## 1. Introduction

[2] Long-period (LP) seismicity, including LP events and tremor, is widely observed at active volcanoes and related areas in association with heightened volcanic activity. The LP event is characterized by decaying harmonic oscillations except for a brief time at the event onset, while tremor is marked by sustained harmonic oscillations. The characteristic frequencies of these signals share a similar typical range between 0.5 and 5 Hz [*Chouet*, 1996], which may represent resonances of a fluid-filled resonator in a magmatic or hydrothermal system. Differences between the LP event and tremor may be attributed to differences in their temporal excitation, which is time-localized in the LP event and sustained for tremor. LP seismicity may be viewed as the dynamic response of a fluid-filled resonator to pressure disturbances associated with mass transport and/or magmatic heat [*Chouet*, 1996]. The quantitative interpretation of these signals is thus critically important to our understanding of physical processes beneath volcanoes, which is crucial to the assessment and mitigation of volcanic hazards, and to eruption prediction.

[3] A number of resonator models with different geometries, including a pipe [*Chouet*, 1985], sphere [*Shima*, 1958; *Kubotera*, 1974; *Crosson and Bame*, 1985; *Fujita et al.*, 1995], or crack [e.g., *Aki et al.*, 1977; *Chouet*, 1986, 1988, 1992], have been proposed for the sources of LP events and tremor. In light of mass transport conditions beneath volcanoes, a crack geometry may be most appropriate for such sources [*Chouet*, 1996]. The crack geometry is supported by recent studies [*Kumagai and Chouet*, 1999, 2000, 2001; *Kumagai et al.*, 2002], which indicate that the acoustic properties of a crack containing various magmatic or hydrothermal fluids can consistently explain the spatial, as well as temporal, variations in the complex frequencies (frequencies and quality factors) of LP events.

[4] Although the above studies are primarily focused on the resonance frequencies of LP events, the LP waveforms themselves can also be used to quantify the source mechanisms of LP events and tremor. *Nakano et al.* [1998] proposed a method to estimate the effective excitation function, that is the apparent excitation observed at an individual receiver, by applying an autoregressive (AR) filter to the LP waveform. M. Nakano et al. (Source mechanism of long-period events at Kusatsu-Shirane Volcano, Japan, inferred from waveform inversion of the effective excitation functions, submitted to *Journal of Volcanology and Geothermal Research*, 2002, hereinafter referred to as Nakano et al., submitted manuscript, 2002), later performed waveform inversions of these excitation functions to estimate the source mechanism of LP events observed at Kusatsu-Shirane Volcano, central Japan. The present paper complements these two studies and uses the oscillatory signatures of the LP waveforms, which were removed by AR filtering in the former studies, to estimate the source properties of LP events.

[5] It is relatively easy to perform waveform inversions of the oscillatory signatures of LP events. Such a study was performed by *Aoyama and Takeo* [2001] for an LP event observed at Asama Volcano, Japan. *Aoyama and Takeo* [2001] assumed a point source and determined the six moment tensor components of the source from a waveform inversion of a few cycles of oscillations in the LP waveforms. The interpretation of results from such waveform inversions may not always be straightforward, however, because the oscillatory signatures usually consist of a superposition of different resonance modes which can display complex spatial patterns of seismic wave excitation at the wall of a resonator of finite size [*Chouet*, 1992, Figure 2]. Detailed examination of the point source representation of such resonance pattern is required for a correct interpretation of results from waveform inversions. In this paper, we perform waveform inversions of synthetic LP signatures radiated by a fluid-filled crack model [*Chouet*, 1986, 1988, 1992] to test the point source representation of LP events. We then apply our inversion method to the oscillatory signatures of an LP event observed at Kusatsu-Shirane Volcano to demonstrate the usefulness of this approach.