–733CrossRefGoogle Scholar
  153. Selva J, Orsi G, Di Vito M, Marzocchi W, Sandri L (2012) Probability hazard map for future vent opening at the Campi Flegrei caldera, Italy. Bull Volcanol 74(2):497–510 doi: 10.1007/s00445-011-0528-2 CrossRefGoogle Scholar
  154. Settle M, McGetchin TR (1980) Statistical analysis of persistent explosive activity at Stromboli, 1971: Implications for eruption prediction. J Volcanol Geotherm Res 8:45–58CrossRefGoogle Scholar
  155. Shelly D, Hill DP (2009) Migrating swarms of brittle-failure earthquakes in the lower crust beneath Mammoth Mountain, California. Geophys Res Lett 38:L20307CrossRefGoogle Scholar
  156. Sigurdsson H (editor in chief) et al (2000) Encyclopedia of volcanoes. Academic Press, San DiegoGoogle Scholar
  157. Simkin T, Siebert L (1994) Volcanoes of the world. Geosciences, Tucson, ArizGoogle Scholar
  158. Smethurst L, James MR, Pinkerton H, Tawn JA (2009) A statistical analysis of eruptive activity on Mount Etna, Sicily. Geophys J Int 179:655–666CrossRefGoogle Scholar
  159. Smith R, Kilburn C (2010) Forecasting eruptions after long repose intervals from accelerating rates of rock fracture: the June 1991 eruption of Mount Pinatubo, Philippines. J Volcanol Geotherm Res 191:129–136CrossRefGoogle Scholar
  160. Sobradelo R, Marti J (2010) Bayesian event tree for long-term volcanic hazard assessment: application to Teide-Pico Viejo stratovolcanoes, Tenerife, Canary Islands. J Geophys Res 115:B05206CrossRefGoogle Scholar
  161. Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt KB, Tignor M, Miller HL, eds. (2007) Climate change 2007: the physical science basis: contribution of Working Group I to the fourth assessment report of the intergovernmental panel on climate change. Cambridge and New York, Cambridge University PressGoogle Scholar
  162. Solow AR (2001) An empirical Bayes analysis of volcanic eruptions. Math Geol 33:95–102CrossRefGoogle Scholar
  163. Sparks RSJ (2003) Forecasting volcanic eruptions. Earth Plan Sci Lett 210:1–15CrossRefGoogle Scholar
  164. Swanson DA, Casadevall TJ, Dzurisin D, Malone SD, Newhall CG, Weaver CS (1983) Predicting eruptions at Mount St Helens, June 1980 through December 1982. Science 221:1369–1376CrossRefGoogle Scholar
  165. Takada A (1997) Cyclic flank-vent and central-vent eruption patterns. Bull Volcanol 58:539–556CrossRefGoogle Scholar
  166. Thelen WA, Malone SD, West ME (2010) Repose time and cumulative moment magnitude: a new tool for forecasting eruptions? Geophys Res Lett 37:L18301CrossRefGoogle Scholar
  167. Thomas ME, Neuberg JW (2012) What makes a volcano tick-A first explanation of deep multiple seismic sources in ascending magma. Geology 40(4):351–354. doi: 10.113/G32868.1 CrossRefGoogle Scholar
  168. Thorlaksson JE (1967) A probability model of volcanoes and the probability of eruptions of Hekla and Katla. Bull Volcanol 31:97–106CrossRefGoogle Scholar
  169. Todesco M, Rinaldi AP, Bonafede M (2010) Modeling of unrest signals in heterogeneous hydrothermal systems. J Geophys Res 115:B09213CrossRefGoogle Scholar
  170. Tokarev PI (1978) Prediction and characteristics of the 1975 eruption of Tolbachik volcano, Kamchatka. Bull Volcanol 41:251–258CrossRefGoogle Scholar
  171. Trasatti E, Bonafede M, Ferrari C, Giunchi C, Berrino G (2011) On deformation sources in volcanic areas: modeling the Campi Flegrei (Italy) 1982–84 unrest. Earth Plan Sci Lett 306:175–185CrossRefGoogle Scholar
  172. Traversa P, Lengliné O, Macedo O, Metaxian J, Grasso J, Inza A, Taipe E (2011) Short term forecasting of explosions at Ubinas volcano, Perù. J Geophys Res 116:B11301CrossRefGoogle Scholar
  173. Turner M, Cronin S, Bebbington M, Platz T (2008a) Developing a probabilistic eruption forecast for dormant volcanos: a case study from Mt Taranaki, New Zealand. Bull Volcanol 70:507–515CrossRefGoogle Scholar
  174. Turner M, Cronin S, Smith I, Bebbington M, Stewart RB (2008b) Using titanomagnetite textures to elucidate volcanic eruption histories. Geology 36:31–34CrossRefGoogle Scholar
  175. Turner M, Bebbington M, Cronin S, Stewart RB (2009) Merging eruption datasets: building an integrated Holocene eruptive record of Mt Taranaki. Bull Volcanol 71:903–918CrossRefGoogle Scholar
  176. UNDRO (1985) Volcanic emergency management. Office of the United Nations Disaster Relief Co-Ordination, GenevaGoogle Scholar
  177. Voight B (1988) A method for prediction of volcanic eruptions. Nature 332:125–130CrossRefGoogle Scholar
  178. Voight B (1989) A relation to describe rate-dependent material failure. Science 243:200–203CrossRefGoogle Scholar
  179. Voight B, Glicken H, Janda RJ, Douglass PM (1981) Catastrophic rockslide avalanche of May 18. In: Lippman PW, Mullineaux DR (eds) The 1980 eruptions of Mount St. Helens, Washington. US Geological Survey Professional Paper, 1250, pp 347–377Google Scholar
  180. Voight B et al (1999) Magma flow instability and cyclic activity at Soufriére Hills volcano, Montserrat British West Indies. Nature 283:1138–1142Google Scholar
  181. Wadge G (1982) Steady state volcanism: evidence from eruption histories of polygenetic volcanoes. J Geophys Res 87:4035–4049CrossRefGoogle Scholar
  182. Wadge G, Burt L (2011) Stress field control of eruption dynamics at a rift volcano: Nyamuragira, D.R.Congo. J Volcanol Geotherm Res 207:1–15CrossRefGoogle Scholar
  183. Wadge G, Cross A (1988) Quantitative methods for detecting aligned points: an application to the volcanic vents of the Michoacan-Guanajuato volcanic field, Mexico. Geology 16:815–818CrossRefGoogle Scholar
  184. Wadge G, Young PAV, McKendrick IJ (1994) Mapping lava flow hazards using computer simulation. J Geophys Res 99:489–504CrossRefGoogle Scholar
  185. Wang T, BebbingtonM(2011) Robust estimation for theWeibull process applied to eruption records. In: Proceedings of the international union of geology and geodesy XXV general assembly, Melbourne, Australia, 28 June–7 July, IAVCEI JV02:920Google Scholar
  186. Watt SFL, Mather TA, Pyle DM (2007) Vulcanian explosion cycles: patterns and predictability. Geology 35:839–842CrossRefGoogle Scholar
  187. Wehrmann H, Dzierma Y (2011) Applicabilty of statistical eruption analysis to the geological record of Villarrica and Llaima Volcanoes, Southern Volcanic Zone, Chile. J Volcanol Geotherm Res 200:99–115CrossRefGoogle Scholar
  188. Weller JN (2004) Bayesian inference in forecasting volcanic hazards: an example from Armenia. MS Thesis Paper 1298, University of South FloridaGoogle Scholar
  189. White RA, Power JA (2001) Distal volcano-tectonic earthquakes: diagnosis and use in eruption forecasting. Trans AGU (Eos) 82:47Google Scholar
  190. Wickman FE (1966a) Repose-period patterns of volcanoes. I. Volcanic eruptions regarded as random phenomena. Arch Miner Geol 4:291–367Google Scholar
  191. Wickman FE (1966b) Repose-period patterns of volcanoes. V. General discussion and a tentative stochastic model. Arch Mineral Geol 4:351–367Google Scholar
  192. Woo G (2008) Probabilistic criteria for volcano evacuation decisions. Nat Hazards 45:87–97. doi: 10.1007/s11069-007-9171-9 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Istituto Nazionale di Geofisica e VulcanologiaRomeItaly
  2. 2.Volcanic Risk SolutionsMassey UniversityPalmerston NorthNew Zealand

Personalised recommendations