Numerical Studies of the Dynamics of Fluid-Filled Cracks Placed in Series: A Model for Inharmonic Peaked Tremor Spectra

Abstract

A volcanic tremor is characterized by peaked spectra with frequencies ranging from 0.15 to 10Hz, which may be explained by resonance set up in magmatic conduits. Temporal changes of volcanic tremor periods have been observed on various volcanoes. Another feature of peaked tremor spectra is that, especially on Mount Etna, higher modes do not appear to be harmonics of the fundamental mode. These observations cannot be explained by a simple model consisting of a single resonating dike, which can only generate harmonic spectra. As an extension to the single dike model, I have considered two or more dikes placed in series with a different characteristic impedance. The characteristic impedance of the dike is determined by the cross-sectional area, the acoustic velocity, and the density of the fluid.

Numerical results obtained using two dikes in series differ considerably from the single dike solution. In particular, spectral peaks are obtained at frequencies which are not harmonics of the fundamental mode. Moreover, the frequency of the fundamental mode may be much lower than that obtained using a single dike with the same length as the two dikes in series.

The symmetry in the inharmonic peaked spectrum, which is independent of the impedance contrast between the dikes, is a common characteristic of all models with complex geometry.