Harmonic tremor model during the 2011 Shinmoe-dake eruption, Japan

Summary The Shinmoe-dake volcano started with three sub-Plinian eruptions from 26 to 27 January 2011, followed by a magma effusive stage from 28 to 31 January 2011, and Vulcanian eruptions occurred frequently during 1 to 10 February 2011. During the magma effusive and Vulcanian stages, multiple episodes of harmonic tremors were observed at stations near the summit crater. Although harmonic tremors have been observed at various volcanoes worldwide, the source mechanism remains poorly understood. This paper proposes a source model for harmonic tremors, which is composed of a nonlinear viscous fluid flow in a flexible channel. A simple lumped parameter model is used to consider the process. The dynamics are described by a third-order system of ordinary differential equations using model variables for a cross-sectional area of the constricted segment and the fluid velocities in the upstream and downstream tubes. This model produces various kinds of trajectories for self-sustained oscillations that change the reservoir pressure connected on the upstream channel of the model. Linearization analysis around the stationary point and global analysis employing nullcline planes reveal the mechanism of self-sustained oscillations of the system qualitatively. To consider both the frequency peaks of the harmonic tremor and the characteristics of observed phase spectra, the qualitative characteristics of an observed phase portrait are compared to those of a simulated one. This tremor model simulates the frequency peaks and the phase portraits of typical harmonic tremors observed during the 2011 Shinmoe-dake eruption. Because this model involves several geometrical configuration parameters, it has the potential to reveal the source mechanism of various kinds of harmonic tremors.

Perception of Vocal Tremor

Vocal tremors characterize many pathological voices, but acoustic-perceptual aspects of tremor are poorly understood. To investigate this relationship, 2 tremor models were implemented in a custom voice synthesizer. The first modulated fundamental frequency (F0) with a sine wave. The second provided irregular modulation. Control parameters in both models were the frequency and amplitude of the F0 modulating waveform. Thirty-two 1-s samples of /a/, produced by speakers with vocal pathology, were modeled in the synthesizer. Synthetic copies of each vowel were created by using tremor parameters derived from different features of F0 versus time plots of the natural stimuli or by using parameters chosen to match the original stimuli perceptually. Listeners compared synthetic and original stimuli in 3 experiments. Sine wave and irregular tremor models both provided excellent matches to subsets of the voices. The perceptual importance of the shape of the modulating waveform depended on the severity of the tremor, with the choice of tremor model increasing in importance as the tremor increased in severity. The average frequency deviation from the mean F0 proved a good predictor of the perceived amplitude of a tremor. Differences in tremor rates were easiest to hear when the tremor was sinusoidal and of small amplitude. Differences in tremor rate were difficult to judge for tremors of large amplitude or in the context of irregularities in the pattern of frequency modulation. These results suggest that difference limens are larger for modulation rates and amplitudes when the tremor pattern is complex. Further, tremor rate, regularity, and amplitude interact, so that the perceptual importance of any one dimension depends on values of the others.