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Beyond the immediate volcano surveillance, it is pivotal to estimate the probability of an impending eruption. This is done with the help of statistical techniques.
Historical and geological eruption records of a volcano are subjected to statistical lifetime and failure analysis to determine the likelihood of future eruptions. The analysis can be performed provided that several pre-requisites are fulfilled: (1) the record is sufficiently comprehensive to grasp the volcano's chronologic behaviour; (2) successive eruptions have to be independent of each other, which can be tested by calculating the correlation between successive repose times (i.e. the time intervals between the onsets of successive eruptions); and (3) the eruption time series have to be stationary, which means the statistical properties of any portion of the data set are identical, no matters which time period is considered. Subsequently, several distribution functions, such as e.g. an exponential, a Weibull, or a log-logistic function can be fit to the data. The exponential function is the most simple case and can be applied if the data follow a Poisson process. The Weibull distribution is a model of simple failure and can accommodate phases of increasing as well as of waning volcanic activity. The log-logistic distribution reflects a situation of competing processes, which often occur in volcanic systems. For example, continuous magma chamber replenishment and differentiaten may contribute to increasing the likelihood of an eruption, while contemporaneous quiescent degassing may reduce pressure and relax the system, thus lowering the eruption probability.
- Connor CB, Sparks RSJ, Mason RM, Bonadonna C (2003): Exploring links between physical and probabilistic models of volcanic eruptions: The Soufrière Hills Volcano, Montserrat. Geophysical Research Letters 30/13, 1701. doi:10.1029/2003GL017384.
- De la Cruz-Reyna S (1996): Long-term probabilistic analysis of future explosive eruptions. In: Scarpa, R., Tilling, R.I., (eds) 1996. Monitoring and mitigation of volcanic hazards. Springer, New York, Berlin.
- Dzierma Y, Wehrmann H (2010): Eruption time series statistically examined: Probabilities of future eruptions at Villarrica and Llaima Volcanoes, Southern Volcanic Zone, Chile. Journal of Volcanology and Geothermal Research 193:82-92, doi:10.1016/j.jvolgeores.2010.03.09.
- Dzierma Y, Wehrmann H (2010): Statistical eruption forecast for the Chilean Southern Volcanic Zone: typical probabilities of volcanic eruptions as baseline for possibly enhanced activity following the large 2010 Concepcion earthquake. Natural Hazards and Earth System Sciences 10:1-16, doi:10.5194/nhess-10-1-2010.
- Mader HM, Coles SG, Connor CB, Connor LJ (eds., 2006): Statistics in Volcanology, Special Publication of IAVCEI 1, Geological Society, London.
- Mendoza-Rosas AT, De la Cruz-Reyna S (2008): A statistical method linking geological and historical eruption time series for volcanic hazard estimations: Application to active polygenetic volcanoes. Journal of Volcanology and Geothermal Research. 176: 277-290, doi:10.1016/j.volgeores.2008.04.005.
- Mendoza-Rosas AT, De la Cruz-Reyna S (2009): A mixture of exponentials distribution for a simple and precise assessment of the volcanic hazard. Nat. Hazards Earth Syst. Sci. 9, 425-431.
- Wehrmann H, Dzierma Y (in press): Applicability of statistical eruption analysis to the geologic record of Villarrica and Lanin volcanoes, Southern Volcanic Zone, Chile. Journal of Volcanology and Geothermal Research, doi:10.1016/j.jvolgeores.2010.11.009
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