Deterministic nonlinear source processes of volcanic tremor signals accompanying the 1996 Vatnajkull eruption, central Iceland

S U M M A R Y Observations and theoretical considerations have cast doubt on the suggestion that volcanic tremor source processes may be modelled by a linear oscillator that is set into resonance by a sustained disturbance. Volcanic tremor signals that accompanied the 1996 Vatnajökull subglacial eruption, central Iceland, have been analysed using methods from the discipline of non-linear dynamics in order to investigate the possibility that they originated from a nonlinear source. The volcano-seismic phenomena associated with the eruption were recorded by a permanent network equipped with broad-band seismometers (HOTSPOT) using a sampling rate of 20 samples s−1. The eruption was preceded by increased seismic activity for a period of 2 days, which also included a large earthquake with a moment magnitude of 5.6. The tremor during the first 2 days of the eruption has a high signal-to-noise ratio at the nearest station to the eruption site and starts as a continuous signal, later evolving to low-amplitude background tremor interrupted by high-amplitude, cigar-shaped bursts having an average duration of 250 s. The phase space, which describes the evolution of the behaviour of a non-linear system, was reconstructed from the original tremor seismograms using the delay embedding theorem suggested by Takens. The delay time used for the reconstruction was selected after examining the autocorrelation function, which showed a first zero crossing at a timelag of 4 samples and the average mutual information that showed no minimum, indicating that the tremor process may have been undersampled. Based also on phase space portraits for different delay times, a delay time of one sample interval (0.05 s) was used. The sufficient embedding dimension for phase space reconstruction was selected by applying the false nearest-neighbours method, which revealed complete unfolding of the tremor attractor at dimensions 7–8, implying upper bounds of its fractal dimension in the range 3.5–4.0. The phase space prediction errors of different segments of the tremor time-series were compared in order to check whether the attractor dynamics change substantially with time. It was found that for continuous tremor there was almost no dynamic variation, in contrast to the background tremor and the superposed bursts that gave a maximum prediction error when the former was used to predict the latter. This difference in dynamics also had an effect on their spectra: the amplitude spectrum of a burst or continuous tremor has a much sharper decay at high frequencies than that of the background tremor. A possible physical mechanism that may explain these observed characteristics involves turbulent slug flow of magma in a narrow cylindrical conduit, generating the different dynamic regimes as the Reynolds number varies.