Statistical methods for assembling and incorporating volcanic records in hazard estimation : 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
The estimation of hazard arising from volcanic eruptions is a research topic of great interest to
New Zealand, given the number and location of active and dormant volcanoes. Probabilistic
temporal models are required to handle the stochastic nature of observed records. Such
models are usually assembled using point process techniques or renewal theory and most are
purely temporal in the sense that they only consider the distribution of event or inter-event
times as predictors of further volcanic activity. I demonstrate using a high-resolution eruption
record from Mt Taranaki (New Zealand) how geochemical data can be incorporated, using
a proportional hazards type approach, to improve the performance of current renewal-type
Probabilistic forecasting relies on the accuracy and completeness of historical eruption records.
This poses the question of how to establish a detailed record of past volcanic events. Multiple
sites are needed to build a composite tephra record, but correctly merging them by recognizing
events in common and site-speci c gaps remains complex. I present an automated
procedure for matching tephra sequences, using stochastic local optimization techniques. Implausible
matches are eliminated through careful reasoning, while heuristically searching over
the remaining alternatives. Possible matches are veri ed using known tephra compositions
and stratigraphic constraints. The method is applied to match tephra records from ve long
sediment cores in Auckland, New Zealand. The correlated record compiled is statistically
more likely than previously published arrangements from this area.
In addition to the matching of tephras found in the Auckland region, the algorithm is applied
to stratigraphic records obtained from Mt Taranaki. With more detailed geochemical
information available, matches are constrained further by considering principle component
analysis of titanomagnetite compositional data.
Finally, after combining the amalgamated record of Mt Taranaki events with point thickness
measurements, the eruptive volume of Mt Taranaki events is estimated. Utilizing isopach
maps and individual point observations a model is formulated, in a Bayesian framework, for
the thicknesses of tephra deposits as a function of the distance and angular direction of each
location. The model estimates, in addition to eruptive volume, the wind and site-speci c
e ects on the thickness deposits. The ndings lead on to methods of incorporating eruptive
volumes in hazard estimation.