ALBERT

Description: 〈span〉〈div〉SUMMARY〈/div〉We perform non-linear time-series analysis on a harmonic tremor seismogram recorded at 830 m away from the centre of the crater during the 2011 eruption at Shinmoedake, Japan. We found features suggesting the existence of period doubling bifurcation in the harmonic tremor signal, implying that the harmonic tremor might be generated by a non-linear process. In order to quantify the non-linearity in the harmonic tremor signal, we measure the correlation dimension 〈span〉D〈/span〉 and the maximal Lyapunov exponent λ. For one short but stable segment of the harmonic tremor seismogram, we obtained 〈span〉D〈/span〉 = 1.12 and λ = 0.03 s〈sup〉−1〈/sup〉. This result implies that the stable oscillation of the harmonic tremor is predominantly a limit cycle with small amounts of chaos present. We then use surrogate data analysis to check that our measurements of 〈span〉D〈/span〉 and λ do not include any false positive detection of non-linearity. Limit cycles imply that the harmonic tremor is generated by self-sustained oscillations. We show that the autonomous Julian tremor model is able to exhibit period doubling bifurcation. We also show that the non-autonomous Julian tremor model with a step like increase and decrease in input pressure is able to exhibit oscillations of varying amplitude while keeping a constant frequency spectrum. Both phenomena were observed at Shinmoedake. We also demonstrate that the non-autonomous Julian tremor model with a transient input pressure is able to exhibit long period-like events in addition to harmonic tremor-like events, implying that the same non-linear mechanism could be responsible for the generation of both type of events.〈/span〉