Excitation of a buried magmatic pipe: A seismic source model for volcanic tremor

Recent observations of seismic events at various volcanoes suggest that harmonic tremor results from the sustained occurrence of so‐called long‐period or low‐frequency events. Accordingly, we can view the long‐period volcanic event as the elementary process of tremor and interpret it as the impulse response of the tremor‐generating system. We present a seismic model in which the source of tremor is the acoustic resonance of a fluid‐filled volcanic pipe triggered by excess gas pressure. The model consists of three elements, namely, a triggering mechanism, a resonator, and a radiator. For simplicity, we assume a hemispherical trigger, cylindrial resonator, and circular radiator set in a vertical configuration with the trigger capping the top of the pipe and the disk‐shaped radiator shutting off its bottom. Considering the simple case of a source buried in a homogeneous half space, we then apply the discrete wave number method to obtain a complete representation of the ground motion response at near and intermediate distances. The results demonstrate that the displacement attributed to the pipe dominates the near‐field motion, while that due to the disk is representative of the intermediate and far fields. The trigger itself has a smaller contribution, mainly limited to the field in the proximity of the source. The characteristics displayed by the free surface response evolve from a strong impulsive signature in the immediate vicinity of the epicenter to a well‐developed harmonic wave train dominated by Rayleigh waves at larger distances. No clear shear arrival can be detected in the synthetic seismograms. The displacement spectrum reflects the organ‐pipe modes of the conduit, and the bandwidth associated with the dominant spectral peak of motion is controlled by the combined losses due to viscous attenuation in the fluid and elastic radiation into the solid. In the case of the cylindrical magma column considered, the radiation loss is proportional to the square of the pipe radius, while the loss related to viscous damping is inversely proportional to the same factor, indicating that the relative importance of the two loss mechanisms is critically dependent on the geometry of the magma reservoir. The relative importance of the pipe and disk elements, likewise, is a function of the conduit cross section. This suggests the possibility of determining the geometry of the source as well as the radiation loss and in situ magma viscosity from a comparison of near‐ and far‐field observations.