Stochastic modelling for time series reconstruction at active volcanoes

The monitoring of active volcanoes using automatic recording devices is particularly prone to data losses because of the inherent geological and environmental conditions encountered in situ. However, most analysis methods applied in the investigation of medium-to-long term volcano dynamics, e.g. statistical methods, require time series without gaps in the observations. An appropriate reconstruction of the missing data in the recorded time series is, therefore, essential. Classical interpolation methods are not suitable for filling gaps in time series; their smoothing properties do not preserve the observed variability of the data. Furthermore, these methods of dominant polynomial nature can usually not be calibrated to the analysed observations. In response to these requirements, an approach based on geostatistical concepts is proposed that allows time series reconstruction by stochastic simulation with the following capabilities: (a) honouring temporal auto-correlation, (b) conservation of the observed variability and (c) conditioning of the data and of their histogram. The developed approach is applied to seismic data monitored at the Stromboli volcano. The obtained results demonstrate the possibilities of this approach; a time series missing 20 % of its values can be reconstructed without gaps while preserving its temporal behaviour in a statistical sense.