Stochastic simulation of volcanic tremor from Ruapehu

Abstract

The most common volcanic tremor produced by Ruapehu is a continuous signal with a dominant frequency of about 2 Hz. This signal has a sharply peaked spectrum, and an autocorrelation function with a high degree of coherence, even for lags of over 20 seconds. These characteristics strongly suggest that the cause of this tremor is a single resonator, probably a fluid-filled cavity resonating in an “organ-pipe” mode. The stochastic simulation of such a resonator uses the equation of motion of a Simple Harmonic Oscillator, which applies to an “organ-pipe” fundamental resonance, with either the characteristics of the oscillator, or the forcing function, containing a random element. A “white noise” forcing function, which would be appropriate for excitation of the cavity by a high pressure gas input, gave good agreement with the observed spectra and autocorrelation functions. Another possible model used an oscillator with a damping factor which varied randomly, and was sometimes negative, so oscillations built up, rather than decayed. This also gave a reasonable simulation of Ruapehu tremor. The third excitation model used a Poisson process, in which during each time interval there was a certain probability of applying a fixed impulse to the resonator. It was found that the impulses had to be frequent, i.e. several times a second, to match the characteristics of Ruapehu tremor. It has been suggested that tremor is composed of a succession of low-frequency (“B-type”) earthquakes. The results of this simulation show that at Ruapehu tremor could be produced by a resonator with positive feedback just sustaining oscillation, or by a resonator excited by external impulses. The most promising model for low-frequency earthquakes describes them as the result of a major external disturbance of the resonator.