pure and applied geophysics

, Volume 121, Issue 5–6, pp 835–852 | Cite as

Eruption patterns of the chilean volcanoes Villarrica, Llaima, and Tupungatito

  • Miguel Muñoz


The historical eruption records of three Chilean volcanoes have been subjected to many statistical tests, and none have been found to differ significantly from random, or Poissonian, behaviour. The statistical analysis shows rough conformity with the descriptions determined from the eruption rate functions. It is possible that a constant eruption rate describes the activity of Villarrica; Llaima and Tupungatito present complex eruption rate patterns that appear, however, to have no statistical significance. Questions related to loading and extinction processes and to the existence of shallow secondary magma chambers to which magma is supplied from a deeper system are also addressed.

The analysis and the computation of the serial correlation coefficients indicate that the three series may be regarded as stationary renewal processes. None of the test statistics indicates rejection of the Poisson hypothesis at a level less than 5%, but the coefficient of variation for the eruption series at Llaima is significantly different from the value expected for a Poisson process. Also, the estimates of the normalized spectrum of the counting process for the three series suggest a departure from the random model, but the deviations are not found to be significant at the 5% level.

Kolmogorov-Smirnov and chi-squared test statistics, applied directly to ascertaining to which probabilityP the random Poisson model fits the data, indicate that there is significant agreement in the case of Villarrica (P=0.59) and Tupungatito (P=0.3). Even though theP-value for Llaima is a marginally significant 0.1 (which is equivalent to rejecting the Poisson model at the 90% confidence level), the series suggests that nonrandom features are possibly present in the eruptive activity of this volcano.

Key words

Eruption patterns Statistical analysis Stochastic processes 


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  1. Bartlett, M. S. (1963),The spectral analysis of point processes, J. Royal Statist. Soc. B25, 264–296.Google Scholar
  2. Casertano, L. (1963),Catalogue of the Active Volcanoes and Solfatara Fields of the Chilean Continent. Catalogue of the Active Volcanoes of the World including Solfatara Fields, International Volcanological Association, Part XV, 55 pp.Google Scholar
  3. Cox, D. R., andLewis, P. A. W.,The Statistical Analysis of Series of Events (Methuen, London 1966) 285 pp.Google Scholar
  4. González-Ferrán, O. (1972),Distribución del volcanismo activo de Chile y la reciente erupción del volcán Villarrica, Apartado del Primer Symposium Cartográfico Nacional, IGM, Santiago, 191–207.Google Scholar
  5. González-Ferrán, O. (1980),Actividad volcánica en Chile en el período Marzo 1979 – Marzo 1980, Informativo 1, Servicio Volcanológico, Depto. de Geofisica, U. de Chile. Tralka1, 221–228.Google Scholar
  6. González-Ferrán, O., andKausel, E. (1980),Antecedentes sobre la actividad volcánica y sísmica de la región Villarrica-Pucón, Depto. de Geofisica, U. de Chile (unpublished report), 86 pp.Google Scholar
  7. Klein, F. W. (1982),Patterns of historical eruptions at Hawaiian volcanoes, J. Volcan. and Geotherm. Res.12, 1–35.CrossRefGoogle Scholar
  8. Lewis, P. A. W. (1966),A computer program for the statistical analysis of series of events, IBM Systems J.,5, 202–225.CrossRefGoogle Scholar
  9. Martin, D. P., andRose, W. I. (1981),Behavioral patterns of Fuego volcano, Guatemala, J. Volcan. and Geotherm. Res.,10, 67–81.CrossRefGoogle Scholar
  10. Owen, D. B.,Handbook of Statistical Tables (Addison-Wesley, Reading, Mass. 1962) 580 pp.Google Scholar
  11. Reyment, R. A. (1969),Statistical analysis of some volcanological data regarded as series of point events, Pure Appl. Geophys.,74, 57–77.CrossRefGoogle Scholar
  12. Thiele, R., andKatsui, Y. (1969),Contribución la conocimiento del volcanismo post-miocénico de los Andes en la provincia de Santiago, Chile, Depto. de Geología, U. de Chile, Publicación35, 7–23.Google Scholar
  13. Weast, R. C. (ed.) (1964),Handbook of Mathematical Tables, Chemical Rubber Co., Cleveland, Ohio, 680 pp.Google Scholar
  14. Wickman, F. E. (1966a),Repose period patterns of volcanoes: I. Volcanic eruptions regarded as random phenomena, Arkiv Miner. Geol.,4, 291–301.Google Scholar
  15. Wickman, F. E. (1966b),Repose period patterns of volcanoes: V. General discussion and a tentative stochastic model, Arkiv Miner. Geol.,4, 351–367.Google Scholar
  16. Wickman, F. E.,Markov models of repose-period patterns of volcanoes, InRandom Processes in Geology (ed. Merriam D. F.) (Springer-Verlag, New York 1976) pp. 135–161.Google Scholar

Copyright information

© Birkhäuser Verlag 1983

Authors and Affiliations

  • Miguel Muñoz
    • 1
  1. 1.Departamento de GeofisicaUniversidad de Chile, CasillaSantiagoChile

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