# Bebbington, Mark

## Intraeruption forecasting using semi-Markov models

### Mark Bebbington^{1} and Susanna Jenkins^{2}

#### 1. Volcanic Risk Solutions, Massey University, Palmerston North

#### 2. Earth Observatory of Singapore, Nanyang Technological University, Singapore

Forecasting eruption onsets has received much attention, in both the short- and long-term. However, unlike an earthquake, an eruption is not easily reduced to an instant in time. Any usable definition of an eruption has to allow for activity over scales ranging from minutes to decades, and can do so only by allowing for multiple eruptive phases. These phases can be defined by having different styles (e.g., effusive and/or explosive) of activity and/or quiescent periods between them. We have coded a database of multiple-phase eruptions into 8 major styles. The result contains c. 700 multi-phase eruptions, with eruptions having up to 33 non-quiescent phases. The resulting record of transitions between states is relatively dense, and so a probability tree is infeasible to model the possible phase sequences. Instead we will turn to Markov chain models. Markov chains describe the state path under the assumption that only the present state determines the probability of the next state, but the definition of ‘state’ can be extended in this case to include preceding or following quiescence. This enables us to calculate likelihoods for the next step of the eruption, conditional on (e.g.) the elapsed duration of the current phase, and the duration of the quiescence preceding it. The results are illustrated on recent eruptions, and the effect of partitioning the data base to isolate volcano types or compositions matching those of the target volcano examined.