Ground motion in the near field of a fluid‐driven crack and its interpretation in the study of shallow volcanic tremor

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Abstract
We present a study of the motion of the ground in the near field of a fluid‐driven tensile crack embedded in a layered half space. The source that we consider is the jerky opening of a channel connecting two fluid‐filled cracks, and the cause of this opening is the excess pressure of fluid in one of the cracks. We make a complete representation of the three components of ground motion in the space, time, and frequency domains and analyze the effects of fluid compressibility, source depth, and medium structure on the ground response. The calculations show the presence of a dominant frequency of motion which depends not only on the source geometry and bulk modulus of the fluid but also on medium characteristics, receiver position, and the component of motion being considered. Using this source model, we view an episode of volcanic tremor as a continuous sequence produced by numerous jerky openings of channels occurring randomly in time along a chain of cracks. Our results are applied to the October 5–6, 1963, east rift eruption of Kilauea volcano, Hawaii, and found to be compatible with available seismic data, suggesting that magma is transported through an ensemble of cracks with the area of 1 × 1 km, each pair of cracks constituting an individual dike segment which opens in discrete increments at a rate of 1/s. We obtain the following parameters for each dike‐segment opening: increase in cavity volume, 40 m3; stress drop, 0.004 bar; seismic moment, 1019 dyn cm; and force applied by the fluid to open the dike, 1014 dyn. The total moment integrated over the entire duration of tremor for the eruption is 0.5 · 1024 dyn cm, roughly equivalent to a single magnitude M = 5 earthquake. The seismic source parameters and other field observations offer constraints on the process of mass transport and are compatible with the excess pressure and viscosity of magma of about 40 bars and 102 P, respectively.