Abstract
The analysis of the patterns of explosive eruption occurrences helps volcanologists and civil defense authorities to make quantitative estimations of the levels of hazard. An important first step in an assessment of volcano hazards is to classify the eruptions by size or magnitude, and to recognize the statistical distributions of the eruption occurrences and repose times between them. For a single volcano, such distributions may be stationary or time dependent. In the latter case, the volcano under study may have different regimes or rates of activity and their distribution should be looked for. The current and future hazard level or probability of eruption occurrence in a certain magnitude range may thus be estimated by Bayesian methods. This type of analysis could prove helpful in assigning priorities for volcano surveillance during repose periods, in decision making during volcanic crises, and in land-use planning. When large populations of volcanoes are considered, as in the global case, the distribution of explosive eruption occurrences seems to approach a stationary pattern, at least for longer times, during which the rate of occurrence of a given class of eruptive magnitude is inversely proportional to the volcanic energy released by eruptions in that magnitude range.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ang A, Tang W (1975) Probability concepts in engineering planning and design. (I) J Wiley, New York, pp 1–409
Björnsson A, Saemundsson K, Einarsson P, Tryggvason E, Grpnvold K (1977) Current rifting episode in North Iceland. Nature 266: 318–323
Burt ML, Wadge G, Scott WA (1994) Simple stochastic modelling of the eruption history of a basaltic volcano: Nyamuragira, Zaire. Bull Volcanol 56: 87–97
Carey S, Sigurdsson H (1989) The intensity of plinian eruptions. Bull Volcanol 51: 28–40
Carta S, Figari R, Sartoris G, Sassi E, Scandone R (1981) A statistical model for Vesuvius and its volcanological implications. Bull Volcanol 44(2): 129–151
Conover WJ (1971) Practical nonparametric statistics. J Wiley, New York, pp 1–462
Cox DR (1955) Some statistical methods connected with series of events. J R Stat Soc B 17: 129 – 164
Cox DR, Isham V (1980) Point processes. Chapman and Hall, London, pp 1–188
Cox DR, Lewis PAW (1966) The statistical analysis of series of events. Methuen, London, pp 1–285
Crisp JA (1984) Rates of magma emplacement and volcanic output. J Volcanol Geotherm Res 20: 177–211
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. Radioactive Waste Manage 3: 167–190
De la Cruz-Reyna S (1991) Poisson-distributed patterns of explosive eruptive activity. Bull Volcanol 54: 57–67
De la Cruz-Reyna S (1993) Random patterns of occurrence of explosive eruptions at Colima Volcano, México. J Volcanol Geotherm Res 55: 51–68
Dubois J, Cheminée JL (1991) Fractal analysis of eruptive activity of some basaltic volcanoes. J Volcanol Geotherm Res 45: 197–208
Esteva L (1976) Seismicity. In: Lomnitz C and Roseblueth E (eds) Seismic risk and engineering decisions. Elsevier, Amsterdam, pp 179–224
Fedotov SA (1985) Estimates of heat and pyroclast discharge by volcanic eruptions based upon the eruption cloud and steady plume observations. J Geodynam 3: 275–302
Ferraes SG (1986) Bayes theorem and the probabilistic prediction of inter-arrival times for strong earthquakes felt in Mexico City. J Phys Earth 34: 71–83
Ferraes SG (1988) The optimum Bayesian probability procedure and the prediction of strong earthquakes felt in Mexico City. Pageoph 127: 561–571
Fournier d’Albe EM (1979) Objectives of volcanic monitoring and prediction. J Geol Soc Lond 136: 321–326
Guschenko II (1979) Eruptions of the volcanoes of the world. Catalogue. NAUKA Moscow, pp 1 – 476 (in Russian)
Hédervári P (1963) On the energy and magnitude of volcanic eruptions. Bull Volcanol 25: 373 – 385
Ho C-H (1990) Bayesian analysis of volcanic eruptions. J Volcanol Geotherm Res 43: 91–98
Ho C-H (1991) Nonhomogeneous Poisson model for volcanic eruptions. Math Geol 23: 167–173
Ho C-H (1992) Risk assessment for the Yucca Mountain high-level nuclear waste repository site: estimation of volcanic disruption. Math Geol 24: 775–787
Howson C, Urbach P (1991) Bayesian reasoning in science. Nature 350: 371–374
Klein FW (1982) Patterns of historical eruptions at Hawaiian volcanoes. J Volcanol Geotherm Res 12: 1–35
Luhr JF (1981) Colima; history and cyclicity of eruptions. Volcano News 7: 1–3
Luhr JF, Carmichael ISE (1982) The Colima Volcanic Complex, Mexico Part III. Ash- and scoriafall deposits from the upper slopes of Volcán Colima. Contrib Mineral Petrol 80: 262–275
Luhr JF, Carmichael ISE (1990) Geology of Volcán de Colima. Bol Inst de Geol UNAM (México) 107: 1–107
McClelland L, Simkin T, Summers M, Nielsen E, Stein T (1989) Global volcanism 1975–1985. Smithsonian Institution, Washington, 655 pp
Mulargia F, Gasperini P, Tinti S (1987) Identifying different regimes in eruptive activity: An application to Etna volcano. J Volcanol Geotherm Res 34: 89–106
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: 187–196
Munoz M (1983) Eruption Patterns of the Chilean Volcanoes Villarrica, Llaima, and Tupungatito. Pageoph 121: 835–852
Nakamura K (1974) Preliminary estimate of global volcanic production rate. In: Colp J, Furimoto AS (eds) Utilization of volcanic energy. Univ Hawaii and Sandia Corp, Hilo, pp 273–285
Newhall CG, Self S (1982) The volcanic explosivity index (VEI): an estimate of explosive magnitude for historical volcanism. J Geophys Res 87C2: 1231–1238
Papoulis A (1984) Probability, random variables and stochastic processes. 2nd edn. McGraw-Hill, Singapore, 576 pp
Peterson DW (1988) Volcanic hazards and public response. J Geophys Res 93B5: 4161–4170
Pyle DM (1995) Mass and energy budgets of explosive volcanic eruptions. Geophys Res Lett 22: 563–566
Reyment RA (1969) Statistical analysis of some volcanologic data. Pageoph 74(III): 57–77
Reyment RA (1976) Markov models of repose-period patterns of volcanoes. In: Merriam DF (ed) Random processes in geology. Springer, Berlin Heidelberg New York, pp 135–161
Robin C, Camus G, Gourgaud A (1991) Eruptive and magmatic cycles at Fuego de Colima volcano (Mexico). J Volcanol Geotherm Res 45: 209–225
Rozanov YA (1977) Probability theory. Dover, New York, 148 pp
Settle M (1978) Volcanic eruption clouds and the thermal power output of explosive eruptions. J Volcanol Geotherm Res 3: 309–324
Settle M, McGetchin TR (1980) Statistical analysis of persistent explosive activity at Stromboli, 1971: implications for eruption prediction. J Volcanol Geotherm Res 8: 45–58
Shaw HR (1987) Uniqueness of volcanic systems. In: Decker RW, Wright TL, Stauffer PH (eds) Volcanism in Hawaii. USGS Prof Pap 1350, Washington, pp 1357–1394
Simkin T, Siebert L (1994) Volcanoes of the World, 2nd edn. Geoscience Press, Missoula, 368 pp
Simkin T, Siebert L, McClelland L, Bridge D, Newhall C, Latter JH (1981) Volcanoes of the world. Smithsonian Institution, Washington, 233 pp
Steven TA, Lipman PW (1976) Calderas of the San Juan volcanic field, southwestern Colorado. USGS Prof Pap 958, Washington, pp 1–35
Thorláksson JE (1967) A probability model of volcanoes and the probability of eruptions of Hekla and Katla. Bull Volcanol 31: 97–106
Tilling RI, Rubin M, Sigurdsson H, Carey S, Duffield W, Rose WI (1984) Holocene eruptive activity of El Chichon Volcano, Chiapas, Mexico. Science 224: 747–749
Tsuya H (1955) Geological and petrological studies of Volcano Fuji, 5. Bull Earthq Res Inst Tokyo Univ 33: 341–384
Wadge G (1982) Steady state volcanism: evidence from eruption histories of polygenetic volcanoes. J Geophys Res 87B5: 4035–4049
Walker GPL (1980) The Taupo pumice: product of the most powerful known (Ultraplinian) eruption?. J Volcanol Geotherm Res 8: 69–94
Wickman FE (1966) Repose period patterns of volcanoes, I. Volcanic eruptions regarded as random phenomena. Ark Mineral Geol 4: 291–301
Wickman FE (1976) Markov models of repose-period patterns of volcanoes. In: Merriam DF (ed) Random processes in geology. Springer, Berlin Heidelberg New York, pp 135–161
Winkler RL, Hays WL (1975) Statistics: probability, inference and decision. 2nd edn, Holt Rinehart and Winston, New York, 889 pp
Yokoyama I (1957) Energetics in active volcanoes. 2nd paper. Bull Earthq Res Inst Tokyo Univ 35: 75–97
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
De La Cruz-Reyna, S. (1996). Long-Term Probabilistic Analysis of Future Explosive Eruptions. In: Monitoring and Mitigation of Volcano Hazards. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80087-0_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-80087-0_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-80089-4
Online ISBN: 978-3-642-80087-0
eBook Packages: Springer Book Archive