Increased complexity of seismic ground motion prior and during the 2014 Holuhraun eruption, Iceland

The complexity of time series can be quantitatively measured using Permutation Entropy (PE). PE has recently been introduced as a potential tool in eruption forecasting by applying it to the seismic time series. Examples of successful applications are the eruptions at Strokkur Geyser, Iceland, the 1996 eruption of Gjálp, Iceland, and the eruptions of Shinmoedake volcano, Japan, in 2011, 2017, and 2018. While PE is able to show temporal changes prior to an eruption, these features are not always prominent. To improve this method, we calculate PE not only for the amplitudes of the seismic signals but also for the seismic instantaneous phases, called Phase Permutation Entropy (PPE). To understand the difference between PE and PPE, we performed synthetic tests by creating several synthetic waveforms using different numbers of sin wave superposition. We used more wave superposition with different frequencies to create complex waves containing broader frequency spectrum, while less superposition is used to create simpler waves containing narrower frequency spectrum. PE and PPE values are both low for simple waves and high for complex waves, but their absolute values differ, which might contain valuable information. The gap, dP = PE-PPE, is found to be smaller for complex waves compared to the more simple waves.  We then calculated PE and PPE for seismic data recorded from January 2014 to December 2015, which covered the eruption period of Holuhraun in Iceland. During the time of quiescence, both PE and PPE exhibit a long period variation which seems to be seasonal. Calculating dP weakens the long period noise and generates a more stable baseline.  We observe that the temporal variation of dP started to decrease below the baseline after 24 May 2014, indicating that the ground motion got more complex. An abrupt drop of dP to its lowest level was observed on 16 August 2014, when the dyke started to propagate from Bardarbunga to Holuhraun. While dP increases after the onset of eruption on 29 and 31August 2014, there is no prominent feature between the dyke propagation and the onset of the eruptions.  During the eruption period, dP stays lower than the background dP, indicating a higher ground motion complexity compared to the quiescence time. After January 2015, the gradual increase of dP back to the baseline level is clearly observed, showing the method’s potential to foresee the end of the eruption.