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The Auckland Volcanic Field (AVF) with 49 eruptive centres in the last c. 250 ka presents many challenges to our understanding of distributed volcanic field construction and evolution. We re-examine the age constraints within the AVF and perform a correlation exercise matching the well-dated record of tephras from cores distributed throughout the field to the most likely source volcanoes, using thickness and location information and a simple attenuation model. Combining this augmented age information with known stratigraphic constraints, we produce a new age-order algorithm for the field, with errors incorporated using a Monte Carlo procedure. Analysis of the new age model discounts earlier appreciations of spatiotemporal clustering in the AVF. Instead the spatial and temporal aspects appear independent; hence the location of the last eruption provides no information about the next location. The temporal hazard intensity in the field has been highly variable, with over 63% of its centres formed in a high-intensity period between 40 and 20 ka. Another, smaller, high-intensity period may have occurred at the field onset, while the latest event, at 504±5 years B.P., erupted 50% of the entire field's volume. This emphasises the lack of steady-state behaviour that characterises the AVF, which may also be the case in longer-lived fields with a lower dating resolution. Spatial hazard intensity in the AVF under the new age model shows a strong NE-SW structural control of volcanism that may reflect deep-seated crustal or subduction zone processes and matches the orientation of the Taupo Volcanic Zone to the south.

S U M M A R YWe examine the application of Hidden Markov Models (HMMs) to volcanic occurrences. The parameters in HMMs can be estimated from data by means of the Expectation-Maximization (EM) algorithm. Various formulations permit modelling the activity level of a volcano through onset counts, the intensity of a Markov Modulated Poisson Process (MMPP), or through the intervals between onsets. More elaborate models allow investigation of the relationship between durations and reposes. After fitting the model, the Viterbi algorithm can be used to identify the underlying (hidden) activity level of the volcano most consistent with the observations. The HMM readily provides forecasts of the next event, and is easily simulated. Data of flank eruptions 1600-2006 from Mount Etna are used to illustrate the methodology. We find that the volcano has longish periods of Poissonian behaviour, interspersed with less random periods, and that changes in regime may be more frequent than have previously been identified statistically. The flank eruptions of Mount Etna appear to have a complex time-predictable character, which is compatible with transitions between an open and closed conduit system. The relationship between reposes and durations appears to characterize the cyclic nature of the volcanoes activity.

The majority of continental arc volcanoes go through decades or centuries of inactivity, thus, communities become inured to their threat. Here we demonstrate a method to quantify hazard from sporadically active volcanoes and to develop probabilistic eruption forecasts. We compiled an eruption-event record for the last c. 9,500 years at Mt Taranaki, New Zealand through detailed radiocarbon dating of recent deposits and a sediment core from a nearby lake. This is the highest-precision record ever collected from the volcano, but it still probably underestimates the frequency of eruptions, which will only be better approximated by adding data from more sediment core sites in different tephradispersal directions. A mixture of Weibull distributions provided the best fit to the inter-event period data for the 123 events. Depending on which date is accepted for the last event, the mixture-of-Weibulls model probability is at least 0.37-0.48 for a new eruption from Mt Taranaki in the next 50 years. A polymodal distribution of inter-event periods indicates that a range of nested processes control eruption recurrence at this type of arc volcano. These could possibly be related by further statistical analysis to intrinsic factors such as step-wise processes of magma rise, assembly and storage.