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

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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.