Permutation entropy (PE) is a complexity metric for time series that is useful in the presence of observational noise. PE encodes the time series into sequences of symbols and is matched with possible patterns as the combination of symbols. Permutation entropy then quantifies the possible permutation pattern that appears in a time series. This study investigated PE variation during three eruptions in 2011, 2017, and 2018 at Shinmoedake volcano, Japan. Shinmoedake had its first magmatic eruption in January 2011 and after 6 years, a new activity began in October 2017 and it was followed by another eruption in March 2018. The frequency range 1 - 7 Hz was used to infer the temporal change of PE in time series data. Permutation entropy calculation was performed by using the embedding dimension (m=5) and embedding delay (L=2) in a 20 minutes time window length. The results showed that PE values decreased before each eruption occurred. Decreasing PE values indicated a reduction of complexity that was associated with volcanic tremor and magma migration to the shallower depth, which caused attenuation of seismic waves. At the end of decreasing pattern, PE also exhibited an increase and sudden decrease just before the eruption events in 2011, 2017, and 2018. In 2011 and 2017, this feature was associated with the bubble bursts due to interaction between the aquifer and high temperature magma ascent. The fractures which were generated by the interaction between the ascending 2018 magma with the 2011 solidified magma influenced PE increase and sudden drop just before the 2018 eruption. We also analyzed the correlation between tremor depth location and PE values that depicted a negative correlation in each eruption period. PE values decreased when tremor occurred at a shallower depth and increased when tremor migrated to larger depths. At shallower depth, volcanic tremor was associated with the presence of steam and bubbles due to the interaction between high temperature magma and the aquifer. This probably attenuated the high frequency (stochastic) signals and produced lower PE values. On the other hand, volcanic tremor at the deeper part was related to the magma pressure build-up as the magma ascended. Steam, bubbles, and high temperature water layer were absent at the deeper part, hence the attenuation of seismic waves was not significant. Therefore, the system became more complex and produced higher PE values.
