pure and applied geophysics

, Volume 74, Issue 1, pp 57–77 | Cite as

Statistical analysis of some volcanologic data regarded as series of point events

  • R. A. Reyment


The case histories of some active volcanoes in various parts of the world are analyzed from the standpoint of their being observations of point events in a time continuum. The eruptive histories of the three Japanese volcanoes included show trend in the rate of occurrence of outbreaks. The possible existence of trend in rate of occurrence of events was found for certain Lower Cretaceous bentonites of Wyoming. The data investigated for Etna derive from a period of persistent activity and here also trend in the rate of occurrence of ejections could be identified. The remaining volcanoes studied do not display significant trend in the rate of occurence of outbreaks over the time interval available. Various statistical tests indicate, that although some of the non-trend volcanoes may be fairly closely approximated as regards rate of occurrence of eruptions by the plausible Poisson model, none agree in all respects with the requirements of this process. The patterns of activity of volcanoes found to differ greatly from the Poisson model are complicated kinds of point processes, but owing to the shortness of the series available and their rather unsatisfactory accuracy, it is not possible to be explicit as to their precise nature. In order to elucidate some aspects of the analysis, a simulated series of outbreaks with exponentially distributed intervals between events was produced. The general scheme of analysis adopted has been firstly to test for trend; if trend in the rate of occurrence of events does not occur, the series have been tested for dependence. If there is no dependence between events, tests for agreement with a Poisson model have been carried out, with a negative conclusion leading to a test for agreement with some kind of renewal process. In order to provide a comparison with another type of natural phenomenon of a random nature, the earthquakes occurring in Fennoscandia over the period 1891 to 1950 were analyzed by the same methods. Perhaps surprisingly, the 322 shocks registered during this time (shocks≧3.0 on the Gutenberg-Richter scale) show an indication of trend with a tendency for a decrease in the rate of occurrence of shocks. The eruption pattern of Mauna Loa is thought to be approximately a simple Poisson process. The patterns for Semeru, Bromo and Peak of Ternate seem to be reasonably consistent with a renewal process model, but appear to differ from a Poisson process. The Indonesian volcanoes have several features in common, among these a high coefficient of variation for the times between eruptions. It is tentatively suggested that this may be of some genetic significance. It is possible, that the Indonesian volcanoes erupt in accordance with a pattern approximating to some kind of stationary point process.


Cretaceous Bentonite Lower Cretaceous Poisson Process Point Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    N. T. J. Baily,The Elements of Stochastic Processes with Applications to the Natural Sciences (Wiley and Sons, 1964).Google Scholar
  2. [2]
    M. S. Bartlett,Introduction to Stochastic Processes (Cambridge University Press, 1955).Google Scholar
  3. [3]
    M. Bath,An Earthquake Catalogue for Fennoscandia for the Years 1891–1950, Årsbok 50, S.G.U. [Ser. C]545 (1956), 52 pp.Google Scholar
  4. [4]
    D. R. Cox andP. A. W. Lewis,The Statistical Analysis of Series of Events (Methuens Monographs on Applied Probability and Statistics, London 1966).Google Scholar
  5. [5]
    D. R. Cox andH. D. Miller,The Theory of Stochastic Processes (Methuen, London 1966).Google Scholar
  6. [6]
    H. Cramer,Mathematical Methods of Statistics (Princeton University Press, 1946).Google Scholar
  7. [7]
    W. Feller,An Introduction to Probability Theory and its Applications, Vol. I (1957) and Vol. II (1966) (Wiley and Son).Google Scholar
  8. [8]
    J. M. Hammersley andD. C. Handscomb,Monte Carlo Methods (Methuen, London 1964).Google Scholar
  9. [9]
    E. J. Hannan,Time Series Analysis (Methuen, London 1960).Google Scholar
  10. [10]
    M. G. Kendall andA. Stuart,The Advanced Theory of Statistics, Vol. 3:Design and Analysis and Time Series (Griffin, London 1966).Google Scholar
  11. [11]
    H. Kuno,Japan, Taiwan and Marianas, Part XI of theInternational Volcanological Association Catalogue of the Active Volcanoes of the World (Naples 1962).Google Scholar
  12. [12]
    P. A. W. Lewis,A Branching Poisson Model for the Analysis of Computer Failure Patterns, J. Roy. Stat. Soc. [B] (1964), 398–456.Google Scholar
  13. [13]
    P. A. W. Lewis,A computer program for the statistical analysis of series of events, IBM Systems Journal4 (1967), 202–225.Google Scholar
  14. [14]
    G. A. MacDonald,Hawaian Islands, Part III of theInternational Volcanological Association Catalogue of the Active Volcanoes of the World (Naples 1955).Google Scholar
  15. [15]
    M. Neumann van Padang,Indonesia, Part I of theInternational Volcanological Association Catalogue of the Active Volcanoes of the World (Naples 1951).Google Scholar
  16. [16]
    F. E. Wickman,Repose Period Patterns of Volcanoes, I:Volcanic Eruptions Regarded as Random Phenomena, Arkiv för Mineralogi och Geologi4 (1966), 291–301.Google Scholar
  17. [17]
    F. E. Wickman,Repose Period Patterns of Volcanoes, II:Eruption Histories of some East Indian Volcanoes,ibid.4 (1966), 303–317.Google Scholar
  18. [18]
    F. E. Wickman,Repose Period Patterns of Volcanoes, III:Eruption Histories of some Japanese Volcanoes,ibid.4 (1966), 319–335.Google Scholar
  19. [19]
    F. E. Wickman,Repose Period Patterns of Volcanoes, IV:Eruption Histories of some Selected Volcanoes,Ibid.4 (1966), 337–350.Google Scholar
  20. [20]
    F. E. Wickman,Repose Period Patterns of Volcanoes, V:General Discussion and a Tentative Stochastic Model,Ibid.4 (1966), 351–367.Google Scholar
  21. [21]
    W. E. Wickman andE. E. El-Hinnawi,The Time Distribution of Lava Fragment Ejection from Volcanoes,Ibid.3 (1963), 363–383.Google Scholar

Copyright information

© Birkhäuser Verlag 1969

Authors and Affiliations

  • R. A. Reyment
    • 1
  1. 1.Department of Historical Geology, Paleontologiska InstitutetUppsala UniversitetUppsala 1Sweden

Personalised recommendations