Source mechanism of volcanic tremor: fluid-driven crack models and their application to the 1963 kilauea eruption

We propose a model for the mechanism of magma transport based on a fluid-filled tensile crack driven by the excess pressure of fluid. Such a transport mechanism can generate seismic waves by a succession of jerky crack extensions, if the fracture strength of rock varies in space, or if there is a difference between the dynamic and static values of the critical stress intensity factor. We also find that the opening and closing of a narrow channel connecting two fluid-filled cracks may be a source of seismic waves. Using the finite-difference method, we calculated the vibration of dry and fluid-filled cracks generated by: (1) a jerky extension at one end or at both ends and (2) a jerky opening of a narrow channel connecting two cracks. We then calculated the far-field and near-field radiation from these vibrating cracks. The spectra show peaked structures, but interestingly, most high-frequency peaks are only present in the near-field and cannot be transmitted to the far-field. The spectral features described above are often observed for volcanic tremors and in some cases for seismic signals associated with hydraulic fracturing experiments.We first consider as a model of volcanic tremor randomly occurring jerky crack extensions, and derive a formula relating the tremor amplitude to the excess pressure in the magma, the incremental area in each extension, and the frequency of extensions. These parameters are also constrained by other observations, such as the rate of magma flow.Our model was tested quantitatively against observations made in one of the best-described case histories of volcanic tremor: the October 5–6, 1963 Kilauea flank eruption. We found that a single, long crack extending from the summit to the eruptive site cannot explain the observations. The model of a steadily expanding crack ran into difficulties when quantitative comparisons were made with observations. The extension of crack area needed to explain the amplitude of volcanic tremor should accompany a large increase in tremor period which was not observed.Our second model is a chain of cracks connected by narrow channels which open and close. The length of each crack is around 1 km, the channel area connecting neighboring cracks is about 10³m², and the channel opens jerkily with the magmatic excess pressure of about 20 bars. The frequency of jerky opening of each channel is about once in 15 seconds. The channel is closed after each jerky opening, as soon as magma is moved through the channel.