The excitation and characteristic frequency of the long‐period volcanic event: An approach based on an inhomogeneous autoregressive model of a linear dynamic system

We present a method to quantify the source excitation function and characteristic frequencies of long‐period volcanic events. The method is based on an inhomogeneous autoregressive (AR) model of a linear dynamic system, in which the excitation is assumed to be a time‐localized function applied at the beginning of the event. The tail of an exponentially decaying harmonic waveform is used to determine the characteristic complex frequencies of the event by the Sompi method. The excitation function is then derived by operating an AR filter constructed from the characteristic frequencies to the entire seismogram of the event, including the inhomogeneous part of the signal. We apply this method to three long‐period events at Kusatsu‐Shirane Volcano, central Japan, whose waveforms display simple decaying monochromatic oscillations except for the beginning of the events. We recover time‐localized excitation functions lasting roughly 1 s at the start of each event and find that the estimated functions are very similar to each other at all the stations of the seismic network for each event. The phases of the characteristic oscillations referred to the estimated excitation function fall within a narrow range for almost all the stations. These results strongly suggest that the excitation and mode of oscillation are both dominated by volumetric change components. Each excitation function starts with a pronounced dilatation consistent with a sudden deflation of the volumetric source which may be interpreted in terms of a choked‐flow transport mechanism. The frequency and Q of the characteristic oscillation both display a temporal evolution from event to event. Assuming a crack filled with bubbly water as seismic source for these events, we apply the Van Wijngaarden‐Papanicolaou model to estimate the acoustic properties of the bubbly liquid and find that the observed changes in the frequencies and Q are consistently explained by a temporal change in the radii of the bubbles characterizing the bubbly water in the crack.