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Título del libro: Extreme Events: Observations, Modeling, And Economics
Título del capítulo: An Extreme Event Approach to Volcanic Hazard Assessment

Autores UNAM:
SERVANDO DE LA CRUZ REYNA; ANA TERESA MENDOZA ROSAS;
Autores externos:

Idioma:

Año de publicación:
2016
Palabras clave:

STATISTICAL-ANALYSIS; EXPLOSIVE ERUPTIONS; FLANK ERUPTIONS; POISSON-PROCESS; ETNA VOLCANO; WIND SPEEDS; SERIES; MODELS


Resumen:

The statistical analysis of size-qualified volcanic eruption time series is an essential step for the assessment of volcanic hazard. Such series generally describe complex processes that may be time dependent, involving different types of eruptions over a wide range of timescales. The hazard assessment thus requires a characterization of the eruptions that reflects their destructive potential, that is, an appropriate measure of their ``size.'' However, available data to size qualify eruptions are frequently unknown and incomplete, as often are their times of occurrence. This is particularly true for ``rare,'' uncommon eruptions exceeding the ``normal'' activity, which may be regarded as extreme events. Here, we describe statistical methods that have proven useful to deal with such difficulties, and describe a procedure to analyze eruptive sequences of individual volcanoes or groups of volcanoes, as illustrated with several examples of hazard estimates. The procedure involves three steps: First, the historical eruptive series is complemented with a series constructed from any available geological-time eruption data. Either series may contain extreme events, but it is more likely that such extreme eruptions belong to the geological record. Both series are then linked assuming a scaling, self-similarity relationship between the eruption size and the occurrence rate of each magnitude class. Second, a Weibull analysis of the distribution of repose times between successive eruptions manifests the time dependence, if any, through its shape parameter. Finally, the linked eruption series are analyzed using extreme value theory as a nonhomogeneous Poisson process with a generalized Pareto distribution as intensity function, from which the probabilities of future eruptions may be estimated.


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