Statistical methods for estimating tephra source and dispersal : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Statistics at Massey University, Palmerston North, New Zealand
Tephra refers to any pyroclastic fragments ejected from a volcanic vent and its dispersal
is one of the major hazards with explosive eruptions. The attenuation of tephra fall
thickness is most commonly estimated after contouring field measurements into smooth
isopachs. I explicitly describe the variability in thickness by using a semiempirical
tephra attenuation relation as a link function. This opens the way to fitting models
to actual tephra observations through maximum likelihood estimation (MLE). The
method is illustrated using data published from the 1973 Heimaey eruption in Iceland.
Complex eruptions commonly produce several phases of tephra fall from multiple vents.
When attempting to precisely reconstruct past eruptions from the geological record
alone, separate phases are often indistinguishable. Augmented by a mixture framework,
the MLE attenuation model was able to identify the sources and directions of tephra
deposition for the 1977 Ukinrek Maars eruption in Alaska, US, from only the tephra
thickness data. It was then applied to the unobserved 1256 AD Al-Madinah eruption
in Saudi Arabia.
The estimation of the spatio-temporal hazard from a monogenetic volcanic field is criti-
cally dependent on a reconstruction of past events. The Auckland Volcanic Field (AVF)
has produced about 50 volcanoes in the last 250,000 years. Although inconsistent, age
data for many of these volcanoes exist from various dating methods with various re-
liabilities. The age order of some pairs is also known due to the overlaying of lavas
(stratigraphy). A discussion is provided on how informative priors are obtained via ex-
pert elicitation, on both the individual volcano ages, and the reliabilities of the dating
methods. A possible Bayesian model for reconciling the available inconsistent volcano
age data to estimate the true eruption ages is also discussed.
To improve these eruption age estimates, some of the volcanoes can be correlated with
the better dated tephra layers recovered from five maars in the field. The likelihood of
any combination of volcano and tephra, incorporating the spatial variability based on
the attenuation model and temporal components, is evaluated and is maximised numer-
ically using linear programming. This statistical matching provides an improvement in
the volcano age-order model and age estimates of the volcanoes in the AVF.