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SIIA Público
SISTEMA INTEGRAL DE INFORMACIÓN ACADÉMICA - PÚBLICO
Título del libro: Extreme Events: Observations, Modeling, And Economics Título del capítulo: An Extreme Event Approach to Volcanic Hazard Assessment
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.