Markov Models of Repose-Period Patterns of Volcanoes

  • F. E. Wickman
Conference paper

Abstract

Six renewal type Markov models illustrating different idealized patterns of volcanic activity are examined: (1) simple two-stage volcano without persistent activity (Fuji type), (2) volcano with “loading time” and dormancies (Hekla type), (3) volcano with “loading time” and persistent activity (Vesuvius type), (4) volcano with lava-lake activity (Kilauea type), (5) volcano with accelerating cycles of eruptions (Asama type), and (6) volcano with both “excitation” and “loading time.”

The models consist of mutually independent Poisson processes with rate parameters independent of time. Explicit expressions for the density function of a repose and its rate function, as well as other characteristic functions, therefore can be derived. The concepts of serial density function and serial eruption rate function are introduced for model 5 because it has a distinctive (culminating) eruption in each cycle. These two functions depend on the serial number of a repose, counted from the previous culminating eruption.

It is concluded that rather simple Markov models can describe the volcanic patterns as observed.

Keywords

Fatigue Depression Welding Dura 

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References

  1. Aramaki, S., 1963, Geology of Asama volcano: Jour. Fac. Sci. Univ. Tokyo, sec. II, v. 14, p. 229–443.Google Scholar
  2. Wickman, F. E., 1966a, Repose-period patterns of volcanoes, I. Volcanic eruptions regarded as random phenomena: Arkiv for Mineralogi och Geologi, Bd 4, Hafte 4, p. 291–301.Google Scholar
  3. Wickman, F. E., 1966b, Repose-period patterns of volcanoes. II. Eruption histories of some East Indian volcanoes: Arkiv for Mineralogi och Geologi, Bd 4, Hafte 4, p. 303–317.Google Scholar
  4. Wickman, F. E., 1966c, Repose-period patterns of volcanoes. III. Eruption histories of some Japanese volcanoes: Arkiv for Mineralogi och Geologi, Bd 4, Hafte 4, p. 319–335.Google Scholar
  5. Wickman, F. E., 1966d, Repose-period patterns of volcanoes. IV. Eruption histories of some selected volcanoes: Arkiv for Mineralogi och Geologi, Bd 4, Hafte 4, p. 337–350.Google Scholar
  6. Wickman, F. E., 1966e, Repose-period patterns of volcanoes. V. General discussion and a tentative stochastic model: Arkiv for Mineralogi och Geologi, Bd 4, Hafte 5, p. 351–367.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1976

Authors and Affiliations

  • F. E. Wickman

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