Spatial extent of a hydrothermal system at Kilauea Volcano, Hawaii, determined from array analyses of shallow long‐period seismicity: 1. Method

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Abstract
We present a probabilistic method to locate the source of seismic events using seismic antennas. The method is based on a comparison of the event azimuths and slownesses derived from frequency‐slowness analyses of array data, with a slowness vector model. Several slowness vector models are considered including both homogeneous and horizontally layered half‐spaces and also a more complex medium representing the actual topography and three‐dimensional velocity structure of the region under study. In this latter model the slowness vector is obtained from frequency‐slowness analyses of synthetic signals. These signals are generated using the finite difference method and include the effects of topography and velocity structure to reproduce as closely as possible the behavior of the observed wave fields. A comparison of these results with those obtained with a homogeneous half‐space demonstrates the importance of structural and topographic effects, which, if ignored, lead to a bias in the source location. We use synthetic seismograms to test the accuracy and stability of the method and to investigate the effect of our choice of probability distributions. We conclude that this location method can provide the source position of shallow events within a complex volcanic structure such as Kilauea Volcano with an error of ±200 m.